Geometrically nonlinear vibro-acoustic analysis of viscoelastic laminated composite and sandwich plates in time domain

Abstract

The geometrically nonlinear steady-state vibro-acoustic analysis of viscoelastic laminated composite/sandwich plates subjected to uniformly distributed transverse harmonic force is carried out in the time domain. Firstly, the incremental algebraic form of viscoelastic constitutive relation in terms of stress/moment resultants is derived from the Boltzmann integral based on generalized Maxwell viscoelastic model and 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 nonlinear equation of motion is obtained using the von-Karman’s geometric nonlinearity and the principle of virtual work. The time domain periodic response is obtained using shooting technique coupled with Newmark’s time integration and arc length continuation method. Finally, the acoustic pressure is evaluated using the time domain Rayleigh integral and elementary radiator approach considering plate vibrations in an infinite baffled plane. The significance of the “zig-zag” function on linear frequencies and nonlinear vibration response is shown through numerical studies. A detailed parametric study is carried out to investigate the effect of boundary conditions, lamination scheme, number of layers, aspect ratio, thickness ratio and core-to-face thickness ratio on the nonlinear vibro-acoustic response of sandwich plates. The influence of these parameters on the A-weighted sound pressure level (dBA) has also been investigated. It is seen that these parameters have significant effects on the vibro-acoustic response of the viscoelastic composite laminated/sandwich plates. The effect of bending-stretching coupling on the nonlinear response of cross-ply antisymmetric plates (evident from the participation of even harmonics) becomes insignificant for square plates with identical boundary conditions on all the edges and rectangular plates with nonidentical boundary conditions.