A novel electromechanical spectral element method for piezoelectric energy harvester plates

Official URL: http://dx.doi.org/10.1016/j.jsv.2021.116139

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.