Free in-plane vibration of heterogeneous nanoplates using Ritz method

In this paper, the Ritz method has been employed to analyze the free inplanevibration of heterogeneous (non-uniform) rectangular nanoplatescorresponding to Eringen’s nonlocal elasticity theory. The non-uniformity is taken into account using combinations of linear and quadratic forms in thethickness, material density and Young’s modulus. Two-dimensional boundary characteristic orthogonal polynomials are applied in the Ritzmethod in order to examine the nonlocal effect, aspect ratio, length of nanoplate and non-uniformity parameters on the vibrational behaviors of thenanoplate. Results are verified with the available published data and goodagreements are observed. The outcomes confirm apparent dependency of inplane frequency of nanoplate on the small scale effect, non-uniformity, aspect ratio and boundary conditions. For instance, frequency parameterdecreases 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 in-plane modes is also presented in this analysis

Keywords:

In-plane vibration , , Rectangular , heterogeneous , nanoplate , Nonlocal elasticity , , theory , Ritz method