CN113609641B - Method for obtaining rotational kinetic energy of foundation vibration isolation structure - Google Patents
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Abstract
The invention discloses a method for acquiring rotational kinetic energy of a basic vibration isolation structure, which comprises the following steps: calculating the response of the basic shock insulation structure under the action of earthquake by utilizing the motion equation of the dynamic analysis model of the multi-particle flat swing system structure; calculating the mass center position of the basic shock insulation structure; determining translational displacement at the mass center according to the mass center position, and calculating the rotational displacement of each mass point around the mass center under the action of an earthquake by using the translational displacement at the mass center; obtaining the angular acceleration of each particle according to the relation between the displacement and the acceleration; and obtaining the rotational kinetic energy of the basic shock insulation structure according to the angular acceleration of each particle. The invention divides the displacement response of the basic shock insulation structure under the action of earthquake into translational displacement and rotational displacement around the mass center, and further obtains the angular acceleration of particles according to the relation between the displacement and the acceleration, further obtains the rotational kinetic energy of the basic shock insulation structure, lays a foundation for improving the limit value of the aspect ratio of the shock insulation structure, and has clear principle and simple and convenient calculation.
Description
Technical Field
The invention relates to a method for obtaining rotational kinetic energy of a basic vibration isolation structure, and belongs to the field of civil engineering.
Background
At present, the earthquake isolation technology is widely applied to high-intensity areas with excellent performance, and when an earthquake occurs, the earthquake is isolated to transmit energy to an upper structure through an earthquake isolation support arranged between a foundation and the bottom of a building, so that damage to the building caused by the earthquake can be obviously reduced. The rotational kinetic energy of the building with larger height and width is larger, so that the shock insulation support generates larger pulling force. If the building with larger height and width is applied to the earthquake isolation technology, accidents such as collapse and the like can occur due to the damage of the earthquake isolation support (poor tensile property of the earthquake isolation support).
Disclosure of Invention
The invention provides a method for obtaining the rotational kinetic energy of a base shock insulation structure, which can be used for obtaining the rotational kinetic energy of the base shock insulation structure.
The technical scheme of the invention is as follows: a method of obtaining rotational kinetic energy of a base seismic isolation structure, comprising:
s1, calculating the response of a basic shock insulation structure under the action of an earthquake by utilizing a motion equation of a multi-particle flat swing system structure dynamic analysis model;
s2, calculating the mass center position of the basic shock insulation structure;
s3, determining translational displacement at the mass center according to the position of the mass center, and calculating rotational displacement of each mass point around the mass center under the action of an earthquake by using the translational displacement at the mass center; obtaining the angular acceleration of each particle according to the relation between the displacement and the acceleration; and obtaining the rotational kinetic energy of the basic shock insulation structure according to the angular acceleration of each particle.
The step S1 specifically comprises the following steps:
s1.1, determining the mass, rigidity, damping and height of each particle of a basic shock insulation structure, and the horizontal rigidity of a shock insulation layer and applied seismic waves;
the displacement of the S1.2 and i-th particles is as shown in formula (1):
x i ＝x g +x b +x θi +x si (1)
the displacement of each particle generated by the rotation of the vibration isolation layer is shown as the formula (2):
x θi ＝θ b ×h i (2)
the equation of motion of the superstructure is as formula (3):
the motion equation of the shock insulation structure system is shown as (4), (5) and (6):
M＝K θ θ b (6)
the response x of the shock insulation structure under the action of the earthquake based on the dynamic analysis model of the multi-particle flat swing system structure can be calculated by the process i 、Wherein x is i 、/>Displacement, velocity, acceleration of the ith particle; wherein: x is x g 、/>-ground seismic displacement, acceleration; x is x b 、/>-horizontal relative displacement, relative velocity, relative acceleration between the top plate of the seismic isolation layer and the foundation; x is x θi 、/>-rotation of the top plate of the seismic isolation layer causes relative displacement of the ith particle of the superstructure to the seismic isolation layer, relative acceleration; x is x si 、-horizontal relative displacement of the ith particle to the top plate of the seismic isolation layer caused by structural translation; θ b -an oscillation angle of the shock insulation layer; h is a i -the height of the ith particle from the top plate of the seismic isolation layer; [ m ]]、[C]、[K]-mass, damping and stiffness matrix of the structure; m is m 0 -the mass of the top plate of the shock insulation layer; m is m i -ith particle mass; />-angular acceleration of the vibration isolation layer oscillation; c-damping of the vibration isolation layer; k-is the horizontal rigidity of the shock insulation layer; bending moment K generated by M-vibration isolation structure swing on bottom layer θ Rotational stiffness of the shock insulation layer.
In the step S2, the mass center of the basic shock insulation structure is calculated as formula (7):
wherein m is i -ith particle mass; h is a i -the height of the ith particle from the top plate of the seismic isolation layer; h is a c -the height from the top plate of the seismic isolation layer at the centroid.
The step S3 specifically comprises the following steps:
s3.1: the translational displacement of the mass center of the shock insulation structure under the action of the earthquake is determined according to the height of the mass center, the translational displacement of each mass point is differentiated from the translational displacement of the mass center, and the rotational displacement of each mass point around the mass center under the action of the earthquake is obtained as follows:
x zi ＝x i -x c (8)
step 3.2: the angular acceleration of the ith particle can be obtained from the relationship between displacement and acceleration:
step 3.3: the rotational kinetic energy of the basic shock insulation structure is calculated as shown in the formula (10):
wherein x is zi 、Rotational displacement, angular acceleration of the ith particle; x is x i 、/>-displacement, acceleration of the ith particle; x is x c 、Translational displacement and translational acceleration of the centroid under the action of earthquake; the rotational kinetic energy of the T-base shock insulation structure; m is m i -the mass of the ith particle; h is a i -the height of the ith particle from the top plate of the seismic isolation layer; h is a c -the height from the top plate of the seismic isolation layer at the centroid.
The translational displacement at the centroid is specifically: if the centroid coincides with the particle then x c The value is the displacement of the particle; otherwise, the translational displacement at the mass center is obtained by using the linear difference value between the height of the mass center from the top plate of the vibration isolation layer and the displacement of the upper mass point and the lower mass point.
The beneficial effects of the invention are as follows: the invention divides the displacement response of the basic shock insulation structure under the action of earthquake into translational displacement and rotational displacement around the mass center, and further obtains the angular acceleration of particles according to the relation between the displacement and the acceleration, further obtains the rotational kinetic energy of the basic shock insulation structure, lays a foundation for improving the limit value of the aspect ratio of the shock insulation structure, and has clear principle and simple and convenient calculation.
Drawings
FIG. 1 is a computational flow chart of the method of the present invention;
FIG. 2 is a schematic structural diagram of an embodiment of the present invention;
fig. 3 is a simplified structural model of an embodiment of the present invention.
Detailed Description
Example 1: as shown in fig. 1-3, a method for obtaining rotational kinetic energy of a base seismic isolation structure includes: s1, calculating the response of a basic shock insulation structure under the action of an earthquake by utilizing a motion equation of a multi-particle flat swing system structure dynamic analysis model;
s2, calculating the mass center position of the basic shock insulation structure;
s3, determining translational displacement at the mass center according to the position of the mass center, and calculating rotational displacement of each mass point around the mass center under the action of an earthquake by using the translational displacement at the mass center; obtaining the angular acceleration of each particle according to the relation between the displacement and the acceleration; and obtaining the rotational kinetic energy of the basic shock insulation structure according to the angular acceleration of each particle.
Further, the invention provides the following procedures:
as shown in fig. 1, the method for obtaining rotational kinetic energy of a basic shock insulation structure according to the present embodiment first analyzes the structure to determine mass, rigidity, damping, height of each particle, shock insulation support parameters and shock waves, and calculates rotational kinetic energy of the structure under the action of the shock, and includes the following steps:
step 1.1: the structure adopted by the specific embodiment of the invention is shown in figure 2, the structure is three particles, and the mass of each particle is 315000kg, 270000kg and 180000kg respectively; the rigidities are 245000000N/m, 196000000N/m and 98000000N/m respectively, and Rayleigh damping is adopted; the horizontal rigidity and the damping of the shock insulation support layer are 980000N/m and 26514 respectively; EI-Centro is selected as the ground vibration input, and the time step is 0.02s and is completed in 1500 steps.
Step 1.2: and (3) bringing the parameters into the formulas (3), (4), (5) and (6) to calculate the response of the structure under the action of the earthquake.
Step 2: the mass center of the basic shock insulation structure is calculated, and the specific method is to calculate the position of the mass center by using a mass center calculation formula. The mass center of the basic shock insulation structure is shown in the following formula:
wherein: m is m i -ith particle mass; h is a i -height of the ith particle from the top plate of the seismic isolation layer.
Step 3.1: determining displacement x of mass center of shock insulation structure under the action of earthquake according to height of mass center c (i.e. translational displacement), the displacement of each particle is differenced from the translational displacement of the mass center to obtain the rotation position of each particle under the action of earthquakeThe method comprises the following steps:
x zi ＝x i -x c
wherein; x is x c -displacement of the centroid under the influence of an earthquake;
step 3.2: the angular acceleration of the ith particle can be obtained from the relationship between displacement and acceleration:
step 3.3: the rotational kinetic energy of the shock insulation structure is calculated as follows
This example is 3 layers on the structural floor, one layer being 3.5 meters high and the remaining layers being 3.0 meters high. Wherein, the mass and rigidity information is shown in figure 2, and Rayleigh damping is adopted; after the ground acceleration is input (taking EI-centro seismic waves as an example), each layer of the three-layer frame is subjected to the action of seismic load, the action time of the seismic load is 30s, the calculated reaction time is 30s, and the maximum time-course acceleration is 400cm/s 2 The time step is 0.02s, which is completed in 1500 steps.
The example structure is analyzed by adopting the steps, the mass center of the structure is calculated to be positioned at the position 5.97m of the building (namely, the position 5.97m away from the top plate of the shock insulation layer), and the maximum translational displacement x of the mass center of the EI-Centro seismic wave is calculated c Is 0.587mm. And (3) the displacement of each particle under the action of the earthquake is differed from the horizontal displacement of the mass center, so that the rotational displacement of each particle can be obtained. Based on the relationship between displacement and velocity, the angular acceleration of each particle can be calculated. And then according to the calculation formula of the rotational kinetic energy, the maximum rotational kinetic energy of the structure under the action of EI-Centro seismic waves is 7.3973 multiplied by 10 6 J, the value can be used for measuring whether the foundation shock insulation building with the large height-width ratio needs to adopt corresponding measures to reduce the rotational kinetic energy.
While the present invention has been described in detail with reference to the drawings, the present invention is not limited to the above embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (4)
1. A method for obtaining the rotational kinetic energy of a basic shock insulation structure is characterized by comprising the following steps: comprising the following steps:
s1, calculating the response of a basic shock insulation structure under the action of an earthquake by utilizing a motion equation of a multi-particle flat swing system structure dynamic analysis model; the response comprises displacement, speed and acceleration of each particle under the action of earthquake;
s2, calculating the mass center position of the basic shock insulation structure;
s3, determining translational displacement at the mass center according to the position of the mass center, and calculating rotational displacement of each mass point around the mass center under the action of an earthquake by using the translational displacement at the mass center; obtaining the angular acceleration of each particle through rotational displacement according to the relation between the displacement and the acceleration; according to the angular acceleration of each particle, the rotational kinetic energy of the basic shock insulation structure is obtained;
the step S1 specifically comprises the following steps:
s1.1, determining the mass, rigidity, damping and height of each particle of a basic shock insulation structure, and the horizontal rigidity of a shock insulation layer and applied seismic waves;
the displacement of the S1.2 and i-th particles is as shown in formula (1):
x i ＝x g +x b +x θi +x si (1)
the displacement of each particle generated by the rotation of the vibration isolation layer is shown as the formula (2):
x θi ＝θ b ×h i (2)
the equation of motion of the superstructure is as formula (3):
the motion equation of the shock insulation structure system is shown as (4), (5) and (6):
M＝K θ θ b (6)
the response x of the shock insulation structure under the action of the earthquake based on the dynamic analysis model of the multi-particle flat swing system structure can be calculated by the process i 、Wherein x is i 、/>Displacement, velocity, acceleration of the ith particle; wherein: x is x g 、/>-ground seismic displacement, acceleration; x is x b 、/>-horizontal relative displacement, relative velocity, relative acceleration between the top plate of the seismic isolation layer and the foundation; x is x θi 、/>-rotation of the top plate of the shock insulation layer causes relative displacement and relative acceleration of the ith particle of the upper structure and the shock insulation layer; x is x si 、/>-horizontal relative displacement of the ith particle and the top plate of the shock insulation layer caused by the translation of the upper structure; θ b -a rotation angle of the shock insulation layer; h is a i -the height of the ith particle from the top plate of the seismic isolation layer; [ m ]]、[C]、[K]-upper partMass, damping and stiffness matrices of the part structure; m is m 0 -the mass of the top plate of the shock insulation layer; m is m i -ith particle mass; />-angular acceleration of rotation of the seismic isolation layer; d-damping of the shock insulation layer; f-is the horizontal rigidity of the shock insulation layer; m-bending moment generated by rotation of vibration isolation layer on upper structure bottom layer, K θ -rotational stiffness of the shock insulation layer; n represents the number of particles.
2. The method for obtaining rotational kinetic energy of a basic shock insulation structure according to claim 1, wherein: in the step S2, the mass center of the basic shock insulation structure is calculated as formula (7):
wherein m is i -ith particle mass; h is a i -the height of the ith particle from the top plate of the seismic isolation layer; h is a c -the height from the top plate of the seismic isolation layer at the centroid.
3. The method for obtaining rotational kinetic energy of a basic shock insulation structure according to claim 1, wherein: the step S3 specifically comprises the following steps:
s3.1: the translational displacement of the mass center of the shock insulation structure under the action of the earthquake is determined according to the height of the mass center, the translational displacement of each mass point is differentiated from the translational displacement of the mass center, and the rotational displacement of each mass point around the mass center under the action of the earthquake is obtained as follows:
x zi ＝x i -x c (8)
step 3.2: the angular acceleration of the ith particle can be obtained by the rotational displacement of the ith particle according to the relationship between displacement and acceleration:
step 3.3: the rotational kinetic energy of the basic shock insulation structure is calculated as shown in the formula (10):
wherein x is zi 、Rotational displacement, angular acceleration of the ith particle; x is x i 、/>-displacement, acceleration of the ith particle; x is x c 、/>Translational displacement and translational acceleration of the centroid under the action of earthquake; the rotational kinetic energy of the T-base shock insulation structure; m is m i -the mass of the ith particle; h is a i -the height of the ith particle from the top plate of the seismic isolation layer; h is a c -the height from the top plate of the seismic isolation layer at the centroid.
4. A method of obtaining rotational kinetic energy of a basic shock insulation structure according to claim 3, wherein: the translational displacement at the centroid is specifically: if the centroid coincides with the particle then x c The value is the displacement of the particle; otherwise, the translational displacement at the mass center is obtained by using the linear difference value between the height of the mass center from the top plate of the vibration isolation layer and the displacement of the upper mass point and the lower mass point.
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| JP5698402B1 (en) * | 2014-06-10 | 2015-04-08 | グローバル・ロジスティック・プロパティーズ株式会社 | Seismic response analysis method for base-isolated buildings and seismic safety evaluation method for base-isolated devices using seismic response analysis method for base-isolated buildings |
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- 2021-07-01 CN CN202110745158.1A patent/CN113609641B/en active Active
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| JP2010203192A (en) * | 2009-03-05 | 2010-09-16 | Shimizu Corp | Connected seismic control structure |
| JP2013104231A (en) * | 2011-11-14 | 2013-05-30 | Takenaka Komuten Co Ltd | Base-isolated building, and design method for the same |
| CN102663246A (en) * | 2012-04-06 | 2012-09-12 | 上海大学 | Analytic method of irregular building seismic response considering SSI (soil-structure interaction) general plane |
| CN103541451A (en) * | 2012-07-11 | 2014-01-29 | 赵世峰 | Anti-overturning, shock insulation, shock absorption and energy consumption system for high-rise structure |
| CN103774772A (en) * | 2014-01-29 | 2014-05-07 | 中国航空规划建设发展有限公司 | Method for controlling torsion of base isolation structure |
| JP5698402B1 (en) * | 2014-06-10 | 2015-04-08 | グローバル・ロジスティック・プロパティーズ株式会社 | Seismic response analysis method for base-isolated buildings and seismic safety evaluation method for base-isolated devices using seismic response analysis method for base-isolated buildings |
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| 翻转动能对基础隔震剪力墙结构高宽比限值的影响分析;赖正聪等;《振动与冲击》;第38卷(第5期);146-154 * |
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