摘要：用减基法（RBM）结合有限元法、傅里叶变换和Newmark直接积分法，研究了压电层合板在机电耦合载荷下的瞬态响应。用层单元将层合板沿厚度方向进行离散，得到时间域内的运动方程，通过傅里叶变换得到波数域内的控制方程。应用Newmark直接积分法求解波数域内的位移和电势，并在Newmark法求解过程嵌入减基法，构造减基空间，把结构的等效刚度矩阵、质量矩阵和载荷列向量映射到减基空间降阶，得到减缩的Newmark增量式，从而快速求解得到原结构波数域响应，通过傅里叶逆变换得到时域内的响应。以PZT-5A/0°PVDF铺层两相材料复合压电层合板为算例,分析了机电耦合线载荷激励下,位移场和电势场的瞬态响应情况。计算结果表明，求解过程引入减基法能更快得到结构的瞬态响应，并保证了精度。

Abstract: The combination of reduced-basis method(RBM)、finite element method、Fourier transformation and Newmark direct integral method was introduced for the analysis of transient response of piezoelectric laminates subjected to coupled electro-mechanical loads. The laminates were discretized in the thickness direction by plate elements, and the governing equations were obtained. The governing equations in wavenumber domain were obtained by Fourier transformation. The Newmark direct integral method was employed to calculate the displacement responses and the potential responses in wavenumber domain. The reduced-basis method was introduced during the using of Newmark direct integral method and a reduced basis space was constructed. The equivalent stiffness matrix、mass matrix and load vector were projected into the space. The reduced Newmark formulation was obtained and the responses in wavenumber domain were calculated efficiency. The transient responses were obtained by using the inverse Fourier transformation. The results of the numerical example provide the transient responses excited by the coupled electro-mechanical line load in a PZT-5A/0°PVDF composite plate. The transient responses of piezoelectric laminates can be performed efficiently and accurately by employing the reduced-basis method.