GMM/弹性板/PZT层状复合结构的纵振磁电响应

利用Hamilton原理推导GMM/弹性板/PZT三层层状复合结构的运动方程，在推导中考虑层间胶层的作用，包括其剪切变形和纵向变形产生的效果；应用运动方程，根据层状复合结构的边界条件，推导复合结构的固有频率方程，并结合压磁和压电方程，得到层状复合结构在不同固有频率处的磁电响应.对比磁电响应的频率特性的理论值和实验值，频率误差在9.42%以内，磁电电压转化系数的理论值与实验值符合，并讨论了弹性板的尺寸变化对层状复合结构谐振频率的影响. 关键词： 层状复合结构 磁电响应 Hamilton原理 运动方程

Magnetoelectric response of GMM/elastic plate/PZT laminated composite in the longitudinal vibration

Strain in a laminated structure is transferred by the interlayer adhesive layer. However, the analysis of the adhesive layer behaviors was rarely carried out. The Hamilton's principle is used to derive the governing motion equation of the GMM/elastic plate/PZT three-layered structure. The effects of the adhesive layer resulting from the shear and longitudinal deformation are considered in the analysis. From the motion equation of the GMM/elastic plate/PZT structure and the structural boundary conditions, the equation predicting the system natural frequencies is derived. Then, using the constitutive equations of magnetostrictive and piezoelectric effects, the magneto-electric response over frequency of underlying structure is obtained. By comparing the theoretical magneto-electric response over frequency with the experimental results，it can be seen that the frequency deviation is below 9.42%，and the values of the theoretical magneto-electric voltage coefficient are in agreement with the experiment ones. The dependence of the resonance frequency of the structure on the length of the elastic plate is also discussed.