基于压电振动能量俘获的弯曲结构损伤监测研究

建立了含裂纹损伤的曲梁压电能量俘获系统在强迫振动下的动力学模型. 基于Prescott型压电曲梁力电耦合振动方程的解析解和裂纹截面处的连续性条件, 求解了含裂纹损伤的压电曲梁的格林函数. 根据线性叠加原理, 对含裂纹的力电耦合模型的系统方程解耦, 得到强迫振动下含裂纹损伤的曲梁压电俘能器的输出电压. 在得到模型的强迫振动解析解后, 提出逆方法检测结构中的裂纹损伤, 这一检测方法适用于处于振动状态下的结构. 在数值计算中, 令裂纹深度为零, 通过对比本文的解析解与现有文献中的解析解, 验证了本文解的有效性. 分别分析了含裂纹损伤的压电曲梁的电压响应与裂纹深度、裂纹位置、材料的几何参数以及阻尼之间的关系. 研究结果表明: 裂纹的存在对曲梁式压电俘能器的影响比直梁式更加复杂; 裂纹出现时, 损伤曲梁在健康曲梁的一阶频率值处一定会出现波动并被激励出二阶频率, 此时的二阶频率是开路中健康压电曲梁的一阶频率值; 通过对电压响应的检测可以确定的损伤裂纹的深度和在结构中出现的位置范围; 利用振动问题的解来检测压电曲梁的健康状况是可行且准确的. 

THE RESEARCH ON DAMAGE DETECTION OF CURVED BEAM BASED ON PIEZOELECTRIC VIBRATION ENERGY HARVESTER

This paper established dynamic model of forced vibration of the curved piezoelectric energy harvesters with cracks. The Green’s function of piezoelectric curved beam with cracks is obtained based on analytical solutions of vibration equation of the electromechanical coupled Prescott models and continuity conditions at crack sections. The system equation of the electromechanical coupled model with cracks is decoupled and the output voltage of the forced vibration of the damaged curved piezoelectric energy harvester under forced vibration is acquired by the linear superposition principle. The damaged conditions of the piezoelectric curved beam can be detected by inverse method, which is proposed in this paper and suitable for the structure in vibration．In the numerical simulations, the analytical solutions of damaged piezoelectric curved beam that have zero crack depth are compared with results in the previous references. The validity of solutions in this paper is verified. The influence of the crack depth, crack location, material geometric parameters and damping on frequency responses of the voltage is investigated separately. The results show that the effect of cracks on the curved piezoelectric energy harvester is more complicated than that of the straight beam model. The voltage response of damaged piezoelectric curved beam is proportionally decrease at the first order frequency that is the first order frequency of heathy curved beam. And the damaged piezoelectric curved beam is excited out the second-order frequency, which is the first order frequency value of healthy piezoelectric curved beam in an short-circuit. The depth of cracks and the range of cracked positions in the piezoelectric curved beam can be determined by monitoring the change of voltage response, which verifies the feasibility of the inverse method. It is feasible and accurate to use the solution of vibration problem to detect the health condition of damaged piezoelectric curved beams.