Forced vibration analysis of composite beams with piezoelectric layers based on the variable separation method

This paper proposes a new strategy based on the proper generalized decomposition method to solve forced vibration problem for bi-dimensional piezoelectric composite beams. The approach considers classical harmonic space-frequency description of dynamic and redefines it by approximating displacement electric potential fields as sum separated functions x (beam axis coordinate), z (thickness coordinate) ω (load frequency). methodology consists in an iterative algorithm that solves three one-dimensional linear problems at each iteration. result is 2D solution frequency domain with 1D computational complexity. Several numerical tests wide range slenderness ratios are considered order assess validity method. Moreover, study different combinations boundary conditions carried out. results terms modal parameters response analysed compared exact elasticity finite element simulations.