Effect of scaling effect parameters on the vibration characteristics of nanoplates

Abstract

The Rayleigh–Ritz method has been applied to solve governing differential equations of the free vibration of nonhomogeneous rectangular nanoplates. Nonhomogeneity is assumed by taking a variety of combinations of linear as well as quadratic variations in the Young's modulus and the density of the material. Boundary characteristic orthogonal polynomials in two variables are used in the Rayleigh–Ritz method and have been generated with the help of the Gram–Schmidt process. The generalized eigenvalue problem has been solved by employing MATLAB code. Both graphical and tabular results are given to show the effects of nonhomogeneous parameters, the nonlocal parameter, boundary conditions, aspect ratio and the length of the nanoplate on the frequency parameters. Results are compared in special cases and are found to be in good agreement.