Free vibration of the piezoelectric laminated composite beams under the elastic foundation

Abstract

Abstract Due to its self-adaptability and electric-mechanical interaction, the piezoelectric laminated composite structure has received increased attention in the engineering community, with the intricacy of the actual scenario, the structural stability based on numerous foundations has also been recognized. In this paper, a unified formulation which is based on classical laminated beam is presented to conduct free vibration analysis of piezoelectric laminated beams subjected to classical boundary conditions with the varied elastic foundations. The semi-analytical solutions of layered beams in various boundaries have been obtained based on the two-dimensional piezoelectric elastic theory and state space-differential quadrature method (SS-DQM), the solution of the general structural equation has been generated introducing the electrical boundary conditions and interlayer continuity conditions with this understanding. The different elastic foundations have been used to calculate the frequency equation of the piezoelectric laminated construction. The proposed finite element model is validated through the analysis of the piezoelectric laminated composite beam (PLCB) using the SS-DQM, and the present solutions are compared with those available in the literature to confirm their validity. A systematic parameter study for the piezoelectric laminated beams with various boundary conditions, piezoelectric parameters, lamina numbers and thickness ratios is also performed. The results of the PLCBs with various boundary constraints under the elastic foundation are presented and they may be served as a benchmark for researchers in this field.