In this study, size‐dependent thermo‐mechanical vibration analysis of nanobeams is examined. Size‐dependent dynamic equations are obtained by implementing Hamilton's principle based on Timoshenko beam theory and then combined with stress equation of nonlocal elasticity theory. The separation of variables total method and finite element formulation is utilized to solve the eigenvalue problem. Local and nonlocal stiffness and mass matrices are firstly derived by using a weighted residual method for the finite element analysis. The accuracy of the finite element solution is demonstrated by comparisons with the earlier studies. Then, nondimensional frequencies of nanobeams with different boundary conditions based on a nonlocal finite element method are presented for vibration analysis that cannot be analytically solved under different parameters. It is aimed to emphasize the importance of the nonlocal finite element method in the size‐dependent vibration behavior of nanobeams which form different components of nano‐electro‐mechanical systems.

SUMMARYIn this study, free vibration of laminated skew plates was investigated. Discrete singular convolution (DSC) method is used for numerical solution of vibration problems. The straight-sided quadrilateral domain is mapped into a square domain in the computational space using a four-node element by using the geometric transformation. Typical results are presented for different geometric parameters and boundary conditions. It is concluded from the results that the skew angle have considerable influence on the variations of the frequencies with fibre orientation angle and number of layers in the laminate. The results obtained by DSC method are compared with those obtained by analytical and numerical approaches. It is shown that reasonable accurate results are obtained. Present work also indicates that the method of DSC is a promising and potential approach for computational mechanics.

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This paper presents the dynamic responses of a fiber-reinforced composite beam under a moving load. The Timoshenko beam theory was employed to analyze the kinematics of the composite beam. The constitutive equations for motion were obtained by utilizing the Lagrange procedure. The Ritz method with polynomial functions was employed to solve the resulting equations in conjunction with the Newmark average acceleration method (NAAM). The influence of fiber orientation angle, volume fraction, and velocity of the moving load on the dynamic responses of the fiber-reinforced nonhomogeneous beam is presented and discussed.

In the current article, in the presence of thermal and diffusion processes, the equations governing elastic materials through thermodiffusion are obtained. The Moore–Gibson–Thompson (MGT) equation modifies and defines the equations for thermal conduction and mass diffusion that occur in solids. This modification is based on adding heat and diffusion relaxation times in the Green–Naghdi Type III (GN-III) models. In an unbounded medium with a cylindrical hole, the built model has been applied to examine the influence of the coupling between temperature and mass diffusion and responses. At constant concentration as well as intermittent and decaying varying heat, the surrounding cavity surface is traction-free and is filled slowly. Laplace transform and Laplace inversion techniques are applied to obtain the solutions of the studied field variables. In order to explore thermal diffusion analysis and find closed solutions, a suitable numerical approximation technique has been used. Comparisons are made between the results obtained with the results of the corresponding previous models. Additionally, to explain and realize the presented model, tables and figures for various physical fields are presented.