Journal of Solid Mechanics
Volume:3 Issue: 3, Summer 2011

in this paper, static and dynamic behavior of a varactor of a micro-phase shifter under DC, step DC and AC voltages and effects of the residual stress on the phase diagram have been studied. By presenting a mathematical modeling, Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, respectively. The calculated static and dynamic pull-in voltages have been validated by previous experimental and theoretical results and a good agreement has been achieved. Then the frequency response and phase diagram of the system have been studied. It has been shown that increasing the bias voltage shifts down the phase diagram and left the frequency response. Also increasing the damping ratio shifts up the phase diagram. Finally, the effect of residual stress on the phase diagram has been studied.

In this study, the torsional stability analysis is presented for thin cylindrical with the functionally graded (FG) middle layer resting on the Winker elastic foundation. The mechanical properties of functionally graded material (FGM) are assumed to be graded in the thickness direction according to a simple power law and exponential distributions in terms of volume fractions of the constituents. The fundamental relations and basic equations of three-layered cylindrical shells with a FG middle layer resting on the Winker elastic foundation under torsional load are derived. Governing equations are solved by using the Galerkin method. The numerical results reveal that variations of the shell thickness-to-FG layer thickness ratio, radius-to-shell thickness ratio, lengths-to-radius ratio, foundation stiffness and compositional profiles have significant effects on the critical torsional load of three-layered cylindrical shells with a FG middle layer. The results are verified by comparing the obtained values with those in the existing literature.

This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each time step is split into two phases: an updated Lagrangian phase followed by an Eulerian phase. The implicit time integration method is applied for solving the transient problem in Lagrangian phase with no convective effects. A mesh motion scheme, in which the related equations need not to be solved at every time step, is proposed in Eulerian phase. The critical dynamic stress intensity factor criterion is used to determine the crack velocity. The variation of dynamic stress intensity factor along the crack front is also studied based on the interaction integral method. The proposed algorithm is applied to investigate the dynamic crack propagation in the DCB specimen subjected to fixed displacement. The predicted results are compared with the experimental study cited in the literature and a good agreement is shown. The proposed algorithm leads to the accurate and efficient analysis of dynamic crack propagation process.

This article presents an exact solution for an axisymmetric functionally graded piezoelectric (FGP) rotating disk with constant thickness subjected to an electric field and thermal gradient. All mechanical, thermal and piezoelectric properties except for Poisson’s ratio are taken in the form of power functions in radial direction. After solving the heat transfer equation, first a symmetric distribution of temperature is produced. The gradient of displacement in axial direction is then obtained by assuming stress equation in axial direction to be zero. The electric potential gradient is attained by charge and electric displacement equations. Substituting these terms in the equations for the dimensionless stresses in the radial and circumferential directions yield these stresses and using them in the mechanical equilibrium equation a nonhomogeneous second order differential equation is produced that by solving it, the dimensionless displacement in radial direction can be achieved. The study results for a FGP rotating hollow disk are presented graphically in the form of distributions for displacement, stresses and electrical potential.

Nonlinear free vibration analysis of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium is studied in this paper based on classical (local) Euler-Bernoulli beam theory.Using the averaging method, the nonlinear free vibration responses of DWCNTs are obtained. The result is compared with the obtained results from the harmonic balance method for single-walled carbon nanotubes (SWCNTs) and DWCNTs. The effects of the surrounding elastic medium, van der waals (vdW) forces and aspect ratio of SWCNTs and DWCNTs on the vibration amplitude are discussed. The error percentage of the nonlinear free vibration frequencies between two theories decreases with increasing the spring constant of elastic medium. Results are also shown that if the value of the spring constant is lower than 107N / m3 (k  107N / m3), the nonlinear free vibration frequencies are increased. In this case, the effect of the spring constant on frequency responses is significant, while if the value of the spring constant is higher than 109N / m3 (k  109N / m3), the curve of frequency responses has a constant value near to 1 and therefore the effect of the spring constant on frequency responses is negligible.

Thermoelastic damping (TED) in a circular micro-plate resonator subjected to an electrostatic pressure is studied. The coupled thermo-elastic equations of a capacitive circular micro plate are derived considering hyperbolic heat conduction model and solved by applying Galerkin discretization method. Applying complex-frequency approach to the coupled thermo-elastic equations, TED is obtained for different ambient temperatures. Effects of the geometrical parameters on TED and the critical thickness are investigated. Furthermore, the effect of applied bias DC voltage on TED for an electrostatically deflected micro-plate is also investigated.

In this paper, analysis for the propagation of general anisotropic media of finite thickness with twothermal relaxation times is studied. Expression of displacements, temperature, thermal stresses,and thermal gradient for most general anisotropic thermoelastic plates of finite thickness are obtained in the analysis. The calculation is then carried forward for slightly more specialized case of a monoclinic plate. Dispersion relations for symmetric and antisymmetric wave modes are obtained. Thermoelastic plates of higher symmetry are contained implicitly in the analysis.Numerical solution of the frequency equation for a representative plate of assigned thickness is carried out, and the dispersion curves for the few lower modes are presented. Coupled thermoelastic thermal motions of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. Some special cases have also been deduced and discussed.

The present article deals with the study of propagation of plane waves in isotropic generalized thermoelastic diffusion with voids under initial stress. It is found that, for two dimensional model of isotropic generalized thermoelastic diffusion with voids under initial stress, there exists four oupled waves namely, P wave, Mass Diffusion (MD) wave, thermal (T) wave and Volume Fraction (VF) wave. The phase propagation velocities and attenuation quality factor of these plane waves are also computed and depicted graphically. In addition, the fundamental solution of system of differential equations in the theory of initially stressed thermoelastic diffusion with voids in case of steady oscillations in terms of elementary functions has been constructed. Some basic properties of the fundamental solution are established and some particular cases are also discussed.