Forced vibration of a loaded rectangular plate with visco-elastic foundation is treated. Two types of visco-elastic material are con¬sidered, Kelvin-Voigt solid and Boltzmann model. Analytic solutions are given for the plate subject to compression and a periodic trans¬verse pressure. A numerical example is worked out for the case of Kelvin-Voigt solid. Some features revealed by the example arena) With visco-elastic effect, the natural vibration damps out rapidly (Fig. 3-5).nb) There exists a critical damping factor ψc For ψ1<ψc the damping is oscillatory (Fig. 3); otherwise the damping is monotonic (Figs. 4, 5).nc) The closerψ1 is toψc in magnitude, the faster the damping.nd) The time required for damping is almost independent of the frequency of the periodic loading.ne) The greater the viscosity coefficientμF, the smaller the amplitude of vibration.
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