On the transient response of viscoelastic beams and plates on viscoelastic medium

•For the first time, critical damping of viscoelastic foundation is presented.•Boltzmann integral and DMA results are considered to describe viscoelasticity.•Using the Galerkin method and QZ algorithm leads to natural frequency of structures.

In the present study, free vibration of isotropic viscoelastic beams and plates on viscoelastic medium is investigated. The Boltzmann superposition integral model with Dynamic Mechanical Analysis (DMA) results is considered for viscoelastic material of the beam and plate to describe more accurately the behavior of material rather than simple complex constants model. The viscoelastic beam and plate on viscoelastic medium modeling are used in railroad vibration with the damping layer on the lateral surface of the rail and the polymeric flooring on the floor as a viscoelastic medium for the beam and the plate, respectively. Weighted residual method and QZ algorithm are applied to obtain beam and plate natural frequency. In addition, medium properties׳ effects on the natural frequencies of the beam and plate are discussed. For the first time, critical damping of viscoelastic beam is presented due to the greater effect of medium viscosity at all boundary conditions. The unknown coefficients of dynamic response function are calculated by Fourier transform. Closed form expressions are obtained for lateral displacement of the beam and plate with various boundary conditions in terms of complex natural frequency, mode numbers, geometry parameters, initial conditions, material and medium properties. Results show excellent agreement with relative studies.