The effects of nonlinearities on the vibration of viscoelastic sandwich plates

• For a sandwich plate, the core's transverse shear strain is assumed to be moderate.
• The moderate rotation in the core is taken into account.
• A nonlinear viscoelastic model is used with moderate shear strains.
• 5th-order MMS is directly applied to study the free and forced vibration.
• Effects of system parameters and different nonlinear terms on results are studied.

The nonlinear free and forced bending vibration of sandwich plates with incompressible viscoelastic core is investigated under the effects of different source of nonlinearities. For the core constrained between stiffer layers, the transverse shear strains, as well as the rotations are assumed to be moderate. The linear and quadratic displacement fields are also adopted for the in-plane and out-of-plane displacements of the core, respectively. The assumption of moderate transverse strains requires a nonlinear constitutive equation which is obtained from a single-integral nonlinear viscoelastic model using the assumed order of magnitudes for linear strains and rotations. The 5th-order method of multiple scales is directly applied to solve the equations of motion. The different-order linear partial differential equations that were obtained during the perturbation solution, are solved by the method of eigenfunction expansion and the nonhomogeneous boundary conditions are dealt with by transforming to homogeneous boundaries, or using the extended Green's formula. The effects of different system parameters on the nonlinear estimation of frequencies, damping ratios, and peak response are studied. Also, the importance of different nonlinear terms arisen from different ordering assumptions is assessed and the ranges of system parameters with higher values of error are identified.