Superharmonic resonance analysis of the sandwich FGM beams with viscoelastic core layer

Abstract

Nonlinear forced vibration analysisof a sandwich beam is investigated using the higher-order shear deformation theories (HSDT's). The sandwich beam is consists of viscoelastic core insert between two Functionally Graded Material layers. Viscoelastic properties are considered according to the Kelvin-Voigt viscoelastic model for isotropic materials. In the analysis, both normal and shear deformations are considered in the core by using the higher-order zig-zag theories. The method of multiple scales is coupled with a one mode Galerkin's procedure for a simply supported beam to achieve analytical frequency amplitude relationships for superharmonic resonance. Parametric study is conducted by considering various geometrical and material parameters, employing HSDT's and first-order deformation theory. The results reveal the effect of the slenderness of the sandwich beams on the hardening changes. In the other hand the results demonstrate the importance of the generic parameter "n"to reduce as far as possible the amplitude responses of the sandwich structures in superharmonic vibration case.