CN109001380B - Method for detecting layered damage position of composite laminated beam - Google Patents
Method for detecting layered damage position of composite laminated beam Download PDFInfo
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- 239000002131 composite material Substances 0.000 title claims abstract description 43
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- 230000032798 delamination Effects 0.000 claims description 17
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- 230000005284 excitation Effects 0.000 claims description 3
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Abstract
The invention discloses a method for detecting the position of a layered damage of a composite laminated beam, which comprises the following steps: measuring the natural frequency before and after 10-order damage of the composite laminated beam and the vibration mode after the damage; calculating the relative change rate of the natural frequency and normalizing the relative change rate; calculating the square of the first derivative of the vibration mode and normalizing the square; calculating the first 10-order single-order hierarchical damage index according to the relative change rate of the standardized natural frequency and the square of the first derivative of the vibration mode, and multiplying the first 10-order single-order hierarchical damage index to obtain an integral hierarchical damage index; and determining the position of the layered damage according to the position of the maximum value of the overall layered damage index. The method can be used for analyzing the natural frequency before and after the layered damage of the composite laminated beam and the vibration mode after the damage, and further judging the layered damage position.
Description
Technical Field
The invention discloses a method for detecting a layered damage position of a composite laminated beam, and particularly relates to the technical field of damage detection of composite laminated beam structures.
Background
The composite laminated beam structure is easy to be impacted to generate fine layered damage in long-term service. These subtle delamination damage can accumulate and evolve into macroscopic damage that compromises the safe and reliable operation of the overall structure. Based on this, various nondestructive testing methods have been rapidly developed in recent years, and local nondestructive testing methods such as ultrasonic waves, electromagnetic fields, eddy currents, and the like have been widely applied to composite laminated beam delamination damage testing. However, these methods generally require that the approximate location of the delamination damage be known in advance, and the delamination damage location must be easily accessible, which is difficult to satisfy in practical applications. And based on the dynamic parameters of the composite laminated beam: the natural frequency and the vibration mode form a delamination damage index, and the research for detecting the delamination damage of the composite laminated beam is not reported yet.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the defects of the prior art, a composite laminated beam layered damage position detection method based on combination of natural frequency and vibration mode is provided.
The invention adopts the following technical scheme for solving the technical problems:
the invention provides a method for detecting a layered damage position of a composite laminated beam, which comprises the following specific steps of:
measuring the inherent frequency before and after m (m is more than or equal to 5) orders of layered damage before the composite laminated beam, calculating the relative change rate of the inherent frequency, and standardizing the relative change rate;
measuring the vibration mode of the composite laminated beam after m (m is more than or equal to 5) orders of layered damage, calculating the square of the first derivative of the vibration mode, and standardizing the square;
calculating the first m-order single-order hierarchical damage index according to the relative change rate of the standardized natural frequency and the square of the first derivative of the vibration mode, and multiplying the first m-order single-order hierarchical damage index to obtain an integral hierarchical damage index;
and step four, determining the layering damage position according to the position where the maximum value of the overall layering damage index appears.
As a further preferable embodiment of the present invention, the specific calculation manner of the first step is as follows:
(1) measuring inherent frequency omega before and after m (m is more than or equal to 5) order delamination damage of composite laminated beamj、
(2) Calculating the relative change rate of the natural frequency:
where j ∈ {1, 2.,. m } is the frequency order.
(3) Normalizing the relative change rate of the natural frequency in a [01] interval:
wherein, δ ωjRepresenting the relative rate of change of the natural frequency for the j-th order normalization.
As a further preferable embodiment of the present invention, the specific calculation manner of the second step is as follows:
(1) measuring vibration mode phi after m (m is more than or equal to 5) order layered damage in front of composite laminated beami,j；
(2) Calculating the square of the first derivative of the mode shape:
wherein i belongs to {1,2,. and n } is a vibration mode measuring point, and h is a measuring point distance;
(3) normalizing the square of the first derivative of the mode shape by [01 ]:
wherein σi,jRepresenting the normalized result of the square of the first derivative of mode shape.
As a further preferable embodiment of the present invention, the specific calculation manner of the step three is as follows:
(1) according to the relative change rate of the normalized natural frequency and the square of the first derivative of the vibration mode, calculating the first m-order single-order hierarchical damage index:
pi,j＝1-|σn+1-i,j-δωj|；
(2) and (3) obtaining an integral layered damage index by multiplying the first m-order single-order layered damage indexes:
as a further preferable scheme of the present invention, the acquisition mode of the natural frequency and the vibration mode of the composite laminated beam in the first and second steps is specifically:
and (3) applying sinusoidal excitation to the position, close to the fixed end, of the composite laminated beam by using a vibration exciter, and measuring the vibration of the front side of the composite laminated beam by using a laser scanning vibration meter to obtain the natural frequency and the vibration mode of the composite laminated beam.
As a further preferable scheme of the invention, the laser scanning vibration meter is a PSV-400 laser scanning vibration meter.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
the detection method provided by the invention can judge the position of the layered damage by analyzing the natural frequency before and after the layered damage of the composite laminated beam and the vibration mode after the layered damage. Compared with the conventional local nondestructive detection method, the method does not need to predict the position of the layered damage and is simple to operate. Meanwhile, the invention can be used in cooperation with advanced sensors such as a laser scanning vibration meter and the like, and is efficiently applied to the layered damage detection of the composite laminated beam structure.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention.
Fig. 2 is a graph showing the natural frequencies before and after the first 10-step delamination damage of the beam according to the present invention.
Fig. 3 is a schematic view of the mode shape of the beam of the present invention after damage to the 1 st order layer.
Fig. 4 is a graph showing normalized natural frequency versus rate of change of the beam in the present invention.
Fig. 5 is a graph showing the square of the first derivative of mode shape for the 1 st order normalization of the beam of the present invention.
FIG. 6 is a schematic diagram of an overall delamination damage index for a beam according to the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
it will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.
As shown in fig. 1, the method for detecting the position of the layered damage of the composite laminated beam provided by the invention comprises the following steps:
1. measuring inherent frequency omega before and after m (m is more than or equal to 5) order delamination damage of composite laminated beamj、
The relative rate of change of the natural frequency is calculated and is taken as [01]]Interval standardization:
wherein j is in the order of frequency, delta omegajRepresenting the relative rate of change of the natural frequency of the j-th order, δ ωjRepresenting the relative rate of change of the natural frequency for the j-th order normalization.
2. Measuring vibration mode phi after m (m is more than or equal to 5) order layered damage in front of composite laminated beami,jThe square of the first derivative of the mode shape is calculated and taken as [01]]Interval standardization:
wherein i belongs to {1, 2., n } is the vibration mode measuring point, and h is the measuring point distance.
3. Calculating the first m-order single-order hierarchical damage index according to the relative change rate of the standardized natural frequency and the square of the first derivative of the vibration mode, and multiplying the first m-order single-order hierarchical damage index to obtain the whole hierarchical damage index:
pi,j＝1-|σn+1-i,j-δωj|, (5)
4. and determining the position of the layered damage according to the position of the maximum value of the overall layered damage index.
The working principle of the invention is as follows: the natural frequency of the composite laminated beam is changed due to the delamination damage of the composite laminated beam, and the change of the natural frequency is related to the position of the delamination damage, so that the delamination damage can be identified through the change of the natural frequency. However, the natural frequency is difficult to provide the position information of the delamination damage as a global dynamic parameter, and the mode shape can effectively provide the position information of the vibration of the composite laminated beam. Based on the method, the natural frequency and the vibration mode are combined to form a layered damage index, whether the layered damage of the composite laminated beam exists or not is judged according to whether a singular peak value appears in the layered damage index, and the layered damage position is determined according to the peak value position.
The detection method of the present invention is illustrated below by way of a specific example:
the GFRP composite laminate beam used in the examples had a length of 490mm, a width of 10mm, a thickness of 1.5mm, and a preformed delamination damage at a distance of 184mm from the fixed end of the beam, the position of which is expressed in dimensionless coordinates as ζ 0.376.
Firstly, a mode vibration exciter is used for applying sinusoidal excitation at a position 5mm away from a fixed end on the back of the beam, meanwhile, a laser scanning vibration meter is used for measuring the vibration on the front of the beam, and the natural frequency before and after 10-step damage of the beam and the vibration mode after the damage are extracted. The natural frequency before 10-step damage in the front of the beam is shown in fig. 2 (a), and the natural frequency after damage is shown in fig. 2 (b), where the horizontal axis m represents the order and the vertical axis f represents the natural frequency. The mode shape of the beam after 1 st order damage is shown in fig. 3, where the horizontal axis ζ represents a dimensionless coordinate and the vertical axis Φ represents the mode shape.
Next, the relative rate of change of the normalized natural frequency of the first 10 th order is obtained from the equations (1) and (2), and as shown in fig. 4, the horizontal axis m represents the order and the vertical axis δ ω represents the relative rate of change of the normalized natural frequency.
Then, the square of the first normalized mode shape first derivative of the first 10 th order is obtained according to the equations (3) and (4), and the square of the first normalized mode shape first derivative of the 1 st order is shown in fig. 5, wherein the horizontal axis ζ represents a dimensionless coordinate and the vertical axis σ represents the square of the normalized mode shape first derivative.
Next, the overall delamination damage index is obtained from the formulas (5) and (6), as shown in fig. 6. From fig. 6, two singular peaks with symmetrical positions can be found, wherein the position corresponding to the maximum peak is the detected position of the layered damage, and coincides with the actual position of the layered damage.
In this embodiment: the laser sensor was a PSV-400 laser scanning vibrometer manufactured by Polytec, Germany.
In conclusion, compared with the conventional local nondestructive detection method, the method does not need to predict the layering damage position, is simple to operate, and can quickly and accurately judge the layering damage and detect the layering damage position.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.
Claims (4)
1. A method for detecting the position of layered damage of a composite laminated beam is characterized by comprising the following specific steps:
measuring inherent frequencies before and after m-order layered damage of a composite laminated beam, calculating the relative change rate of the inherent frequencies, and standardizing the relative change rate, wherein m is more than or equal to 5;
measuring the vibration mode of the composite material laminated beam after m-order layered damage, calculating the square of the first derivative of the vibration mode, and standardizing the square;
calculating the first m-order single-order hierarchical damage index according to the relative change rate of the standardized natural frequency and the square of the first derivative of the vibration mode, and multiplying the first m-order single-order hierarchical damage index to obtain an integral hierarchical damage index;
determining the position of the layering damage according to the position of the maximum value of the overall layering damage index;
the specific calculation mode of the first step is as follows:
(1) measuring natural frequency omega before and after m-order layered damage of composite laminated beamj、
(2) Calculating the relative change rate of the natural frequency:
wherein j belongs to {1, 2.,. m } is a frequency order;
(3) normalizing the relative change rate of the natural frequency in a [01] interval:
wherein, δ ωjRepresents the relative rate of change of the natural frequency normalized by the j-th order;
the specific calculation mode of the second step is as follows:
(1) measuring vibration mode phi after m-order layered damage before composite laminated beami,j；
(2) Calculating the square of the first derivative of the mode shape:
wherein i belongs to {1,2,. and n } is a vibration mode measuring point, and h is a measuring point distance;
(3) normalizing the square of the first derivative of the mode shape by [01 ]:
wherein σi,jA normalization result representing the square of the first derivative of the mode shape;
the specific calculation mode of the third step is as follows:
(1) according to the relative change rate of the normalized natural frequency and the square of the first derivative of the vibration mode, calculating the first m-order single-order hierarchical damage index:
pi,j＝1-|σn+1-i,j-δωj|；
(2) and (3) obtaining an integral layered damage index by multiplying the first m-order single-order layered damage indexes:
2. the method for detecting the position of the layered damage of the composite laminated beam according to claim 1, wherein the acquisition modes of the natural frequency and the vibration mode of the composite laminated beam in the first step and the second step are specifically as follows:
and (3) applying sinusoidal excitation to the position, close to the fixed end, of the composite laminated beam by using a vibration exciter, and measuring the vibration of the front side of the composite laminated beam by using a laser scanning vibration meter to obtain the natural frequency and the vibration mode of the composite laminated beam.
3. The method for detecting the layered damage position of the composite laminated beam according to claim 2, wherein the laser scanning vibration meter is a PSV-400 laser scanning vibration meter.
4. The method for detecting the position of the delamination damage of the composite laminated beam according to any one of claims 1 to 3, wherein the value of m is 10.
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| CN109946057B (en) * | 2019-03-28 | 2020-09-01 | 湖南科技大学 | Wind turbine blade damage diagnosis method based on natural frequency |
| CN110427652B (en) * | 2019-07-08 | 2022-08-19 | 河海大学 | Beam type structure damage initial positioning method based on frequency characteristic curve |
| CN110411387B (en) * | 2019-07-31 | 2021-06-22 | 河海大学 | Frequency-based beam type structure additional mass preliminary positioning method |
| CN110988119A (en) * | 2019-10-31 | 2020-04-10 | 河海大学 | Method for detecting layered damage of composite laminated plate by measuring equivalent pseudo load through laser |
| CN111707731A (en) * | 2020-06-28 | 2020-09-25 | 河海大学 | Pile body crack detection method for measuring axial equivalent pseudo load by three-dimensional laser scanning |
| CN113720907B (en) * | 2021-08-02 | 2022-08-12 | 北京航空航天大学 | Composite material layered damage identification method for contour and depth sequence identification |
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