Postbuckling of viscoelastic micro/nanobeams embedded in visco-Pasternak foundations based on the modified couple stress theory

This paper investigates the postbuckling analysis of a viscoelastic microbeam embedded in a double layer viscoelastic foundation. This viscoelastic microbeam is modeled using the Kelvin–Voigt model and the modified couple stress theory. A material length scale parameter is utilized to describe the size-dependent behavior of the viscoelastic microbeam. The visco-Pasternak foundation used in this study contains a viscoelastic medium and a shear layer. This microbeam is subjected to an axial compressive load at the beam ends which can change as a function of time. According to the Euler–Bernoulli beam theory and von-Karman nonlinearity, the time-dependent equations of motion are derived by Hamilton’s principle. The nonlinear equations of motion are directly solved under the simply supported boundary condition. Both time-dependent deflection and viscoelastic buckling load are investigated. Finally, the influences of the material length scale parameter, parameters of the visco-Pasternak foundation and the material viscosity coefficient on the dynamic postbuckling response are studied.