12 - Nonlinear vibration and transient analysis of hybrid laminated plates

Abstract

This chapter describes the non-linear free and forced vibration of shear deformable hybrid laminated plates. The material properties are assumed to be temperature-dependent. The formulations, including thermo-piezoelectric effects, are based on Reddy's higher-order shear deformation plate theory and general von Kármán-type equations. An improved perturbation technique is employed to determine the non-linear frequencies and dynamic responses of the hybrid laminated plate. Extensive numerical results are presented showing the effects of varying the load and geometric parameters of the plate on the different response characteristics. The chapter also discusses the non-linear vibration and dynamic response of an unsymmetric cross-ply laminated plate with piezoelectric layers. In order to assess the effects of temperature dependency, temperature field, and control voltage on the vibration characteristics of hybrid laminated plates, a fully non-linear free and forced vibration analysis has been described. The governing equations are based on a higher-order shear deformation plate theory that includes thermo-piezoelectric effects. An improved perturbation technique is employed to determine non-linear frequencies and dynamic responses of hybrid laminated plates. Numerical calculations have been made for (1) fiber-reinforced composite antisymmetric angle-ply and symmetric cross-ply laminated plates; (2) unsymmetric cross-ply laminated plates with surface-bonded or embedded piezoelectric actuators; and (3) FGM plates with fully covered piezoelectric actuators. The results reveal that in these cases, the plate has lower vibration frequencies and larger transient deflections when the temperature-dependent properties are taken into account.