Nonlinear dynamic instability analysis of sandwich beams with integral viscoelastic core using different criteria

This paper deals with the nonlinear dynamic instability analysis of three-layered composite beams with viscoelastic core subjected to combined lateral and axial loadings. The Full-Layerwise theory (FLWT) based on the assumptions of advanced first-order shear deformation theory (AFSDT) is employed to model the sandwich beam. The viscoelastic constitutive equation is considered as the Boltzmann's integral form with the Koltunov-Rzhanitsyn kernel. The obtained nonlinear integro-partial differential equations (IPDEs) of motion are solved by using Galerkin's discretization method in combination with Newton-Raphson algorithm. The dynamic instability is analysed by using the Budiansky-Hutchinson, modified-Budiansky and Volmir criteria in conjunction with the phase-plane analysis of the studied cases. It is observed that, the modified-Budiansky criterion and the phase-plane analysis are more appropriate to investigate the dynamic instability of the beams especially with the viscoelastic cores. In addition, the effects of different rheological parameters (R-Ps) of viscoelastic core on the dynamic instability of sandwich beams are investigated by using modified-Budiansky criterion and the phase-plane analysis.