Nonlinear damping and forced vibration analysis of sandwich functionally graded material beams with composite viscoelastic core layer

In the present article, an analytical model is proposed to assess the nonlinear damping and frequency curves of the three layered sandwich beams, constituted with FGM faces and viscoelastic core layers. The proposed analytical model is formulated in the context of forced vibration analysis. The kinematical model developed for the purpose is based on the higher order zig-zag theories coupled with the higher order shear deformation theory (HSDT), employing shear functions, formulated by Timoshenko, Reddy, and Touratier. The frequency response curves and the nonlinear loss factors are provided by resourcing to analytical solution, derived from the harmonic balance technique coupled with the one mode of Galerkin's method. The elastic moduli of the viscoelastic material are described with complex numbers in the frequency domain. The material proprieties of the FGM beams vary gradually along the thickness direction, transiting from metal to ceramic materials. The effect of the geometrical and material parameters of the FGM and viscoelastic composite layers on the damping and frequency response curves of the sandwich beams are studied according to the first and higher-order shear deformation theories. Basing on the proposed analytical model, numerical results are presented to study the effect of the FGM parameters and the fiber orientation angle of the composite core on the nonlinear damping evolution with the vibration amplitude and the frequency curves.