Spectral Finite Element for Dynamic Analysis of Piezoelectric Laminated Composite Beams

Abstract

In this paper, a frequency-domain spectral finite element model (SFEM) is developed for dynamic analysis of piezoelectric laminated composite beams. The displacement field of the beam is represented by the first-order shear deformation theory (FSDT). The electric potential for the piezoelectric layer is expressed in two ways: (i) distributed linearly through the thickness and (ii) layerwise through thickness distribution consistent with the FSDT. The governing differential equation of motion for piezoelectric laminated composite beam is obtained using Hamilton’s principle. These time-domain equations are transformed to frequency domain using the Fourier transformation. The spectral element is derived from the exact solution of the frequency domain governing equations of motion. The formulation is validated by comparing the results of the natural frequencies with the published finite element method (FEM) results. The developed element is used to perform dispersion, free vibration analysis, and elastic wave propagation in laminated composite beam fully or partially covered with surface-bonded piezoelectric layer.