Free in-plane vibration of heterogeneous nanoplates using Ritz method

In this paper, the Ritz method has been employed to analyze the free inplane vibration of heterogeneous (nonuniform) rectangular nanoplates corresponding to Eringen’s nonlocal elasticity theory. The nonuniformity is taken into account using combinations of linear and quadratic forms in the thickness, material density and Young’s modulus. Twodimensional boundary characteristic orthogonal polynomials are applied in the Ritz method in order to examine the nonlocal effect, aspect ratio, length of nanoplate and nonuniformity parameters on the vibrational behaviors of the nanoplate. Results are verified with the available published data and good agreements are observed. The outcomes confirm apparent dependency of inplane frequency of nanoplate on the small scale effect, nonuniformity, aspect ratio and boundary conditions. For instance, frequency parameter decreases by increasing the nonlocal parameter in all vibration modes; the frequency parameters increase with length and aspect ratio of nanoplates. Furthermore, the effect of nonlocal parameters on the frequency parameter is more prominent at the higher aspect ratios. Finally, the effect of nonlocal parameter on the inplane modes is also presented in this analysis.