This research proves a novel closed-form solution for the forced vibration analysis of a Mindlin viscoelastic plate subjected to harmonic transversal load and constant in-plane compression, simultaneously.

The excitation frequency of the harmonic transversal load is considered as equal to the natural frequency of the viscoelastic plate. The viscoelastic properties obey the Boltzmann integral law with constant bulk modulus. The displacement field is approximated by the product of a known geometrical function and an unknown time function. The simple hp cloud method is employed for discretization. Calculating the natural and viscous damping frequencies, geometry, mass and stiffness matrices in the Laplace–Carson domain, and introducing the best values to replace the Laplace parameter, the dynamic responses of Mindlin viscoelastic plates are determined.

The transient, steady-state and total dynamic responses of moderately thick viscoelastic plates are explicitly formulated in the time domain based on the elastic bending analysis at time zero, for the first time. In the numerical results, the effects of material properties and loading on the total dynamic responses are investigated.