Nonlinear free vibration, postbuckling and nonlinear static deflection of piezoelectric fiber-reinforced laminated composite beams

Large static deflection, mechanical and thermal buckling, postbuckling and nonlinear free vibration of laminated composite beams with surface bonded piezoelectric fiber reinforced composite (PFRC) layers under a combined mechanical, thermal and electrical loading are studied in this paper. The temperature rise is considered to be one-dimensional steady state heat conduction in the thickness direction. The governing equations of the piezoelectric fiber reinforced laminated composite beams are derived based on Euler-Bernoulli beam theory and geometric nonlinearity of von Kármán. Rectangular representative volume element (RVE) with rectangular fibers has been considered for piezoelectric fiber reinforced composite. Analytical solution of nonlinear bending and postbuckling analyses has been carried out. A perturbation method is then employed to determine the nonlinear vibration behavior and the nonlinear natural frequencies of the beams with simply supported and clamped boundary conditions. Post-buckling load-deflection and maximum transverse load-deflection relations have been obtained for the beam under consideration. The effects of the temperature rise, beam geometry parameter, and the volume fraction of the piezoelectric fibers on the linear and nonlinear fundamental natural frequencies of the piezoelectric fiber reinforced composites are investigated through a comprehensive parametric study.