Nonlinear periodic vibration analysis of sandwich plates with viscoelastic core using shooting technique

The nonlinear periodic response analysis of sandwich composite plates with viscoelastic core subjected to transverse harmonic excitation is carried out in time domain considering geometric nonlinearity and generalized Maxwell viscoelastic model expressed in the form of Boltzmann integral. The integral form of the constitutive relation is converted to an incremental algebraic form for finite element-based solution using the first-order shear deformation theory incorporating "zig-zag" function to account for the slope discontinuity of in-plane displacements at the layer interfaces. The difficulty of retaining solution history is eliminated through recursive relation. The periodic response is obtained using shooting technique coupled with Newmark's time integration and arc length continuation method. The nonlinear periodic vibration characteristics, such as frequency response, damping factor, steady-state response history, phase plane plots, and frequency spectra, are presented for sandwich plates with different core-to-face thickness ratios, boundary conditions, areal density and lamination schemes. Further, the influence of viscoelasticity of laminated face sheets on frequency response characteristics is also investigated. It is seen that the shooting technique is capable of predicting periodic responses of viscoelastic dynamical systems directly from the second-order equations of motion and is more efficient than the direct time integration method. The effect of core-to-face thickness ratio on nonlinear response and damping characteristics of the sandwich plates is significant depending on the change in areal density.