Free damped vibration analysis of Mindlin plates with hybrid material-foundation viscoelasticity

Abstract

Suppressed vibration of shear deformable plates with hybrid viscoelastic damping of material and foundation is investigated. Viscoelasticity of foundation is established by adopting Kelvin-Voigt model while viscoelasticity of materials is expressed by Boltzmann superposition integral, which uses dynamic mechanical analysis (DMA) results in terms of Prony series. Application of Laplace transformation and Mindlin plate theory with Hamilton principle led to a system of coupled integro-PDE of motions. Weighted residual method, numerical iterative algorithm and Fourier transform are implemented to achieve complex frequencies and transient responses of plates. Assessment of accuracy is carried out in the both elastic and viscoelastic domains. In the earlier, the frequencies are compared with counterparts obtained by p-version Ritz method and in the latter, dynamic characteristics of Mindlin and classic plates are examined that represent acceptable correlation. The influences of hybrid material-foundation damping, edge conditions, foundation characteristics and geometrical parameters on dynamic characteristics of plates are studied via a set of parametric study.