Free vibration analysis of thick viscoelastic composite plates on visco-Pasternak foundation using higher-order theory

Free vibration of laminated viscoelastic composite plates on Pasternak viscoelastic medium with simply supported edge conditions is investigated. The composite plate consists of linear viscoelastic polymeric matrix reinforced by transversely isotropic elastic fibers. Multi-cell micromechanical approach together with relaxation functions of bulk/shear moduli and Boltzmann superposition principle are adopted to establish time-dependent stiffness coefficients of laminates. The coupled integro-PDEs of motions are derived based on third-order shear deformation theory by Laplace transformation and Hamilton principle. Complex frequencies and closed form solutions for transient response are achieved by weighted residual method, iterative numerical algorithm and Fourier transform. To verify, the results are compared for thick elastic composite plates on Pasternak elastic foundation and thick viscoelastic composite sandwich plates without foundation that represent acceptable accuracy. By parametric study, effects of materials, lamination scheme, geometry and medium on dynamic characteristics are scrutinized.