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Free vibration analysis of curved structural components such as truncated conical shells, circular cylindrical shells and annular plates has been investigated numerically in this paper. The method of discrete singular convolution (DSC) and the method differential quadrature (DQ) are used for numerical simulations, respectively. Related partial differential equations governed the motion of the structures obtained from higher-order shear deformation theory have been solved by using these two methods in the space domain. Different material properties have been considered such as isotropic, laminated and functionally graded material (FGM). Four-parameter power law and simple power law distributions have been used for ceramic volume fraction in FGM cases. The numerical results related to free vibration of conical shells have obtained by the present two techniques compare well with the results available in the literature. Results for circular cylindrical shells and annular plates have also been presented for different geometric and material parameters. The effects of grid number and types of the grid distribution have also been investigated for annular plate and shells.

Free thermal vibration analysis of nanobeams surrounded by an elastic matrix is examined via nonlocal elasticity and Timoshenko beam theories in this article. Elastic matrix is formulated with a two-parameter elastic foundation modelled by combining Winkler and Pasternak assumptions. The equation of motion for free vibration is reached via Hamilton’s principle and solved by analytical method (separation of variable). However, since the separation of variable cannot be applied for boundary conditions other than simply supported nanobeams, a weighted residue-based finite element formulation is developed. Within the scope of numerical results, firstly, it is understood from the comparisons given for nondimensional frequencies that the nonlocal finite element formulation has a high accuracy and then, using this formulation, nondimensional frequencies of nanobeams with different boundary conditions are computed under different parameters. Additionally, the detailed discussions of the numerical results are presented. Finally, by giving some general results, the effect of size dependency and environmental factors on the dynamic behavior of nanobeams is expressed.