Asymmetric Vibrations of Functionally Graded Annular Nanoplates under Thermal Environment Using Nonlocal Elasticity Theory with Modified Nonlocal Boundary Conditions

Abstract

Analysis and numerical results are presented for the free asymmetric vibrations of functionally graded (FG) annular nanoplates subjected to nonlinearly varying temperature. The mechanical properties of the plate material were assumed to be temperature-dependent and to vary according to the power-law model in the thickness direction. Because the material is asymmetric in the thickness direction of the nanoplate, the physical neutral plane was obtained and incorporated in the analysis. The governing equations for the presented model were derived using Hamilton’s principle based on first-order shear deformation theory together with Eringen’s nonlocal elasticity theory. Modified size-dependent boundary conditions were derived to handle the paradoxical behavior of the free vibration of nanoplates with a free boundary due to nonlocal parameter and thermal environment. Two different approaches in the quadrature method along with the Chebyshev collocation method were adopted, and it was found that Chebyshev collocation method had a faster rate of convergence than the other two methods. Hence, the Chebyshev collocation method was employed to obtain the numerical values of frequencies. The effect of various parameters together with nonlocal boundary conditions on the nondimensional frequencies was studied. The results were compared with those available in the literature to validate the accuracy of the results and the efficiency of the authors’ technique.