Fundamental size dependent natural frequencies of non-uniform orthotropic nano scaled plates using nonlocal variational principle and finite element method

摘要: Abstract In the present study, a nonlocal continuum model based on Eringen’s theory is developed for vibration analysis of orthotropic nano-plates with arbitrary variation in thickness. Variational principle and Ritz functions are employed to calculate size dependent natural frequencies non-uniform basis classical plate (NCLPT). The eliminate need mesh generation thus large degrees freedom arising discretization methods such as finite element (FE). Effect thickness examined different parameters, mode numbers, geometries boundary conditions. It found that accompanying small scale effect has noticeable plates at nano scale. Also comparison solution performed show ability fast converging exact results. anticipated presented results can be used helpful source design frequency optimization scaled plates.