压电-压磁板中的波动瞬态响应及其应用研究

Because the electric - magnetic - elastic materials have significant application value in dynamic measurement, nondestructive testing, artificial intelligence and other high-tech industries, it is very important to research the dynamic characteristics of the material and the method of the reverse material constant. The wave equations of the magnetic-electro-elastic plate is first solved by the reduced-basis method combining with Fourier transform method,and the transient response of waves are obtained. the key problems to deal with are the various working conditions coupling, singular integral, electrode and poles loads and solution efficiency, etc. An experiment equipment is designed to evaluate the correctness of the forward solving method, the measure method of electric potential and magnetic potential is the key problem.After the input and output variables are determined and the sensitivity analysis is finished, the transient response of elastic waves is used to inverse piezoelectric and piezomagnetic constants of materials.It is very important for the inverse techniques that the stability and efficiency of the solution method are obtained and the ill-posed problem is removed, and the uncertain parameters influence must be considered. It is the objective to make computational inversion technology suitable for the engineering practice of inversing the piezoelectric and piezomagnetic constants.

由于电-磁-弹材料在动力测量、无损检测、人工智能等高新技术产业中有重要的应用价值，研究这种材料的动力学特性以及反求材料常数非常重要。本项目首先应用减基法结合傅里叶变换方法高效求解压电-压磁板的波动方程，得到波动瞬态响应，重点解决多种工况耦合、奇异积分、电极和磁极激励载荷的处理和求解高效性等问题；设计实验装置验证波动瞬态响应求解方法的正确性，重点解决板在极化方向的电势和磁势的测量问题；然后确定输入输出变量并对其进行敏感度分析；最后基于所开发的正问题求解器利用结构的波动瞬态响应反求压电、压磁常数，重点解决病态问题，获得稳定而高效的求解方法，并考虑参数非确定性影响，使得计算反演技术能够适合工程实际中的压电、压磁常数反求问题。

本项目以压电-压磁功能梯度材料板为研究对象，压电-压磁材料是新型的智能材料，在超声影像器件、传感器、作动器等中有广泛的应用前景，对这种材料的力学性质的研究具有十分重要的意义。对简支和夹支的压电-压磁功能梯度材料板的动力响应对材料参数的敏感度进行了研究，研究发现一些材料参数对板的动力响应特别敏感而一些材料参数对板的动力学响应的敏感度非常小，还发现材料参数对某些频率的激振响应特别敏感而对某些频率的激振响应很不敏感，有些参数对所有频率响应都不敏感。这些结果对振动控制和材料参数反求具有非常重要的意义，振动控制时应该通过调整敏感度大的参数提高振动控制的效果，参数反求时应选用敏感度最高的频率进行激振，以防病态问题的出现，而对于那些对所有频率激振都不敏感的参数，需要解决参数反求中的病态问题。对含不确定材料参数的压电-压磁功能梯度材料板的动力响应的不确定性进行了研究，研究发现弹性参数的不确定性会引起动力响应的不确定性，对于具有同样不确定度的弹性参数，高阶固有频率的不确定度比低阶固有频率的不确定度大；对于同阶固有频率，固有频率的不确定度随着梯度指数的增大而增大；压电参数和压磁参数的不确定性对固有频率的影响非常小可以忽略不计。