This article employs the classical Euler–Bernoulli beam theory in connection with Green–Naghdi’s generalized thermoelasticity theory without energy dissipation to investigate the vibrating microbeam. The microbeam is considered with linearly varying thickness and subjected to various boundary conditions. The heat and motion equations are obtained using the modified couple stress analysis in terms of deflection with only one material length-scale parameter to capture the size-dependent behavior. Various combinations of free, simply-supported, and clamped boundary conditions are presented. The effect of length-to-thickness ratio, as well as the influence of both couple stress parameter and thermoelastic coupling, are all discussed. Furthermore, the effect of reference temperature on the eigenfrequency is also investigated. The vibration frequencies indicate that the tapered microbeam modeled by modified couple stress analysis causes more responses than that modeled by classical continuum beam theory, even the thermoelastic coupled is taken into account.
This article investigates the solution of exponentially graded (EG) thick rectangular plates resting on two-parameter elastic foundations according to a trigonometric plate theory (TPT). This theory includes the effect of both shear and normal strains thickness without needing to any shear correction factor. The displacement fields contains initial terms of a power series across plate thickness as well as additional trigonometric terms. The material properties of plate is graded such that Lamé’s coefficients convert exponentially in a given constant orientation. Equilibrium equations according to the EG plate resting on Pasternak’s foundations are derived. The solution is obtained by using Navier’s technique. Numerical results for the EG thick plate on elastic foundations are presented, and compared with those available in the literature. The influences of Winkler’s and Pasternak’s parameters, side-to-thickness ratio, inhomogeneity parameter and aspect ratio on the bending responses of EG plates are investigated.
In the present article, we introduced a new model of the equations of general ized thermoelasticity for unbounded orthotropic body containing a cylindrical cavity. We applied this model in the context of generalized thermoelasticity with phase-lags under the effect of rotation. In this case, the thermal conductivity of the material is considered to be variable. In addition, the cylinder surface is traction free and subjected to a uniform unit step temperature. Using the Laplace transform technique, the distributions of the temperature, displacement, radial stress and hoop stress are determined. A detailed analysis of the effects of rotation, phase-lags and the variability thermal conductivity parameters on the studied fields is discussed. Numerical results for the studied fields are illustrated graphically in the presence and absence of rotation.
Analytical and numerical nonlinear solutions for rotating variable-thickness functionally graded solid and annular disks with viscoelastic orthotropic material properties are presented by using the method of successive approximations. Variable material properties such as Young’s moduli, density and thickness of the disk, are first introduced to obtain the governing equation. As a second step, the method of successive approximations is proposed to get the nonlinear solution of the problem. In the third step, the method of effective moduli is deduced to reduce the problem to the corresponding one of a homogeneous but anisotropic material. The results of viscoelastic stresses and radial displacement are obtained for annular and solid disks of different profiles and graphically illustrated. The calculated results are compared and the effects due to many parameters are discussed.