Method for testing the degradation of the properties of a macro-fiber piezoelectric composite

By comparing the voltage output signal and strain response data before and after degradation, the problems of large measurement error and inconsistent clamping in traditional methods are solved, and the accuracy and reliability of performance degradation testing of macrofiber piezoelectric composite materials are realized.

CN116718640BActive Publication Date: 2025-12-09NORTHWESTERN POLYTECHNICAL UNIV
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Patent Information

Application Number
CN202310387722.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-04-12
Publication Date
2025-12-09
Estimated Expiration
2043-04-12

AI Technical Summary

Technical Problem

Traditional methods for measuring the performance degradation of macrofiber piezoelectric composites suffer from problems such as large measurement errors and insufficient accuracy due to inconsistent clamping methods, making it difficult to accurately characterize their performance degradation.

Method used

By acquiring voltage output signals and piezoelectric cantilever beam root strain response data before and after degradation, the performance degradation results are determined through comparative analysis. Sinusoidal test loads and high-voltage signals are used to acquire data, and the designed test fixture is used to maintain clamping consistency.

Benefits of technology

This improves the accuracy of performance degradation testing for macrofiber piezoelectric composite materials, enabling accurate determination of their degradation behavior and physical mechanisms.

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Abstract

The application provides a macro-fiber piezoelectric composite performance degradation test method, comprising the following steps: obtaining initial test data, then performing degradation test on the macro-fiber piezoelectric composite in the piezoelectric beam, obtaining the macro-fiber piezoelectric composite performance data after the degradation test, finally comparing and analyzing the macro-fiber piezoelectric composite performance data before and after the degradation, and determining the macro-fiber piezoelectric composite performance degradation test result. The application compares the voltage output signal and the piezoelectric cantilever beam root strain response data of the macro-fiber piezoelectric composite before and after the degradation, and determines the macro-fiber piezoelectric composite performance degradation test result. Based on the degradation data of the piezoelectric beam, the macro-fiber piezoelectric composite degradation curve can be obtained, the degradation behavior is determined, and the macro-fiber piezoelectric composite degradation behavior is interpreted from the physical mechanism.
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Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of piezoelectric material degradation test, and particularly relates to a performance degradation test method for macro-fiber piezoelectric composite material. BACKGROUND

[0002] Piezoelectric composite material is a new type of material emerging in recent decades. Due to its excellent performance and environmental adaptability, piezoelectric composite material has shown broad application prospects in the fields of vibration and noise control, intelligent sensing, and health monitoring. In the field of aviation structure engineering, piezoelectric composite material has good application prospects in high-performance fighter tail flutter response control, wing or tail flutter suppression, wing leading edge vibration deicing, and structure health monitoring.

[0003] In recent years, the piezoelectric performance degradation phenomenon of piezoelectric composite material under repeated stress field has attracted widespread attention. A large number of experimental research results show that piezoelectric composite material will undergo significant piezoelectric performance degradation due to stress depolarization effect under stress field. The degradation of piezoelectric performance of the material will directly lead to the degradation of the function of piezoelectric composite material, and eventually cause the failure of piezoelectric structure vibration control.

[0004] The traditional measurement method generally measures the peak value of the tip displacement response of a cantilever beam to characterize the actuation ability of macro-fiber piezoelectric composite material. However, due to the four-point bending fatigue test, the piezoelectric beam is generally thick, which leads to small tip displacement of the piezoelectric cantilever beam. External disturbance and noise will cause certain errors to the test results. At the same time, the clamping form of the piezoelectric cantilever beam before and after the degradation test also needs to be kept consistent. The peak value of the sinusoidal response data obtained by measurement will also fluctuate. These will result in that the precision of the performance degradation result of macro-fiber piezoelectric composite material cannot be guaranteed.

[0005] Therefore, a performance degradation test method for macro-fiber piezoelectric composite material is provided. SUMMARY

[0006] The technical problem to be solved by the present application is to provide a performance degradation test method for macro-fiber piezoelectric composite material to solve the problems in the background art.

[0007] To solve the above technical problems, the technical scheme adopted by the present application is as follows: a performance degradation test method for macro-fiber piezoelectric composite material, comprising the following steps:

[0008] The initial test data is acquired, then the macro-fiber piezoelectric composite material in the piezoelectric beam is subjected to a degradation test, and the performance data of the macro-fiber piezoelectric composite material after the degradation test is acquired, specifically the voltage output signal and the strain response data of the piezoelectric cantilever beam root of the macro-fiber piezoelectric composite material after the degradation test are acquired, finally the performance data of the macro-fiber piezoelectric composite material before and after the degradation is compared and analyzed to determine the performance degradation test result of the macro-fiber piezoelectric composite material.

[0009] Further, the initial test data is acquired, that is, the voltage output signal and the strain response data of the piezoelectric cantilever beam root of the macro-fiber piezoelectric composite material in the non-degradation state are acquired;

[0010] The process of acquiring the voltage output signal and the strain response data of the piezoelectric cantilever beam root of the macro-fiber piezoelectric composite material includes the following steps:

[0011] First, a sinusoidal test load is applied to the piezoelectric beam, and then the voltage signal data output by the macro-fiber piezoelectric composite material on the piezoelectric beam is collected;

[0012] Then, the piezoelectric beam is clamped into a cantilever beam form to form a piezoelectric cantilever beam based on the designed test fixture, a high-voltage test signal is input to the piezoelectric cantilever beam, and the strain response data of the piezoelectric cantilever beam root is collected.

[0013] Further, the process of degrading the macro-fiber piezoelectric composite material on the piezoelectric beam is specifically to apply a single load or a comprehensive load to the macro-fiber piezoelectric composite material on the piezoelectric beam to cause the performance of the macro-fiber piezoelectric composite material to degrade.

[0014] Further, the comprehensive load includes at least two different kinds of single loads, and the single load is a preset number of force load, voltage or a preset time of temperature load.

[0015] Further, the process of acquiring the voltage output signal and the strain response data of the piezoelectric cantilever beam root of the macro-fiber piezoelectric composite material after the degradation test includes the following steps:

[0016] First, a sinusoidal test load is applied to the piezoelectric beam after the degradation test;

[0017] The voltage output signal data of the macro-fiber piezoelectric composite material on the piezoelectric beam after the degradation test is collected;

[0018] The piezoelectric beam after the degradation test is clamped into a cantilever beam form to form a piezoelectric cantilever beam based on the designed test fixture;

[0019] A high-voltage test signal is input to the macro-fiber piezoelectric composite material after the degradation test, and the strain response data of the piezoelectric cantilever beam root after the degradation test is collected.

[0020] Further, the process of acquiring the voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever includes the following steps:

[0021] A sinusoidal test load is applied to the piezoelectric beam to generate stress on the macro-fiber piezoelectric composite material on the piezoelectric beam;

[0022] The voltage signal data generated by the macro-fiber piezoelectric composite material on the piezoelectric beam is collected;

[0023] The piezoelectric beam is clamped by a test fixture to form a piezoelectric cantilever in the form of a cantilever beam;

[0024] A sinusoidal sweep high-voltage signal is applied to the piezoelectric cantilever, and the sinusoidal sweep high-voltage signal and the strain response data of the root of the piezoelectric cantilever are collected. The collected sinusoidal sweep high-voltage signal and the strain response data of the root of the piezoelectric cantilever are processed to obtain the first order natural frequency of the piezoelectric cantilever as the excitation frequency for subsequent tests;

[0025] A sinusoidal high-voltage test signal at the first order natural frequency is applied to the piezoelectric cantilever, and the strain response data of the root of the piezoelectric cantilever is collected.

[0026] Further, the voltage output signal data of the macro-fiber piezoelectric composite material is used to characterize the sensing performance of the macro-fiber piezoelectric composite material, and the strain response data of the root of the piezoelectric cantilever is used to characterize the actuation performance of the macro-fiber piezoelectric composite material.

[0027] Further, the performance data of the macro-fiber piezoelectric composite material before and after degradation is compared and analyzed according to the voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever collected before and after the degradation to determine the performance degradation result of the macro-fiber piezoelectric composite material;

[0028] The step of determining the performance degradation result of the macro-fiber piezoelectric composite material according to the voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever collected before and after the degradation includes:

[0029] The voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever collected before and after the degradation are compared to determine the difference between the voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever before and after the degradation;

[0030] The difference between the voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever before and after the degradation is determined to determine the performance degradation test result of the macro-fiber piezoelectric composite material.

[0031] Compared with the prior art, the present application has the following advantages:

[0032] The application determines the degradation test result of the macro-fiber piezoelectric composite material performance by comparing the voltage output signal and the piezoelectric cantilever beam root strain response data of the macro-fiber piezoelectric composite material before and after degradation. Based on the degradation data of the piezoelectric beam, the degradation curve of the macro-fiber piezoelectric composite material can be obtained, and the degradation behavior is determined, so as to interpret the degradation behavior of the macro-fiber piezoelectric composite material from the physical mechanism. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 is a step flow chart of the application;

[0034] Figure 2 is a schematic diagram of the placement of the piezoelectric beam when a sinusoidal test load is applied or a degradation test is performed in the experimental example of the application

[0035] Figure 3 is a test fixture suitable for the piezoelectric cantilever beam in the experimental example of the application

[0036] Figure 4 is a clamping schematic diagram of the piezoelectric cantilever beam in the application.

[0037] BRIEF DESCRIPTION OF DRAWINGS:

[0038] 1 - strain gauge; 2 - macro-fiber piezoelectric composite material; 3 - piezoelectric beam; 101 - test fixture hollow part; 102 - test fixture clamping part. EMBODIMENT

[0039] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only a part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the application.

[0040] As shown in the embodiment, the application provides a technical solution: a performance degradation test method of a macro-fiber piezoelectric composite material, comprising the following steps: Figure 1

[0041] First, the initial test data is obtained, and the initial test data is the voltage output signal and the piezoelectric cantilever beam root strain response data of the macro-fiber piezoelectric composite material in the undegraded state;

[0042] The process of obtaining the voltage output signal and the piezoelectric cantilever beam root strain response data of the macro-fiber piezoelectric composite material comprises the following steps:

[0043] First, a sinusoidal test load is applied to the piezoelectric beam, and then the voltage signal data output by the macro-fiber piezoelectric composite material on the piezoelectric beam is collected; ​

[0044] The piezoelectric beam is clamped into a cantilever beam form by a designed test fixture to form a piezoelectric cantilever beam, a high-voltage test signal is input to the piezoelectric cantilever beam, and piezoelectric cantilever beam root strain response data is collected.

[0045] The macro-fiber piezoelectric composite material in the piezoelectric beam is subjected to a degradation test, and the process of the degradation test on the macro-fiber piezoelectric composite material on the piezoelectric beam is specifically to apply a single load or a comprehensive load to the macro-fiber piezoelectric composite material, so that the performance of the macro-fiber piezoelectric composite material is degraded.

[0046] The comprehensive load includes at least two different kinds of single loads, and the single load is a preset number of force load, voltage or preset time temperature load.

[0047] The performance data of the macro-fiber piezoelectric composite material after the degradation test is obtained, specifically the voltage output signal of the macro-fiber piezoelectric composite material after the degradation test and the piezoelectric cantilever beam root strain response data are obtained, and the voltage output signal of the macro-fiber piezoelectric composite material after the degradation test and the piezoelectric cantilever beam root strain response data are obtained, including the following steps:

[0048] First, a sinusoidal test load is applied to the piezoelectric beam after the degradation test;

[0049] The voltage output signal data of the macro-fiber piezoelectric composite material on the piezoelectric beam after the degradation test is collected;

[0050] The piezoelectric beam after the degradation test is clamped into a cantilever beam form by a designed test fixture to form a piezoelectric cantilever beam;

[0051] A high-voltage test signal is input to the macro-fiber piezoelectric composite material after the degradation test, and piezoelectric cantilever beam root strain response data of the piezoelectric cantilever beam after the degradation test is collected.

[0052] The process of obtaining the voltage output signal of the macro-fiber piezoelectric composite material and the piezoelectric cantilever beam root strain response data includes the following steps:

[0053] A sinusoidal test load is applied to the piezoelectric beam, so that stress is generated on the macro-fiber piezoelectric composite material on the piezoelectric beam;

[0054] The voltage signal data generated by the macro-fiber piezoelectric composite material on the piezoelectric beam is collected;

[0055] The piezoelectric beam is clamped into a cantilever beam form by a test fixture to form a piezoelectric cantilever beam;

[0056] A sinusoidal sweep high voltage signal is applied to the piezoelectric cantilever beam, and sinusoidal sweep high voltage signal and piezoelectric cantilever beam root strain response data are collected, and the collected sinusoidal sweep high voltage signal and piezoelectric cantilever beam root strain response data are processed to obtain the first order natural frequency of the piezoelectric cantilever beam as the excitation frequency of the subsequent test.

[0057] A sinusoidal high voltage test signal at the first order natural frequency is applied to the piezoelectric cantilever beam, and the piezoelectric cantilever beam root strain response data are collected.

[0058] The macro-fiber piezoelectric composite voltage output signal data are obtained for characterizing the sensing performance of the macro-fiber piezoelectric composite, and the piezoelectric cantilever beam root strain response data are used to characterize the actuation performance of the macro-fiber piezoelectric composite.

[0059] Finally, the performance data of the macro-fiber piezoelectric composite before and after degradation are compared and analyzed to determine the performance degradation test results of the macro-fiber piezoelectric composite.

[0060] Specifically, the performance data of the macro-fiber piezoelectric composite before and after degradation are compared and analyzed to determine the performance degradation results of the macro-fiber piezoelectric composite according to the collected macro-fiber piezoelectric composite voltage output signal and piezoelectric cantilever beam root strain response data before and after degradation;

[0061] The step of determining the performance degradation results of the macro-fiber piezoelectric composite according to the collected macro-fiber piezoelectric composite voltage output signal and piezoelectric cantilever beam root strain response data before and after degradation includes:

[0062] The collected macro-fiber piezoelectric composite voltage output signal and piezoelectric cantilever beam root strain response data before and after degradation are compared to determine the difference between the macro-fiber piezoelectric composite voltage output signal and piezoelectric cantilever beam root strain response data before and after degradation;

[0063] The difference between the macro-fiber piezoelectric composite voltage output signal and piezoelectric cantilever beam root strain response data before and after degradation is used to determine the performance degradation test results of the macro-fiber piezoelectric composite.

[0064] In the experimental example, M5628-P1 macro-fiber piezoelectric composite is used to paste the center of a steel beam with material 65Mn by vacuum bag method, the macro-fiber piezoelectric composite is 67mm long, 35mm wide and 0.3mm thick, and the steel beam is 400mm long, 35mm wide and 5mm thick.

[0065] First, the sensing performance and actuation performance of the macro-fiber piezoelectric composite in the undegraded state are obtained, i.e. the macro-fiber piezoelectric composite voltage output signal and piezoelectric cantilever beam root strain response data.

[0066] The designed piezoelectric beam isFigure 2 The components are placed on a fatigue testing machine in the form of: 1-strain gauge; 2-macrofiber piezoelectric composite material; 3-piezoelectric beam; R=5mm. A sinusoidal test load is applied to the piezoelectric beam to generate stress on the macrofiber piezoelectric composite material on the piezoelectric beam, and the voltage signal data generated by the macrofiber piezoelectric composite material on the piezoelectric beam are collected.

[0067] Using piezoelectric beams Figure 3 The test fixture is used for clamping Figure 4 The piezoelectric cantilever beam shown is of the form in which Figure 3 This is a top view of the test fixture. The hollow part 101 of the test fixture is used to fix the position of the piezoelectric cantilever beam, and the clamping part 102 of the test fixture is used to clamp the piezoelectric cantilever beam. The test fixture can ensure consistent clamping each time. A sinusoidal sweep frequency high voltage signal is applied to the piezoelectric cantilever beam, and the sinusoidal sweep frequency high voltage signal and the strain response data at the root of the piezoelectric cantilever beam are collected. The collected sinusoidal sweep frequency high voltage signal and the strain response data at the root of the piezoelectric cantilever beam are processed to obtain its frequency response function, and the first natural frequency of the piezoelectric cantilever beam is determined as the excitation frequency for subsequent tests. A sinusoidal high voltage test signal with the first natural frequency is applied to the macrofiber piezoelectric composite material to drive the piezoelectric cantilever beam to vibrate, and the strain response data at the root of the piezoelectric cantilever beam is collected.

[0068] Traditional methods characterize the actuation performance by measuring the tip displacement response of a piezoelectric cantilever beam. According to mechanics of materials, the first mode shape of the cantilever beam is:

[0069]

[0070] In the formula,

[0071] Furthermore, due to the rectangular cross-section beam

[0072]

[0073] W is the section modulus for bending resistance.

[0074] Since its mode shape remains unchanged, the bending moment at point i is proportional to the tip displacement, and the strain at point i is proportional to the tip displacement. The root strain response can be used to characterize the dynamic performance of macro-fiber piezoelectric composite materials, and the root strain response is large, so external disturbances have little effect on it.

[0075] Degradation tests were conducted on the macrofiber piezoelectric composite material in the piezoelectric beam;

[0076] piezoelectric beam with Figure 2 The composite material is placed on a fatigue testing machine and subjected to a fixed number of four-point bending fatigue tests. The four-point bending ensures that the nominal stress on the macrofiber piezoelectric composite material inside the two upper loading points is equal.

[0077] Step 2: Obtain the performance data of macro-fiber piezoelectric composite after degradation experiment;

[0078] Obtain the sensing performance and actuating performance of macro-fiber piezoelectric composite after degradation, that is, the voltage output signal of macro-fiber piezoelectric composite and the strain response data of the root of piezoelectric cantilever beam.

[0079] Place the designed piezoelectric beam in the form of Figure 2 on the fatigue testing machine, apply a sinusoidal test load to the piezoelectric beam, so that stress is generated on the macro-fiber piezoelectric composite on the piezoelectric beam, and collect the voltage signal data generated by the macro-fiber piezoelectric composite on the piezoelectric beam;

[0080] Clamp the test fixture of the piezoelectric beam Figure 3 into the form of a piezoelectric cantilever beam as shown in Figure 4 , which can ensure consistent clamping each time. Apply a sinusoidal sweep high voltage signal to the piezoelectric cantilever beam, collect the sinusoidal sweep high voltage signal and the strain response data of the root of the piezoelectric cantilever beam, process the collected sinusoidal sweep high voltage signal and the strain response data of the root of the piezoelectric cantilever beam, obtain the frequency response function, and determine the first order natural frequency of the piezoelectric cantilever beam as the excitation frequency for subsequent tests. Apply a sinusoidal high voltage test signal at the first order natural frequency to the macro-fiber piezoelectric composite to drive the piezoelectric cantilever beam to vibrate, and collect the strain response data of the root of the piezoelectric cantilever beam.

[0081] Finally, compare and analyze the performance data of macro-fiber piezoelectric composite before and after degradation;

[0082] According to the voltage output signal of macro-fiber piezoelectric composite and the strain response data of the root of piezoelectric cantilever beam collected before and after degradation, determine the performance degradation result of macro-fiber piezoelectric composite;

[0083] The steps for determining the performance degradation result of macro-fiber piezoelectric composite are as follows:

[0084] According to the voltage output signal of macro-fiber piezoelectric composite and the strain response data of the root of piezoelectric cantilever beam collected before and after degradation, determine the degradation characteristic parameters of macro-fiber piezoelectric composite as the peak values and frequency spectra of the two data. By comparing the peak value differences of the voltage output signal of macro-fiber piezoelectric composite and the strain response data of the root of piezoelectric cantilever beam collected before and after degradation, determine the performance degradation test result of macro-fiber piezoelectric composite.

[0085] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting; it is not intended to exclude myriad other embodiments of the present application that other inventors can develop based on the same general inventive concepts embodied by the described embodiments. That is, although the present application is described in terms of particular embodiments and illustrative figures, it should be apparent that the scope of the present application is not limited to these specific embodiments.

[0086] While the embodiments of the application have been shown and described herein, it is to be understood that the scope of the application, jointly pointed out in the appended claims, is not to be limited to the above-described embodiments but can be otherwise variously changed, modified, replaced, and altered within the principles and spirit of the present application.

Claims

1. A method of testing the degradation of the properties of a macrofiber piezoelectric composite, characterized in that, The method comprises the following steps: First, obtaining initial test data, which is to obtain the voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever beam in the undegraded state; Then, performing a degradation test on the macro-fiber piezoelectric composite material in the piezoelectric beam: placing the piezoelectric beam on a fatigue testing machine, wherein the macro-fiber piezoelectric composite material is placed in the middle of the bottom surface of the piezoelectric beam, and the strain gauge is placed on the bottom surface of the macro-fiber piezoelectric composite material, and then performing a four-point bending fatigue test on it for a fixed number of times to cause the performance of the macro-fiber piezoelectric composite material to degrade; Obtaining the performance data of the macro-fiber piezoelectric composite material after the degradation test, which is to obtain the voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever beam after the degradation test; The process of obtaining the voltage output signal of the macro-fiber piezoelectric composite material and the strain response data of the root of the piezoelectric cantilever beam comprises the following steps: Placing the piezoelectric beam on a fatigue testing machine, first applying a sinusoidal test load to the piezoelectric beam to cause stress on the macro-fiber piezoelectric composite material on the piezoelectric beam, and then collecting the voltage signal data output by the macro-fiber piezoelectric composite material on the piezoelectric beam; Based on the designed test fixture, clamping the piezoelectric beam into a cantilever beam form to form a piezoelectric cantilever beam, inputting a high-voltage test signal to the piezoelectric cantilever beam, collecting the strain response data of the root of the piezoelectric cantilever beam, processing the collected sinusoidal sweep high-voltage signal and the strain response data of the root of the piezoelectric cantilever beam to obtain the frequency response function, determining the first-order natural frequency of the piezoelectric cantilever beam as the excitation frequency for the subsequent test, applying a sinusoidal high-voltage test signal with the first-order natural frequency to the macro-fiber piezoelectric composite material to drive the piezoelectric cantilever beam to vibrate, and collecting the strain response data of the root of the piezoelectric cantilever beam; Finally, comparing and analyzing the performance data of the macro-fiber piezoelectric composite material before and after degradation to determine the performance degradation test result of the macro-fiber piezoelectric composite material.

2. The method of claim 1, wherein the macro-fiber piezoelectric composite is a unidirectional composite. The voltage output signal data of the macro-fiber piezoelectric composite material is used to represent the sensing performance of the macro-fiber piezoelectric composite material, and the strain response data of the root of the piezoelectric cantilever beam is used to represent the actuation performance of the macro-fiber piezoelectric composite material.

3. The method of claim 1, wherein the macro-fiber piezoelectric composite is a unidirectional composite. Comparing and analyzing the performance data of the macro-fiber piezoelectric composite material before and after degradation is to determine the performance degradation result of the macro-fiber piezoelectric composite material according to the voltage output signal and the strain response data of the root of the piezoelectric cantilever beam collected before and after degradation; The step of determining the performance degradation result of the macro-fiber piezoelectric composite material according to the voltage output signal and the strain response data of the root of the piezoelectric cantilever beam collected before and after degradation comprises: Comparing the voltage output signal and the strain response data of the root of the piezoelectric cantilever beam collected before and after degradation to determine the difference between the voltage output signal and the strain response data of the root of the piezoelectric cantilever beam before and after degradation; Determining the performance degradation test result of the macro-fiber piezoelectric composite material according to the difference between the voltage output signal and the strain response data of the root of the piezoelectric cantilever beam before and after degradation.

Citation Information

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