Free and forced vibration analysis of Kelvin-Voigt viscoelastic rectangular nanoplate based on the modified couple stress theory

In this paper, free and forced vibration of viscoelastic nanoplate on the Pasternak viscoelastic foundation will be studied. In this study, due to the inability of classical theories to describe the behavior of nano-dimensional structures, the non-classical modified couple stress theory has been used for express the size effect. By using the Galerkin semi-analytic method, free vibrations analysis for six different boundary conditions are discussed; also, forced vibration of rectangular viscoelastic nanoplate is studied by using the Navier method for simply supported boundary condition. Kelvin-Voigt model are used to simulate the behavior of viscoelastic nanoplate. In the results analysis section, the effect of small-scale factor, structural viscoelastic coefficient, linear elastic coefficient of foundation, external damping coefficient of foundation and shear coefficient of foundation on the natural frequency, maximum dynamic deflection and resonance phenomenon are presented. The obtained results show that considering length scale parameter leads to increasing the natural frequency of nanoplate and occurring the resonance phenomena in the higher frequencies. On the other hand linear elastic and shear coefficients of foundation result in occurring the resonance in the lower frequencies.