Nonlinear finite element model for the dynamic analysis of sandwich beams with a frequency-dependent viscoelastic core layer considering normal transverse stresses

Abstract

In this work the nonlinear forced vibration problem of sandwich beams is approached with the Finite element modelling method. In the analytical formulation, in addition to axial normal and shear stresses, the normal transverse stress was also considered. The refined higher-order zig-zag theory is employed in the kinematic model to assess the non-linear vibration of sandwich beams, whose core's elastic modulus and loss factor vary with frequency. Applying the Hamilton's principle has resulted in the governing equations of motion. The finite element method and the arc-length method are used to solve a system of nonlinear equations, resulting in the nonlinear frequency response. The results indicate that the sandwich structures exhibit different nonlinear hardening behavior by changing the viscoelastic layer's geometric and material characteristics. The impact of boundary conditions on the frequency-response curves and the contribution of transverse normal stress are considered in the parametric investigation.