JP4584852B2 - Sawtooth type soundproof panel, soundproof wall, structure, and noise reduction method - Google Patents
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Description
本発明は、鋸歯型防音パネル、防音壁、構造物、及び騒音低減方法にかかり、特に、ベクトル・ポテンシャルと鋸歯型形状のエッジの縁辺ベクトル（稜線ベクトル）との内積の和が最小になるように設計することにより防音効果を向上させた鋸歯型防音パネル、及びこの鋸歯型防音パネルの鋸歯型形状のエッジを利用した防音壁、構造物、及び騒音低減方法に関する。 The present invention relates to a sawtooth type soundproof panel, a soundproof wall, a structure, and a noise reduction method. In particular, the sum of inner products of vector potentials and edge vectors (edge line vectors) of sawtooth shaped edges is minimized. The present invention relates to a saw-tooth type soundproof panel that is improved in soundproofing effect by designing, a soundproof wall, a structure, and a noise reduction method using a sawtooth-shaped edge of the sawtooth type soundproof panel.
従来より、上辺が平坦な直立型の防音壁の上辺に特殊な形状のエッジを有する構造物を取り付けることにより、同じ高さの上辺が平坦な直立型の防音壁より大きな減音効果が得られるようにした防音壁が知られている（例えば、非特許文献１、特許文献１〜特許文献４）。
しかしながら、上記の従来技術では、いずれも二等辺三角形等の同一形状のユニットを繰り返し複数個配列することにより形成したエッジを用いている。このため、ユニットの各々から回折する多くのパルスが同じ時間間隔で正面の受音点に到達することになることから、櫛形フィルターと同一に作用し、平坦エッジを有する通常の防音壁より騒音レベルが大きくなる周波数帯が発生する、という問題がある。 However, each of the above conventional techniques uses an edge formed by repeatedly arranging a plurality of units having the same shape such as an isosceles triangle. For this reason, many pulses diffracted from each of the units reach the sound receiving point in the front at the same time interval, so that the noise level is higher than that of a normal sound barrier having a flat edge, acting in the same way as a comb filter. There is a problem that a frequency band in which the frequency becomes large is generated.
本発明は、上記問題点を解消するために成されたもので、防音効果をより向上させた鋸歯型防音パネル、この鋸歯型防音パネルを供えた防音壁、及びこの鋸歯型防音パネルの鋸歯型形状のエッジを利用した防音壁を提供することを目的とする。 The present invention has been made to solve the above-mentioned problems, and has a saw-tooth type soundproof panel with improved soundproofing effect, a soundproof wall provided with this sawtooth type soundproof panel, and a sawtooth type of this sawtooth type soundproof panel. An object of the present invention is to provide a soundproof wall using an edge of a shape.
上記目的を達成するために本発明の鋸歯型防音パネルは、一端側から他端側に辿ったとき、鉛直上方に向かう第１の鉛直辺、該第１の鉛直辺の終端から鉛直方向に対して第１の所定角度傾斜して鉛直下方に向かう第１の斜辺、該第１の斜辺の終端から鉛直方向に対して第２の所定角度傾斜して鉛直上方に向かう第２の斜辺、及び該第２の斜辺の終端から鉛直下方に向かう第２の鉛直辺を組合せた形状を有する第１のユニットと、一端側から他端側に辿ったとき、鉛直方向に対して第３の所定角度傾斜して鉛直上方に向かう第３の斜辺、及び該第３の斜辺の終端から鉛直方向に対して第４の所定角度傾斜して鉛直下方に向かう第４の斜辺を組合せた形状を有する第２のユニットと、を交互に配置した形状の鋸歯型エッジを備えた鋸歯型防音パネルであって、ベクトルポテンシャＢを、受音点から前記鋸歯型エッジに想定された複数の縁辺ベクトルｄｇの始点の各々までの大きさで該受音点から該始点の各々に向かう複数の第１のベクトルｌの各々と、音源から前記縁辺ベクトルｄｇの始点の各々までの大きさで該音源から該始点の各々に向かう複数の第２のベクトルｍの各々との外積を含んで表わしたとき、前記ベクトル・ポテンシャルＢの各々と、前記複数の縁辺ベクトルｄｇの各々との内積の和が所定値以下の値になるように前記第１のユニット及び第２のユニットの形状を定めたものである。 In order to achieve the above object, the sawtooth type soundproof panel of the present invention has a first vertical side that extends vertically upward from the one end side to the other end side, and a vertical direction from the end of the first vertical side. A first hypotenuse inclined at a first predetermined angle and vertically downward, a second hypotenuse inclined at a second predetermined angle with respect to the vertical direction from the end of the first hypotenuse and directed vertically upward, and the A first unit having a shape in which the second vertical sides extending vertically downward from the end of the second hypotenuse and a third predetermined angle tilt with respect to the vertical direction when traced from one end to the other end And a second hypotenuse having a combination of a third hypotenuse that extends vertically upward, and a fourth hypotenuse that is inclined at a fourth predetermined angle with respect to the vertical direction from the end of the third hypotenuse and goes vertically downward. Sawtooth type soundproofing panel with sawtooth type edges in the shape of alternating units The vector potentiometer B has a size from the sound receiving point to each of the start points of the plurality of edge vectors dg assumed for the sawtooth edge, and a plurality of first points from the sound receiving point to each of the start points. And the outer product of each of a plurality of second vectors m directed from the sound source to each of the start points with a size from the sound source to each of the start points of the edge vector dg, The shapes of the first unit and the second unit are determined so that the sum of the inner products of each of the vector potentials B and each of the plurality of edge vectors dg is a predetermined value or less. .
本発明の鋸歯型防音パネルでは、防音パネルのエッジを形成する第１のユニット及び第２のユニットの形状が、ベクトル・ポテンシャルＢの各々と、複数の縁辺ベクトルｄｇの各々との内積の和が所定値以下の値になるように定められているので、防音効果を大きくすることができ、内積の和が最小になるように第１のユニット及び第２のユニットの形状を定めることにより、防音効果を最大にすることができる。 In the sawtooth type soundproof panel of the present invention, the shape of the first unit and the second unit forming the edge of the soundproof panel is the sum of the inner products of the vector potential B and each of the plurality of edge vectors dg. Since it is determined to be a value equal to or less than a predetermined value, the soundproofing effect can be increased, and the soundproofing can be achieved by determining the shapes of the first unit and the second unit so that the sum of the inner products is minimized. The effect can be maximized.
ベクトル・ポテンシャルＢの各々は、以下の式で定めることができる。 Each of the vector potentials B can be determined by the following equation.
ただし、θは１つの縁辺ベクトルに関してベクトルｌとベクトルｍとがなす角、ｎはベクトルｌとベクトルｍとの外積ベクトルの方向の単位ベクトルである。 Here, θ is an angle formed by the vector l and the vector m with respect to one edge vector, and n is a unit vector in the direction of the outer product vector of the vector l and the vector m.
また、虚音源を考慮する場合には、ベクトルポテンシャＢの各々は、受音点から前記縁辺ベクトルｄｇの始点の各々に向かう前記複数の第１のベクトルｌの各々と、音源に対する虚音源から前記縁辺ベクトルｄｇの始点の各々までの大きさで該虚音点から該始点の各々に向かうに複数の第３のベクトルｍ’の各々との外積を更に含んで表わされた以下の式で定めることができる。 Further, when considering the imaginary sound source, each of the vector potentiators B includes each of the plurality of first vectors l from the sound receiving point to each of the start points of the edge vector dg and the imaginary sound source for the sound source. It is determined by the following expression that further includes an outer product with each of the plurality of third vectors m ′ from the imaginary sound point toward each of the start points with a size up to each of the start points of the edge vector dg. be able to.
ただし、θは１つの縁辺ベクトルに関してベクトルｌとベクトルｍとがなす角、ｎはベクトルｌとベクトルｍとの外積ベクトルの方向の単位ベクトル、θ’は１つの縁辺ベクトルに関してベクトルｌとベクトルｍ’とがなす角、ｎ’はベクトルｌとベクトルｍ’との外積ベクトルの方向の単位ベクトルである。 Where θ is an angle formed by the vector l and the vector m with respect to one edge vector, n is a unit vector in the direction of the outer product vector of the vector l and the vector m, and θ ′ is the vector l and the vector m ′ with respect to one edge vector. N ′ is a unit vector in the direction of the outer product vector of the vector l and the vector m ′.
また、本発明の第１のユニットと第２のユニットとを交互に配置した形状の鋸歯型エッジを備えた鋸歯型防音パネルは、前記第１の鉛直辺の始端、前記第１の斜辺の終端、前記第２の斜辺の始端、第２の鉛直辺の終端、前記第３の斜辺の始端、及び前記第４の斜辺の終端を同一直線状上に位置させ、前記第１のユニットの高さ及び前記第２のユニットの高さを同一とし、前記第１の所定角度、前記第２の所定角度、前記第３の所定角度、及び前記第４の所定角度の少なくとも２つの所定角度の大きさが各々異なるように前記第１のユニット及び第２のユニットの形状を定めるようにしてもよい。この場合、大きさを異ならせる所定角度以外の所定角度の大きさは任意であり、同じ大きさとしてもよく、または異なる大きさとしてもよいが、第１の所定角度〜前記第４の所定角度の全ての所定角度の大きさが各々異なるようにするのがより好ましい。 In addition, a sawtooth type soundproof panel having a sawtooth type edge having a shape in which the first unit and the second unit of the present invention are alternately arranged has a start edge of the first vertical side and a terminal end of the first oblique side. The first end of the second hypotenuse, the end of the second vertical side, the start of the third hypotenuse, and the end of the fourth hypotenuse are located on the same straight line, and the height of the first unit And the height of the second unit is the same, and the size of at least two predetermined angles of the first predetermined angle, the second predetermined angle, the third predetermined angle, and the fourth predetermined angle. The shapes of the first unit and the second unit may be determined so that they are different from each other. In this case, the size of the predetermined angle other than the predetermined angle for varying the size is arbitrary, and may be the same size or different sizes, but may be the first predetermined angle to the fourth predetermined angle. It is more preferable that the sizes of all the predetermined angles are different from each other.
これにより、上記で説明したように、ベクトル・ポテンシャルＢの各々と、複数の縁辺ベクトルｄｇの各々との内積の和が所定値以下の値になるので、防音効果を大きくすることができ、内積の和が最小になるように第１のユニット及び第２のユニットの形状を定めることにより、防音効果を最大にすることができる。 As a result, as described above, the sum of the inner products of each of the vector potential B and each of the plurality of edge vectors dg becomes a value equal to or smaller than a predetermined value, so that the soundproofing effect can be increased. The soundproofing effect can be maximized by determining the shapes of the first unit and the second unit so that the sum of the two is minimized.
本発明では、第２の鉛直辺の終端と前記第３の斜辺の始端とを一致させると共に、前記第４の斜辺の終端と前記第１の鉛直辺の始端とを一致させて、前記第１のユニットと前記第２のユニットとを交互に配置することができ、前記第１のユニットと前記第２のユニットとの間に、鉛直方向に向かう第３の鉛直辺と直線または曲線状の第５の斜辺とを備えた形状を有する第３のユニットを、前記第１のユニット及び前記第２のユニットの各々と一点で連続させて配置して組合せユニットとし、該組合せユニットを一点で連続させて複数個配置することができる。 In the present invention, the end of the second vertical side and the start of the third hypotenuse coincide with each other, the end of the fourth hypotenuse and the start of the first vertical side coincide with each other, The second unit and the second unit can be alternately arranged, and a third vertical side and a straight or curved second extending in the vertical direction between the first unit and the second unit. A third unit having a shape with 5 hypotenuses is arranged continuously at one point with each of the first unit and the second unit to form a combination unit, and the combination unit is made continuous at one point. Can be arranged.
また、前記第１のユニットと前記第２のユニットとの間に、鉛直方向に向かう第３の鉛直辺と直線または曲線状の第５の斜辺とを備えた形状を有する第３のユニットを、前記第１のユニット及び前記第２のユニットの各々と一点で連続させて配置して組合せユニットとし、該組合せユニットの間に、鉛直方向に向かう第４の鉛直辺と直線または曲線状の第６の斜辺とを備えた形状を有する第４のユニットを、該組合せユニットの各々に一点で連続させて、該組合せユニットを複数個配置してもよい。 Further, a third unit having a shape with a third vertical side and a fifth oblique side that is straight or curved between the first unit and the second unit, Each of the first unit and the second unit is arranged continuously at one point to form a combination unit. Between the combination units, a fourth vertical side and a straight or curved sixth extending in the vertical direction. A plurality of combination units may be arranged such that a fourth unit having a shape with a hypotenuse is continuous with each of the combination units at one point.
前記第１のユニット及び前記第２のユニットの高さｈは、周波数レスポンスが所定レベル以下となる最低周波数をｆlow、音速をｃとしたとき、以下の大きさにすることができる。 The height h of the first unit and the second unit can be set to the following magnitude, where f low is the lowest frequency at which the frequency response is below a predetermined level, and c is the sound speed.
ｈ＝ｃ／ｆlow
このとき、第１のユニット及び第２のユニットの幅は、高さｈの１／２以下とするのが好ましい。
h = c / f low
At this time, it is preferable that the width of the first unit and the second unit is not more than ½ of the height h.
本発明の鋸歯型防音パネルは、従来の上辺が平坦な防音壁の上辺に取り付けて防音効果の大きな防音壁を構成することができる。 The sawtooth type soundproof panel of the present invention can be attached to the top side of a conventional soundproof wall having a flat upper side to constitute a soundproof wall having a large soundproofing effect.
また、上記の鋸歯型形状のエッジを上辺に形成して防音効果の大きな防音壁を構成することもできる。 Also, a soundproof wall having a large soundproofing effect can be formed by forming the sawtooth-shaped edge on the upper side.
本発明の鋸歯型形状のエッジは、防音壁以外の構造物にも適用することができ、また鋸歯型形状のエッジを利用して騒音を低減する低減方法にも適用することができる。 The sawtooth-shaped edge of the present invention can be applied to structures other than the soundproof wall, and can also be applied to a reduction method for reducing noise using the sawtooth-shaped edge.
以上説明したように本発明によれば、ベクトル・ポテンシャルと鋸歯型形状のエッジの縁辺ベクトルとの内積の和を所定値以下にしているため、防音効果をより向上させることができる、という効果が得られる。 As described above, according to the present invention, since the sum of the inner products of the vector potential and the edge vector of the sawtooth-shaped edge is set to a predetermined value or less, the effect of further improving the soundproofing effect can be obtained. can get.
以下、図面を参照して本発明の実施の形態を詳細に説明する。まず、障壁のエッジからの境界回折波を、任意形状の剛平面開口からの回折波に対するＭａｇｇｉ−Ｒｕｂｉｎｏｗｉｃｚ理論に基づいて説明する。 Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. First, boundary diffracted waves from the edge of the barrier will be described based on Maggi-Rubinowics theory for diffracted waves from a rigid plane opening of an arbitrary shape.
図１に示すように、点音源をＳ、点音源に対する観測点（受音点）をＰとし、剛で厚さの無視できる有限長障壁１０が存在するとき、受音点Ｐの速度ポテンシャルは、障壁面の裏側の速度ポテンシャルを０と近似した場合、Ｍａｇｇｉ−Ｒｕｂｉｎｏｗｉｃｚ表示により障壁のエッジΓに沿う線積分によって、以下の（１）式で与えられる。なお、座標は、鉛直上方を正とする鉛直方向のｚ軸、点音源方向を正とする障壁面に垂直なｘ軸、障壁面に沿ったｙ軸を備えたｘｙｚ座標を用い、座標の原点を障壁面の中心を通る鉛直線と障壁面の下辺との交点に一致させている。 As shown in FIG. 1, when the point sound source is S, the observation point (sound receiving point) with respect to the point sound source is P, and there is a rigid finite-length barrier 10 with negligible thickness, the velocity potential of the sound receiving point P is When the velocity potential on the back side of the barrier surface is approximated to 0, the following equation (1) is given by line integration along the edge Γ of the barrier by Maggi-Rubinowics display. In addition, the coordinate is the origin of the coordinates using the z-axis in the vertical direction with the vertical upper direction being positive, the x-axis being perpendicular to the barrier surface with the point sound source direction being positive, and the y-axis along the barrier surface. Is made to coincide with the intersection of the vertical line passing through the center of the barrier surface and the lower side of the barrier surface.
ここで、ｄｇはΓに沿う微小ベクトルである縁辺ベクトル、太字のlは受音点Ｐを始点とし縁辺ベクトルｄｇの始点を終点とするベクトル、太字のｍは音源Ｓを始点とし縁辺ベクトルｄｇの始点を終点とするベクトル、太字のｍ’は障壁により生じる音源Ｓの虚音源Ｓ’を始点とし縁辺ベクトルｄｇの始点を終点とするベクトル、細字のｌ， ｍ， ｍ’はこれらのベクトルの大きさである。また、ｄ、ｄ’はそれぞれＳＰ間とＳ’Ｐ間の距離、εは観測点である受音点Ｐが音源Ｓの照射領域内、領域外にある場合、各々１、０をとる定数、ε’は受音点Ｐが虚音源ＳとエッジГとでできる錘面の内部、錘面上、外部にある場合、各々1、１／２、０をとる定数である。 Here, dg is an edge vector that is a small vector along Γ, bold l is a vector starting from the sound receiving point P and starting from the start of the edge vector dg, and bold m is the sound source S starting and the edge vector dg A vector whose start point is the end point, bold m ′ is a vector whose start point is the imaginary sound source S ′ of the sound source S generated by the barrier and whose start point is the start point of the edge vector dg, and small characters l, m, m ′ are the sizes of these vectors That's it. D and d ′ are distances between SP and S′P, respectively, and ε is a constant that takes 1 and 0 when the sound receiving point P, which is an observation point, is outside and within the irradiation area of the sound source S, ε ′ is a constant that takes 1, 1/2, and 0 when the sound receiving point P is inside, on, or outside the weight surface formed by the imaginary sound source S and the edge Γ.
上記(１)式の第１項は直接波、第２項は障壁からの反射波、第３項は障壁のエッジΓからの境界回折波を各々表わしている。なお、(１)式において、キルヒホッフ境界条件近似を除けば、その導出過程での数式的操作は厳密である。また、ｋはω／ｃ（ωは角速度、ｃは音速）で表わされる波長定数であり、時間因子ｅｘｐ（ｉωｔ）は省略した。 In the above equation (1), the first term represents the direct wave, the second term represents the reflected wave from the barrier, and the third term represents the boundary diffraction wave from the edge Γ of the barrier. In equation (1), except for the Kirchhoff boundary condition approximation, the mathematical operation in the derivation process is exact. Further, k is a wavelength constant represented by ω / c (ω is an angular velocity and c is a sound velocity), and the time factor exp (iωt) is omitted.
本実施の形態では、回折界を時間領域で考察する。その理由は、有限長の障壁を対象にしてその頂点エッジからの回折波を取り扱う場合、障壁の両サイドからの回折波や地表面反射波は不要であるので、これらを時間領域において除去するためである。さらに、重要な理由は、三角形状のエッジなど平坦でない頂点エッジからの回折音の特徴抽出は時間領域のインパルス応答によって可能となるからである。 In this embodiment, the diffraction field is considered in the time domain. The reason for this is that when dealing with diffracted waves from the top edge of a finite length barrier, diffracted waves from both sides of the barrier and ground surface reflected waves are unnecessary, so these are removed in the time domain. It is. Furthermore, an important reason is that feature extraction of diffracted sound from a non-flat vertex edge such as a triangular edge is enabled by a time domain impulse response.
したがって、本実施の形態では、回折波のインパルス応答表示ｈ(Ｐ，ｔ)を用いることとする。インパルス応答は、式(１)をフーリエ変換することで次の（２）式で与えられる。 Therefore, in this embodiment, the impulse response display h (P, t) of the diffracted wave is used. The impulse response is given by the following equation (2) by subjecting equation (1) to Fourier transform.
ただし、δ（ｔ）はデルタ関数であり、 (２) 式の第３項は有限長のエッジに対する線積分で与えられている。以下ではこの線積分で与えられている項を境界回折波のインパルス応答ｈ(ｔ)と呼ぶ。 However, δ (t) is a delta function, and the third term of the equation (2) is given by a line integral for a finite length edge. In the following, the term given by this line integral is called the impulse response h (t) of the boundary diffraction wave.
上記(２) 式中の境界回折波のインパルス応答ｈ(ｔ)は、ベクトル形式で表現されているが、次の（３）式で示すようにスカラー表示することができる。 The impulse response h (t) of the boundary diffracted wave in the above equation (2) is expressed in a vector format, but can be displayed in scalar as shown in the following equation (3).
ただし、θ、θ'は各々ベクトルｌとベクトルｍ、ベクトルｌとベクトル ｍ’のベクトル外積の内角であり、ｎ、ｎ’はベクトル外積の単位方向ベクトルである（図１参照）。また、右辺大カッコ内を次の（４)式に示すベクトル・ポテンシャルＢと定義する。 Here, θ and θ ′ are inner angles of vector outer products of vector l and vector m, and vector l and vector m ′, respectively, and n and n ′ are unit direction vectors of the vector outer product (see FIG. 1). Also, the bracket in the right side is defined as the vector potential B shown in the following equation (4).
ベクトルｌとベクトルｍ、ベクトルｌとベクトルｍ’を Vector l and vector m, vector l and vector m '
とすれば、ベクトルｌとベクトルｍ、 ベクトルｌとベクトル ｍ’のベクトル外積のｘ、ｙ、ｚ成分ｎｘ，ｎｙ，ｎｚ、ｎ’ｘは次の（５）式によって与えられる。 Then, the x, y, z components nx, ny, nz, n'x of the vector outer product of the vector l and the vector m and the vector l and the vector m 'are given by the following equation (5).
すなわち、 That is,
とすると、次の関係が存在する。 Then, the following relationship exists.
以上より、境界回折波のインパルス応答は次のような性質を持つ。
（１）境界回折波は、音源Ｓから放射された音波が障壁のエッジの微小要素ｄ|ｇ|に入射し、その入射点から距離ｌ離れた受音点Ｐに到達する現象の総和として表わされる。各微小要素の受音点Ｐに対する寄与はベクトル・ポテンシャルＢと縁辺ベクトルｄｇの内積で与えられる。その振幅は１／ｌｍに反比例し、受音点Ｐへの到達時間は（ｌ＋ｍ）／ｃである。
（２）ベクトル・ポテンシャルＢは、音源と虚音源の２つの寄与から構成される。障壁の裏側の回折波領域では音源からの寄与が大きく、一方、音源側では虚音源からの寄与が大きい。このことは障壁と音源、虚音源、及び受音点により決まるθとθ'の大きさを比較すれば、θは１３５°程度、θ'は１５°程度であることからも理解でき、回折波領域である受音点側の音場を検討する場合には上記（４）式の第２項を無視することができる。
From the above, the impulse response of the boundary diffraction wave has the following properties.
(1) The boundary diffracted wave is expressed as the sum of phenomena in which the sound wave radiated from the sound source S is incident on the minute element d | g | at the edge of the barrier and reaches the sound receiving point P that is a distance l from the incident point. It is. The contribution of each microelement to the sound receiving point P is given by the inner product of the vector potential B and the edge vector dg. The amplitude is inversely proportional to 1 / lm, and the arrival time at the sound receiving point P is (l + m) / c.
(2) The vector potential B is composed of two contributions: a sound source and an imaginary sound source. The contribution from the sound source is large in the diffracted wave region on the back side of the barrier, while the contribution from the imaginary sound source is large on the sound source side. This can be understood from the fact that θ is about 135 ° and θ ′ is about 15 ° by comparing the magnitudes of θ and θ ′ determined by the barrier, the sound source, the imaginary sound source, and the sound receiving point. When the sound field on the sound receiving point side, which is a region, is considered, the second term of the above equation (4) can be ignored.
従って、上記（３）式を最小にする条件を求めれば、受音点における音場を最小にすることができる。上記（３）式を最小にするためには、近似的に下記（６）式で表わされるベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの内積（スカラー積）の和を最小にする条件を求めればよい。 Therefore, if the condition for minimizing the above equation (3) is obtained, the sound field at the sound receiving point can be minimized. In order to minimize the above expression (3), a condition for approximately minimizing the sum of the inner product (scalar product) of the vector potential B and the edge vector dg represented by the following expression (6) may be obtained. .
上記（６）式におけるｓｉｎθ／（１＋ｃｏｓ）・ｎは音源正面で最大値になり、方向は水平になる。従って、スカラー積ｓｉｎθ／（１＋ｃｏｓθ）ｎ・ｄｇを小さくするためにはθは大きい程よい。 In the above equation (6), sin θ / (1 + cos) · n is the maximum value in front of the sound source, and the direction is horizontal. Accordingly, in order to reduce the scalar product sin θ / (1 + cos θ) n · dg, it is better that θ is larger.
本発明者等は、ベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの内積の和を最小にする解として、図２に示す各々形状が異なる第１のユニット、及び第２のユニットの２種類の形状のユニットを組合せて形成した鋸歯型形状のエッジを防音壁の上辺に設けることにより、上記の内積の和を最小にすることができることを見出した。 As a solution for minimizing the sum of the inner products of the vector potential B and the edge vector dg, the present inventors have two types of shapes, a first unit and a second unit, each having a different shape, as shown in FIG. It has been found that the sum of the inner products can be minimized by providing a sawtooth-shaped edge formed by combining units on the upper side of the soundproof wall.
なお、虚音源も考慮する場合には、ベクトル・ポテンシャルＢとして以下の（７）式を用いればよい。 When the imaginary sound source is also considered, the following equation (7) may be used as the vector potential B.
上記の第１のユニット、及び第２のユニットの形状を図２を参照して説明する。第１のユニットｕ１は、一端側から他端側にエッジを辿ったときに、鉛直上方に向かう第１の鉛直辺ｖ１、第１の鉛直辺ｖ１の終端から鉛直方向に対して第１の所定角度α１傾斜して鉛直下方に向かう第１の斜辺ｓ１、第１の斜辺ｓ１の終端から鉛直方向に対して第２の所定角度α２傾斜して鉛直上方に向かう第２の斜辺ｓ２、及び第２の斜辺ｓ２の終端から鉛直下方に向かう第２の鉛直辺ｖ２を組合せた形状を有している。 The shapes of the first unit and the second unit will be described with reference to FIG. When the first unit u1 traces an edge from one end side to the other end side, the first predetermined side from the first vertical side v1 that goes vertically upward and the end of the first vertical side v1 is a first predetermined value with respect to the vertical direction. A first hypotenuse s1 inclined at an angle α1 and going vertically downward; a second hypotenuse s2 inclined at a second predetermined angle α2 with respect to the vertical direction from the end of the first hypotenuse s1; And the second vertical side v2 that extends vertically downward from the end of the oblique side s2.
第１のユニットｕ１の第１の斜辺ｓ１の長さと第２の斜辺ｓ２の長さとは異なる大きさであり、第１の鉛直辺ｖ１の長さ及び第２の鉛直辺ｖ２の長さは、同一の大きさである。 The length of the first hypotenuse s1 and the length of the second hypotenuse s2 of the first unit u1 are different sizes, and the length of the first vertical side v1 and the length of the second vertical side v2 are: They are the same size.
また、第１の鉛直辺ｖ１の始端、第１の斜辺ｓ１の終端（第２の斜辺ｓ２の始端と同じ）、及び第２の鉛直辺ｖ２の終端は、同一直線上、例えば水平線上に位置している。第１の斜辺ｓ１の長さと第２の斜辺ｓ２の長さとが異なっているため、第１の所定角度α１と第２の所定角度α２とは異なった大きさとなっている。 Also, the beginning of the first vertical side v1, the end of the first hypotenuse s1 (same as the start of the second hypotenuse s2), and the end of the second vertical side v2 are located on the same straight line, for example, on the horizontal line is doing. Since the length of the first hypotenuse s1 and the length of the second hypotenuse s2 are different, the first predetermined angle α1 and the second predetermined angle α2 have different sizes.
第２のユニットｕ２は、一端側から他端側にエッジを辿ったときに、鉛直方向に対して第３の所定角度α３傾斜して鉛直上方に向かう第３の斜辺ｓ３、及び第３の斜辺ｓ３の終端から鉛直方向に対して第４の所定角度α４傾斜して鉛直下方に向かう第４の斜辺ｓ４を組合せた形状を有している。 When the second unit u2 traces the edge from one end side to the other end side, the third hypotenuse s3 and the third hypotenuse that are inclined vertically upward by a third predetermined angle α3 with respect to the vertical direction It has a shape obtained by combining a fourth hypotenuse s4 that is inclined at a fourth predetermined angle α4 with respect to the vertical direction from the end of s3 and goes vertically downward.
第２のユニットｕ２の第３の斜辺ｓ３の長さと第４の斜辺ｓ４の長さとは異なる大きさであり、従って、第３の所定角度α３の大きさと第４の所定角度α４の大きさとは異なっている。 The length of the third hypotenuse s3 and the length of the fourth hypotenuse s4 of the second unit u2 are different from each other. Therefore, the magnitude of the third predetermined angle α3 and the magnitude of the fourth predetermined angle α4 are Is different.
また、第３の斜辺ｓ３の始端、及び第４の斜辺ｓ４の終端は、第１のユニットで説明した直線と同一の直線上に位置している。そして、第３の斜辺ｓ３の終端から第３の斜辺ｓ３の始端が位置している直線までの距離、すなわち、第３の斜辺ｓ３及び第４の斜辺ｓ４によって形成される三角形の高さは、第１の鉛直辺ｖ１の長さ（従って、第２の鉛直辺ｖ２の長さ）と同一の大きさになるように形成されている。 Further, the start end of the third hypotenuse s3 and the end of the fourth hypotenuse s4 are located on the same straight line as the straight line described in the first unit. The distance from the end of the third hypotenuse s3 to the straight line where the start end of the third hypotenuse s3 is located, that is, the height of the triangle formed by the third hypotenuse s3 and the fourth hypotenuse s4, It is formed to have the same size as the length of the first vertical side v1 (therefore, the length of the second vertical side v2).
このように、第１の鉛直辺ｖ１の始端、第１の斜辺ｓ１の終端、第２の斜辺ｓ２の始端、第２の鉛直辺ｖ１の終端、第３の斜辺ｓ３の始端、及び第４の斜辺ｓ４の終端が同一直線状上に位置し、第１の鉛直辺ｖ１、第２の斜辺ｓ２、及び第２のユニットの高さが同一になっているため、第１のユニットｕ１の高さ及び第２のユニットｕ２の高さは同一に形成されている。また、第１の所定角度α１、第２の所定角度α２、第３の所定角度α３、及び第４の所定角度α４の大きさは各々異なっており、第２の鉛直辺ｖ２の終端と第３の斜辺ｓ３の始端とが一致すると共に、第４の斜辺ｓ４の終端と他の第１のユニットの第１の鉛直辺ｖ１の始端とが一致している。 Thus, the start end of the first vertical side v1, the end of the first hypotenuse s1, the start of the second hypotenuse s2, the end of the second vertical side v1, the start of the third hypotenuse s3, and the fourth Since the end of the hypotenuse s4 is located on the same straight line, and the first vertical side v1, the second hypotenuse s2, and the second unit have the same height, the height of the first unit u1 The height of the second unit u2 is the same. In addition, the first predetermined angle α1, the second predetermined angle α2, the third predetermined angle α3, and the fourth predetermined angle α4 are different from each other, and the end of the second vertical side v2 and the third predetermined angle α3 are different from each other. And the end of the fourth hypotenuse s4 coincides with the start of the first vertical side v1 of the other first unit.
本実施例の鋸歯型形状のエッジの形状が上記のように形成されていることから、ベクトル・ポテンシャルＢの各々と、複数の縁辺ベクトルｄｇの各々との内積の和は最小になり、受音点の音場を最小にすることができる。本実施の形態において、受音点の音場を最小にするのが最適であるが、上記内積の和が、最小付近の所定値以下になるように鋸歯型形状のエッジの形状を定め、受音点の音場を最小付近の所定値以下になるようにしてもよい。 Since the shape of the sawtooth-shaped edge of the present embodiment is formed as described above, the sum of the inner products of each of the vector potential B and each of the plurality of edge vectors dg is minimized, and the sound reception is performed. The sound field of the point can be minimized. In the present embodiment, it is optimal to minimize the sound field at the sound receiving point, but the edge shape of the sawtooth shape is determined so that the sum of the inner products is not more than a predetermined value near the minimum. You may make it the sound field of a sound point become below predetermined value near the minimum.
図３は、鋸歯型エッジの変形例を示すもので、第１のユニットｕ１と第２のユニットｕ２との間に、第２の鉛直辺ｖ２の終端から鉛直方向に対して所定角度α５傾斜して鉛直上方に向かう第５の斜辺ｓ５と、第５の斜辺ｓ５の終端から鉛直下方に向かう上記第１の鉛直辺ｖ１と同じ長さの第３の鉛直辺ｖ３とを備えた形状を有する第３のユニットｕ３を配置し、第１のユニットｕ１、第２のユニットｕ２、及び第３のユニットｕ３を組合せたユニットを下端の一点で連続させて複数個配置することによりエッジを形成したものである。 FIG. 3 shows a modification of the serrated edge, and is inclined between the first unit u1 and the second unit u2 by a predetermined angle α5 with respect to the vertical direction from the end of the second vertical side v2. A fifth hypotenuse s5 heading vertically upward and a third vertical side v3 having the same length as the first vertical side v1 going vertically downward from the end of the fifth hypotenuse s5. Three units u3 are arranged, and an edge is formed by arranging a plurality of units, which are a combination of the first unit u1, the second unit u2, and the third unit u3, continuously at one point at the lower end. is there.
この変形例の第５の斜辺ｓ５の始端は第１のユニットの第２の鉛直辺ｖ２の終端と一致し、第３の鉛直辺ｖ３の終端は第２のユニットｕ２の第３の斜辺ｓ３の始端と一致しており、第１のユニットｕ１、第２のユニットｕ２、及び第３のユニットｕ３は、下端の一点で連続している。また、第１のユニットｕ１、第２のユニットｕ２、及び第３のユニットｕ３の斜辺及び鉛直辺で形成される三角形の各々の高さは同一に形成されている。 The start end of the fifth hypotenuse s5 of this modification coincides with the end of the second vertical side v2 of the first unit, and the end of the third vertical side v3 is the end of the third hypotenuse s3 of the second unit u2. It coincides with the start end, and the first unit u1, the second unit u2, and the third unit u3 are continuous at one point at the lower end. The heights of the triangles formed by the oblique sides and the vertical sides of the first unit u1, the second unit u2, and the third unit u3 are the same.
なお、上記では第１のユニットｕ１、第２のユニットｕ２、及び第３のユニットｕ３を組合せたユニットを連続させた例について説明したが、第１のユニットｕ１と第２のユニットｕ２とを交互に配置し、第１のユニットｕ１と第２のユニットｕ２との間、及び第２のユニットｕ２と第１のユニットｕ１との間の各々に、第１のユニットｕ１及び第２のユニットｕ２と下端の一点で連続させて第３のユニットｕ３を配置するようにしてもよい。この場合、図４に示すように、第３のユニットｕ３の斜辺の各々を曲線状に形成するようにしてもよく、第３のユニットｕ３の斜辺の各々を交互に、すなわち一つおきに曲線状に形成するようにしてもよい。 In addition, although the example which made the unit which combined the 1st unit u1, the 2nd unit u2, and the 3rd unit u3 continued was demonstrated above, the 1st unit u1 and the 2nd unit u2 are alternated. Between the first unit u1 and the second unit u2, and between the second unit u2 and the first unit u1, respectively, and the first unit u1 and the second unit u2. The third unit u3 may be arranged continuously at one point at the lower end. In this case, as shown in FIG. 4, each of the hypotenuses of the third unit u3 may be formed in a curved line, and each of the hypotenuses of the third unit u3 is alternately, that is, every other curve. You may make it form in a shape.
次に、第１のユニット及び第２のユニットの変形例について図５及び図６を参照して説明する。図５に示す変形例は、第１のユニットｕ１の第１の鉛直辺ｖ１の始端から第２の鉛直辺ｖ２の終端までの距離（第１のユニットの幅）Ｌｗと、第２のユニットｕ２の第３の斜辺ｓ３の始端から第４の斜辺ｓ４の終端までの距離（第２のユニットの幅）Ｌｗを同一の長さにし、第４の斜辺ｓ４の長さと第２の斜辺ｓ２の長さとを同一に形成したものである。第４の斜辺ｓ４の長さと第２の斜辺ｓ２の長さとが同一であるため、第２の所定角α２と第４の所定角α４の大きさは同一である。図６に、図５に示した変形例の第１のユニット及び第２のユニットを用いた場合の鋸歯型エッジの形状を示す。 Next, modified examples of the first unit and the second unit will be described with reference to FIGS. The modification shown in FIG. 5 includes a distance (first unit width) Lw from the start end of the first vertical side v1 to the end of the second vertical side v2 of the first unit u1, and the second unit u2. The distance from the start end of the third hypotenuse s3 to the end of the fourth hypotenuse s4 (the width of the second unit) Lw is the same, and the length of the fourth hypotenuse s4 and the length of the second hypotenuse s2 Are formed identically. Since the length of the fourth hypotenuse s4 and the length of the second hypotenuse s2 are the same, the second predetermined angle α2 and the fourth predetermined angle α4 have the same size. FIG. 6 shows the shape of the saw-toothed edge when the first unit and the second unit of the modification shown in FIG. 5 are used.
図６に示す変形例は、第１のユニットｕ１の第１の鉛直辺ｖ１の始端から第２の鉛直辺ｖ２の終端までの距離（第１のユニットの幅）Ｌｗ１と、第２のユニットｕ２の第３の斜辺ｓ３の始端から第４の斜辺ｓ４の終端までの距離（第２のユニットの幅）Ｌｗ２との比を異ならせて、例えば１０：７とし、第４の斜辺ｓ４の長さと第２の斜辺ｓ２の長さとが異なるように形成したものである。この変形例では、第４の斜辺ｓ４の長さと第２の斜辺ｓ２の長さとを異ならせてある。このため、第２の所定角α２と第４の所定角α４の大きさは異なっている。図８に、図６に示した変形例の第１のユニット及び第２のユニットを用いた場合の鋸歯型エッジの形状を示す。 The modification shown in FIG. 6 includes a distance (first unit width) Lw1 from the start end of the first vertical side v1 to the end of the second vertical side v2 of the first unit u1, and the second unit u2. The ratio of the distance from the start end of the third hypotenuse s3 to the end of the fourth hypotenuse s4 (the width of the second unit) Lw2 is different, for example 10: 7, and the length of the fourth hypotenuse s4 It is formed so that the length of the second hypotenuse s2 is different. In this modification, the length of the fourth hypotenuse s4 and the length of the second hypotenuse s2 are different. For this reason, the magnitudes of the second predetermined angle α2 and the fourth predetermined angle α4 are different. FIG. 8 shows the shape of the saw-toothed edge when the first unit and the second unit of the modification shown in FIG. 6 are used.
上記の実施の形態及び変形例において、第１のユニット及び第２のユニットの高さｈは、
周波数レスポンスが所定レベル以下となる最低周波数をｆlow、音速をｃとしたとき、以下の大きさに形成することが好ましい。最低周波数は、鋸歯型形状のエッジのインパルス応答の周波数特性が、このエッジの平均高さと同じ高さの平坦エッジのインパルス応答の周波数特性と比較して所定レベル以下となる最低周波数である。
In the embodiment and the modification described above, the height h of the first unit and the second unit is
When the minimum frequency at which the frequency response is equal to or lower than a predetermined level is f low and the sound speed is c, it is preferable to form the following size. The lowest frequency is the lowest frequency at which the frequency characteristic of the impulse response of the sawtooth-shaped edge is equal to or lower than a predetermined level as compared with the frequency characteristic of the impulse response of the flat edge having the same height as the average height of the edge.
ｈ＝ｃ／ｆlow
また、第１のユニット及び第２のユニットの幅ＬＷは以下の式を満たすように定めることが可能である。
h = c / f low
The width LW of the first unit and the second unit can be determined so as to satisfy the following expression.
０＜ＬＷ≦ｈ／２
次に、図９及び図１０を参照して、二等辺三角形を配列したエッジの内積の和の大きさと、本実施の形態の図２に示した鋸型形状のエッジの内積の和の大きさとを比較して説明する。
0 <LW ≦ h / 2
Next, referring to FIG. 9 and FIG. 10, the magnitude of the sum of the inner products of the edges in which the isosceles triangles are arranged and the magnitude of the sum of the inner products of the saw-shaped edges shown in FIG. Will be described.
二等辺三角形を配列したエッジの場合、エッジの形状は、第１停留点を通る鉛直線に対して線対称になっている。このため、同時刻に受音点Ｐに到来するエッジの点Ｃ１、点Ｃ２から伝播する音場を考えた場合、点Ｃ１では、ベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの向きが逆向きになっているので、鉛直線の左側及び右側で内積Ｂ・ｄｇは負になり、受音点で強めあうことになる。 In the case of an edge in which isosceles triangles are arranged, the shape of the edge is axisymmetric with respect to a vertical line passing through the first stop point. For this reason, when considering the sound field propagating from the point C1 and the point C2 of the edge arriving at the sound receiving point P at the same time, the direction of the vector potential B and the edge vector dg is reversed at the point C1. Therefore, the inner product B · dg becomes negative on the left and right sides of the vertical line, and strengthens at the sound receiving point.
また、点Ｃ２では、ベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの向きが同じ向きになっているので、鉛直線の左側及び右側で内積Ｂ・ｄｇは正になり、受音点で強めあうことになる。 At the point C2, since the vector potential B and the edge vector dg are in the same direction, the inner product B · dg becomes positive on the left and right sides of the vertical line, and strengthens at the sound receiving point. Become.
このように、二等辺三角形を配列したエッジの場合には、エッジの微小部分から回折して同時刻に受音点に到来する音が強め合うことになるので、受音点の音場は高くなる。 In this way, in the case of an edge in which isosceles triangles are arranged, the sound diffracting from a minute portion of the edge and arriving at the sound receiving point at the same time strengthens, so the sound field at the sound receiving point is high. Become.
一方、本実施の形態の鋸型形状のエッジの場合、エッジの形状は、第１停留点を通る鉛直線に対して非対称になっている。このため、同時刻に受音点に到来するエッジの点Ｃ３、点Ｃ４、点Ｃ５から伝播する音場を考えた場合、点Ｃ３では、ベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの向きが鉛直線の左側では逆向きになっているので、内積Ｂ・ｄｇは負になり、鉛直線の右側ではベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの向きが同じ向きになっているので、内積Ｂ・ｄｇは正になる。このため、点Ｃ３から回折する音は受音点で弱め合うことになる。 On the other hand, in the case of the saw-shaped edge of the present embodiment, the shape of the edge is asymmetric with respect to the vertical line passing through the first stop point. Therefore, when considering the sound field propagating from the point C3, the point C4, and the point C5 of the edge arriving at the sound receiving point at the same time, the direction of the vector potential B and the edge vector dg is a vertical line at the point C3. Since the inner product B · dg is negative, the vector potential B and the edge vector dg are in the same direction on the right side of the vertical line, so the inner product B · dg is Become positive. For this reason, the sound diffracted from the point C3 is weakened at the sound receiving point.
点Ｃ４では、ベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの向きが鉛直線の左側では同じ向きになっているので、内積Ｂ・ｄｇは正になり、鉛直線の右側ではベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの向きが逆向きになっているので、内積Ｂ・ｄｇは負になる。このため、点Ｃ４から回折する音は受音点で弱め合うことになる。 At the point C4, the vector potential B and the edge vector dg are oriented in the same direction on the left side of the vertical line, so the inner product B · dg becomes positive, and on the right side of the vertical line, the vector potential B and the edge vector Since the direction with respect to dg is opposite, the inner product B · dg becomes negative. For this reason, the sound diffracted from the point C4 is weakened at the sound receiving point.
そして、点Ｃ５では、ベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの向きが鉛直線の左側では同じ向きになっているので、内積Ｂ・ｄｇは正になり、鉛直線の右側ではベクトル・ポテンシャルＢと縁辺ベクトルｄｇとの向きが逆向きになっているので、内積Ｂ・ｄｇは負になる。このため、点Ｃ５から回折する音は受音点で弱め合うことになる。 At the point C5, the direction of the vector potential B and the edge vector dg is the same on the left side of the vertical line, so the inner product B · dg is positive, and on the right side of the vertical line, the vector potential B and Since the direction of the edge vector dg is opposite, the inner product B · dg becomes negative. For this reason, the sound diffracted from the point C5 is weakened at the sound receiving point.
このように、本実施の形態の鋸型形状のエッジの場合には、エッジの微小部分から回折して同時刻に受音点に到来する音が弱め合うことになるので、受音点の音場は最小値に近づく。 In this way, in the case of the saw-shaped edge of the present embodiment, the sound diffracted from the minute part of the edge and arriving at the sound receiving point at the same time is weakened. The field approaches the minimum value.
本発明の実施の形態の防音壁について説明する。図１１（１）に示すように、本実施の形態の防音壁１０は、従来の上辺が平坦な防音壁１２の上辺に、上記のように形成された鋸歯型形状のエッジ（図１１（１）では、図３に示したエッジを用いている）を有する鋸歯型防音パネル１４を取り付けて構成されている。鋸歯型防音パネル１４は、基板の上辺に、鋸歯型形状のエッジを形成することにより構成されている。鋸歯型防音パネル１４は、基板を用いることなく、第１のユニット及び第２のユニットのみを組合せることで、または第１のユニット、第２のユニット、及び第３のユニットのみを組合わせることで鋸歯型形状のエッジを構成してもよい。 The soundproof wall according to the embodiment of the present invention will be described. As shown in FIG. 11 (1), the soundproof wall 10 of the present embodiment is a sawtooth-shaped edge (FIG. 11 (1)) formed on the top side of a conventional soundproof wall 12 having a flat upper side. ) Is provided with a sawtooth type soundproof panel 14 having the edge shown in FIG. The sawtooth type soundproof panel 14 is configured by forming a sawtooth shaped edge on the upper side of the substrate. The sawtooth type soundproof panel 14 can be obtained by combining only the first unit and the second unit without using a substrate, or combining only the first unit, the second unit, and the third unit. A sawtooth-shaped edge may be formed.
上記で説明した鋸歯型防音パネル１４の厚みは、防音壁１２の厚みと略同一としたが、防音壁１２より薄く構成するようにしても、厚く構成するようにしてもよい。 Although the thickness of the sawtooth type soundproof panel 14 described above is substantially the same as the thickness of the soundproof wall 12, it may be configured to be thinner or thicker than the soundproof wall 12.
また、図１１（２）に示すように、鋸歯型防音パネルを用いることなく、上辺に鋸型形状のエッジを形成することによって、防音壁１０を構成するようにしてもよい。 In addition, as shown in FIG. 11B, the soundproof wall 10 may be configured by forming a saw-shaped edge on the upper side without using a sawtooth soundproof panel.
図１２は、従来の平坦エッジと本実施の形態の鋸歯型形状のエッジのインパスル応答ｈ（ｔ）を比較して示すものであり、図１３は、インパスル応答の周波数特性（インパスル応答ｈ（ｔ）の高速フーリエ変換（ＦＦＴ）の結果）を示す線図である。 FIG. 12 shows the impulse response h (t) of the conventional flat edge and the sawtooth-shaped edge of the present embodiment, and FIG. 13 shows the frequency characteristic of the impulse response (impulse response h (t ) Is a diagram showing the results of Fast Fourier Transform (FFT).
平坦エッジのインパスル応答ｈ（ｔ）は、先鋭なパルス状であり、１点にエネルギーが集中している。本実施の形態の鋸歯型形状のエッジでは、上向きの矢印で示されているように、エネルギーは集中することなく分散されて複数パルスになっている。 The impulse response h (t) of the flat edge has a sharp pulse shape, and energy is concentrated at one point. At the edge of the sawtooth shape of the present embodiment, as shown by the upward arrow, energy is dispersed without being concentrated into a plurality of pulses.
図１３には、平坦エッジの先鋭なパルスの周波数応答が破線で示されている。周波数レスポンスはなだらかに減少している。これに対して、本実施の形態の鋸歯型形状のエッジでは、実線で示すように、最低周波数ｆlow以上の周波数領域において周波数レスポンスが急激に減少している。 In FIG. 13, the frequency response of a sharp pulse with a flat edge is indicated by a broken line. The frequency response is decreasing gradually. On the other hand, at the edge of the sawtooth shape according to the present embodiment, as shown by the solid line, the frequency response sharply decreases in the frequency region above the lowest frequency f low .
なお、上記では、第１の所定角度〜第４の所定角度の全ての所定角度の大きさを異ならせる例について説明したが、第１の所定角度〜第４の所定角度のいずれか２つの所定角の大きさを異ならせて他の所定角度の大きさを同じ大きさとしてもよい。 In the above description, the example in which the sizes of all the predetermined angles from the first predetermined angle to the fourth predetermined angle are different has been described. However, any two predetermined values from the first predetermined angle to the fourth predetermined angle are described. The size of the other predetermined angle may be the same size by changing the size of the corner.
上記では、防音壁の上辺に鋸歯型防音パネルを取り付ける例について説明したが、防音壁の上辺自体に鋸歯型防音パネルの鋸歯型形状のエッジと同一形状のエッジを形成するようにしてもよい。 In the above, an example in which the sawtooth type soundproof panel is attached to the upper side of the soundproof wall has been described. However, an edge having the same shape as the sawtooth type edge of the sawtooth type soundproof panel may be formed on the upper side of the soundproof wall itself.
また、本発明は、防音壁以外の他の構造物にも適用することができる。 The present invention can also be applied to structures other than the sound barrier.
１２ 防音壁
１４ 鋸歯型防音パネル
12 Soundproof wall 14 Sawtooth type soundproof panel
Claims (19)
一端側から他端側に辿ったとき、鉛直方向に対して第３の所定角度傾斜して鉛直上方に向かう第３の斜辺、及び該第３の斜辺の終端から鉛直方向に対して第４の所定角度傾斜して鉛直下方に向かう第４の斜辺を組合せた形状を有する第２のユニットと、
を交互に配置した形状の鋸歯型エッジを備えた鋸歯型防音パネルであって、
ベクトルポテンシャＢを、受音点から前記鋸歯型エッジに想定された複数の縁辺ベクトルｄｇの始点の各々までの大きさで該受音点から該始点の各々に向かう複数の第１のベクトルｌの各々と、音源から前記縁辺ベクトルｄｇの始点の各々までの大きさで該音源から該始点の各々に向かう複数の第２のベクトルｍの各々との外積を含んで表わしたとき、
前記ベクトル・ポテンシャルＢの各々と、前記複数の縁辺ベクトルｄｇの各々との内積の和が所定値以下の値になるように前記第１のユニット及び第２のユニットの形状を定めた鋸歯型防音パネル。 The first vertical side that goes vertically upward when traced from one end side to the other end side, and the first vertical side that tilts a first predetermined angle with respect to the vertical direction from the end of the first vertical side and goes downward vertically A hypotenuse, a second hypotenuse inclined vertically upward from the end of the first hypotenuse by a second predetermined angle with respect to the vertical direction, and a second vertical side going vertically downward from the end of the second hypotenuse A first unit having a combined shape;
When traced from the one end side to the other end side, the third hypotenuse which is inclined at a third predetermined angle with respect to the vertical direction and goes vertically upward, and the fourth hypothesis from the end of the third hypotenuse to the vertical direction A second unit having a shape that is a combination of a fourth hypotenuse inclined at a predetermined angle and directed vertically downward;
A sawtooth type soundproof panel having sawtooth type edges in the shape of alternately arranged,
The vector potentiometer B has a size from the sound receiving point to each of the start points of the plurality of edge vectors dg assumed for the sawtooth-type edge, and a plurality of first vectors l directed from the sound receiving point to each of the start points. Each including a cross product of each of a plurality of second vectors m from the sound source to each of the start points with a size from the sound source to each of the start points of the edge vector dg.
Sawtooth type soundproofing in which the shapes of the first unit and the second unit are determined such that the sum of the inner products of each of the vector potentials B and each of the plurality of edge vectors dg is a predetermined value or less. panel.
一端側から他端側に辿ったとき、鉛直方向に対して第３の所定角度傾斜して鉛直上方に向かう第３の斜辺、及び該第３の斜辺の終端から鉛直方向に対して第４の所定角度傾斜して鉛直下方に向かう第４の斜辺を組合せた形状を有する第２のユニットと、
を交互に配置した形状の鋸歯型エッジを備えた鋸歯型防音パネルであって、
前記第１の鉛直辺の始端、前記第１の斜辺の終端、前記第２の斜辺の始端、第２の鉛直辺の終端、前記第３の斜辺の始端、及び前記第４の斜辺の終端を同一直線状上に位置させ、
前記第１のユニットの高さ及び前記第２のユニットの高さを同一とし、
前記第１の所定角度、前記第２の所定角度、前記第３の所定角度、及び前記第４の所定角度の少なくとも２つの所定角度の大きさが各々異なるように前記第１のユニット及び第２のユニットの形状を定めた鋸歯型防音パネル。 The first vertical side that goes vertically upward when traced from one end side to the other end side, and the first vertical side that tilts a first predetermined angle with respect to the vertical direction from the end of the first vertical side and goes downward vertically A hypotenuse, a second hypotenuse inclined vertically upward from the end of the first hypotenuse by a second predetermined angle with respect to the vertical direction, and a second vertical side going vertically downward from the end of the second hypotenuse A first unit having a combined shape;
When traced from the one end side to the other end side, the third hypotenuse which is inclined at a third predetermined angle with respect to the vertical direction and goes vertically upward, and the fourth hypothesis from the end of the third hypotenuse to the vertical direction A second unit having a shape that is a combination of a fourth hypotenuse inclined at a predetermined angle and directed vertically downward;
A sawtooth type soundproof panel having sawtooth type edges in the shape of alternately arranged,
The beginning of the first vertical side, the end of the first hypotenuse, the start of the second hypotenuse, the end of the second vertical side, the start of the third hypotenuse, and the end of the fourth hypotenuse. Located on the same straight line,
The height of the first unit and the height of the second unit are the same,
The first unit and the second unit may have different sizes of at least two of the first predetermined angle, the second predetermined angle, the third predetermined angle, and the fourth predetermined angle. Sawtooth type soundproof panel that defines the shape of the unit.
ｈ＝ｃ／ｆlow The height h of the first unit and the second unit is set to the following magnitude when the lowest frequency at which the frequency response is below a predetermined level is f low and the sound speed is c. The sawtooth type soundproof panel according to any one of the above.
h = c / f low
一端側から他端側に辿ったとき、鉛直方向に対して第３の所定角度傾斜して鉛直上方に向かう第３の斜辺、及び該第３の斜辺の終端から鉛直方向に対して第４の所定角度傾斜して鉛直下方に向かう第４の斜辺を組合せた形状を有する第２のユニットと、
を交互に配置した形状の鋸歯型エッジを備えた防音壁であって、
ベクトルポテンシャＢを、受音点から前記鋸歯型エッジに想定された複数の縁辺ベクトルｄｇの始点の各々までの大きさで該受音点から該始点の各々に向かう複数の第１のベクトルｌの各々と、音源から前記縁辺ベクトルｄｇの始点の各々までの大きさで該音源から該始点の各々に向かう複数の第２のベクトルｍの各々との外積を含んで表わしたとき、
前記ベクトル・ポテンシャルＢの各々と、前記複数の縁辺ベクトルｄｇの各々との内積の和が所定値以下の値になるように前記第１のユニット及び第２のユニットの形状を定めた防音壁。 The first vertical side that goes vertically upward when traced from one end side to the other end side, and the first vertical side that tilts a first predetermined angle with respect to the vertical direction from the end of the first vertical side and goes downward vertically A hypotenuse, a second hypotenuse inclined vertically upward from the end of the first hypotenuse by a second predetermined angle with respect to the vertical direction, and a second vertical side going vertically downward from the end of the second hypotenuse A first unit having a combined shape;
When traced from the one end side to the other end side, the third hypotenuse which is inclined at a third predetermined angle with respect to the vertical direction and goes vertically upward, and the fourth hypothesis from the end of the third hypotenuse to the vertical direction A second unit having a shape that is a combination of a fourth hypotenuse inclined at a predetermined angle and directed vertically downward;
Is a soundproof wall with sawtooth-shaped edges in a shape of alternately arranged,
The vector potentiometer B has a size from the sound receiving point to each of the start points of the plurality of edge vectors dg assumed for the sawtooth-type edge, and a plurality of first vectors l directed from the sound receiving point to each of the start points. Each including a cross product of each of a plurality of second vectors m from the sound source to each of the start points with a size from the sound source to each of the start points of the edge vector dg.
A soundproof wall in which the shapes of the first unit and the second unit are determined so that the sum of the inner products of each of the vector potential B and each of the plurality of edge vectors dg is a predetermined value or less.
一端側から他端側に辿ったとき、鉛直方向に対して第３の所定角度傾斜して鉛直上方に向かう第３の斜辺、及び該第３の斜辺の終端から鉛直方向に対して第４の所定角度傾斜して鉛直下方に向かう第４の斜辺を組合せた形状を有する第２のユニットと、
を交互に配置した形状の鋸歯型エッジを備えた防音壁であって、
前記第１の鉛直辺の始端、前記第１の斜辺の終端、前記第２の斜辺の始端、第２の鉛直辺の終端、前記第３の斜辺の始端、及び前記第４の斜辺の終端を同一直線状上に位置させ、
前記第１のユニットの高さ及び前記第２のユニットの高さを同一とし、
前記第１の所定角度、前記第２の所定角度、前記第３の所定角度、及び前記第４の所定角度の少なくとも２つの所定角度の大きさが各々異なるように前記第１のユニット及び第２のユニットの形状を定めた防音壁。 The first vertical side that goes vertically upward when traced from one end side to the other end side, and the first vertical side that tilts a first predetermined angle with respect to the vertical direction from the end of the first vertical side and goes downward vertically A hypotenuse, a second hypotenuse inclined vertically upward from the end of the first hypotenuse by a second predetermined angle with respect to the vertical direction, and a second vertical side going vertically downward from the end of the second hypotenuse A first unit having a combined shape;
When traced from the one end side to the other end side, the third hypotenuse which is inclined at a third predetermined angle with respect to the vertical direction and goes vertically upward, and the fourth hypothesis from the end of the third hypotenuse to the vertical direction A second unit having a shape that is a combination of a fourth hypotenuse inclined at a predetermined angle and directed vertically downward;
Is a soundproof wall with sawtooth-shaped edges in a shape of alternately arranged,
The beginning of the first vertical side, the end of the first hypotenuse, the start of the second hypotenuse, the end of the second vertical side, the start of the third hypotenuse, and the end of the fourth hypotenuse. Located on the same straight line,
The height of the first unit and the height of the second unit are the same,
The first unit and the second unit may have different sizes of at least two of the first predetermined angle, the second predetermined angle, the third predetermined angle, and the fourth predetermined angle. A soundproof wall that defines the shape of the unit.
ｈ＝ｃ／ｆlow The height h of the first unit and the second unit is set to the following size when the lowest frequency at which the frequency response is below a predetermined level is f low and the sound speed is c. The soundproof wall according to any one of 16.
h = c / f low
一端側から他端側に辿ったとき、鉛直方向に対して第３の所定角度傾斜して鉛直上方に向かう第３の斜辺、及び該第３の斜辺の終端から鉛直方向に対して第４の所定角度傾斜して鉛直下方に向かう第４の斜辺を組合せた形状を有する第２のユニットと、
を交互に配置した形状の鋸歯型エッジを備えた構造物であって、
ベクトルポテンシャＢを、受音点から前記鋸歯型エッジに想定された複数の縁辺ベクトルｄｇの始点の各々までの大きさで該受音点から該始点の各々に向かう複数の第１のベクトルｌの各々と、音源から前記縁辺ベクトルｄｇの始点の各々までの大きさで該音源から該始点の各々に向かう複数の第２のベクトルｍの各々との外積を含んで表わしたとき、
前記ベクトル・ポテンシャルＢの各々と、前記複数の縁辺ベクトルｄｇの各々との内積の和が所定値以下の値になるように前記第１のユニット及び第２のユニットの形状を定めた構造物。 The first vertical side that goes vertically upward when traced from one end side to the other end side, and the first vertical side that tilts a first predetermined angle with respect to the vertical direction from the end of the first vertical side and goes downward vertically A hypotenuse, a second hypotenuse inclined vertically upward from the end of the first hypotenuse by a second predetermined angle with respect to the vertical direction, and a second vertical side going vertically downward from the end of the second hypotenuse A first unit having a combined shape;
When traced from the one end side to the other end side, a third hypotenuse inclined at a third predetermined angle with respect to the vertical direction and directed vertically upward, and a fourth hypothesis from the end of the third hypotenuse with respect to the vertical direction. A second unit having a shape that is a combination of a fourth hypotenuse inclined at a predetermined angle and directed vertically downward;
A structure with sawtooth-shaped edges of alternating shapes,
The vector potentiometer B has a size from the sound receiving point to each of the start points of the plurality of edge vectors dg assumed for the sawtooth-type edge, and a plurality of first vectors l directed from the sound receiving point to each of the start points. Each including a cross product of each of a plurality of second vectors m from the sound source to each of the start points with a size from the sound source to each of the start points of the edge vector dg.
A structure in which the shapes of the first unit and the second unit are determined so that the sum of the inner products of each of the vector potential B and each of the plurality of edge vectors dg becomes a value equal to or less than a predetermined value.
一端側から他端側に辿ったとき、鉛直方向に対して第３の所定角度傾斜して鉛直上方に向かう第３の斜辺、及び該第３の斜辺の終端から鉛直方向に対して第４の所定角度傾斜して鉛直下方に向かう第４の斜辺を組合せた形状を有する第２のユニットと、
を交互に配置した形状の鋸歯型エッジを用いて騒音を低減する騒音低減方法であって、
ベクトルポテンシャＢを、受音点から前記鋸歯型エッジに想定された複数の縁辺ベクトルｄｇの始点の各々までの大きさで該受音点から該始点の各々に向かう複数の第１のベクトルｌの各々と、音源から前記縁辺ベクトルｄｇの始点の各々までの大きさで該音源から該始点の各々に向かう複数の第２のベクトルｍの各々との外積を含んで表わしたとき、
前記ベクトル・ポテンシャルＢの各々と、前記複数の縁辺ベクトルｄｇの各々との内積の和が所定値以下の値になるように前記第１のユニット及び第２のユニットの形状を定めた騒音低減方法。 The first vertical side that goes vertically upward when traced from one end side to the other end side, and the first vertical side that tilts a first predetermined angle with respect to the vertical direction from the end of the first vertical side and goes downward vertically A hypotenuse, a second hypotenuse inclined vertically upward from the end of the first hypotenuse by a second predetermined angle with respect to the vertical direction, and a second vertical side going vertically downward from the end of the second hypotenuse A first unit having a combined shape;
When traced from the one end side to the other end side, the third hypotenuse which is inclined at a third predetermined angle with respect to the vertical direction and goes vertically upward, and the fourth hypothesis from the end of the third hypotenuse to the vertical direction A second unit having a shape that is a combination of a fourth hypotenuse inclined at a predetermined angle and directed vertically downward;
A noise reduction method for reducing noise by using saw-toothed edges with shapes alternately arranged,
The vector potentiometer B has a size from the sound receiving point to each of the start points of the plurality of edge vectors dg assumed for the sawtooth-type edge, and a plurality of first vectors l directed from the sound receiving point to each of the start points. Each including a cross product of each of a plurality of second vectors m from the sound source to each of the start points with a size from the sound source to each of the start points of the edge vector dg.
A noise reduction method in which the shapes of the first unit and the second unit are determined so that the sum of the inner products of each of the vector potentials B and each of the plurality of edge vectors dg is a predetermined value or less. .
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