This paper presents a novel spectral element method to predict the electromechanical dynamics of panels having arbitrary geometries and multiple surface-bonded piezo-patches. The boundary value problem is derived following kinematic equations based on first order shear deformation and the generalized Hamilton’s principle. To solve the derived boundary value problem, a spectral element method based on Chebyshev polynomials is developed. The method combines the flexibility of the finite element method and the accuracy of the meshless methods. Thus, it includes three main parts. First, the whole domain is divided into elements, and then the system matrices for each element is derived using spectral Chebyshev approach. Finally, the individual system matrices are assembled to construct the overall/global system matrices of the investigated structure. The spectral Chebyshev approach enables capturing the structural and electromechanical dynamic behaviour of structures having arbitrary geometries (using a cross-section mapping) and boundary conditions. To demonstrate the performance and validate the accuracy of the presented spectral element method, four case studies are investigated. In each case study, the predicted natural frequencies, structural and voltage FRFs are compared to those obtained from a finite element approach.

本文提出了一种新颖的频谱元素方法来预测具有任意几何形状和多个表面粘结压电贴片的面板的机电动力学。基于一阶剪切变形和广义汉密尔顿原理，根据运动学方程推导了边值问题。为了解决导出的边值问题，提出了一种基于切比雪夫多项式的谱元方法。该方法结合了有限元方法的灵活性和无网格方法的准确性。因此，它包括三个主要部分。首先，将整个域划分为元素，然后使用频谱Chebyshev方法导出每个元素的系统矩阵。最后，组装各个系统矩阵以构造所研究结构的整体/全局系统矩阵。频谱切比雪夫方法可以捕获具有任意几何形状（使用横截面贴图）和边界条件的结构的结构和机电动力学行为。为了演示性能并验证所提出的光谱元素方法的准确性，对四个案例研究进行了研究。在每个案例研究中，将预测的固有频率，结构和电压FRF与通过有限元方法获得的固有频率，结构和电压进行比较。