Frequency analysis of orthotropic Kelvin-Voigt viscoelastic circular and elliptical nanoplates using boundary characteristic orthogonal polynomials and Rayleigh-Ritz method

The present paper investigates a continuum model based on the nonlocal viscoelasticity theory for the vibration behavior of orthotropic circular and elliptical nanoplates.The Kelvin–Voigt viscoelastic model and nonlocal classical plate theory (CPT) are employed to establish the governing equations and boundary conditions for the transverse vibration of nanoplates. Boundary characteristic orthogonal polynomials and Rayleigh-Ritz method are applied to obtain a quadratic functional. Gram-Schmidt process has been used to generate these orthogonal polynomials. Numerical results have been computed for clamped and simply supported edges. A comparison of the present results with those available in the literature has been made. Effects of nonlocal parameter, lengths of nanoplates, aspect ratio, viscoelastic structural damping, initial uniaxial pre-load and boundary condition on the viscoelastic nanoplates natural frequencies are investigated. The results indicate that the non-dimensional natural frequency becomes equal to zero when the in-plane compressive pre-load reach its critical value. The present work is useful in study of nano-electromechanical systems (NEMS).