This paper presents size dependent stability analysis a cantilever micro laminated beam embedded in elastic medium by using the Modified Coupled Stress Theory which includes the length scale parameter. The micro beam subjected to compressive load is considered as three composite laminas and embedded in elastic medium which is modelled in the Winkler foundation model. In the obtaining of the governing equations, the energy principle is used. In the solution of the buckling problem, the energy based Ritz method is implemented with algebraic polynomials. In order to accuracy obtained expressions and used method, a comparative study is performed. Many parametric studies are presented in order to investigate the buckling of laminated micro beams. For this purpose, effects of stacking sequence of laminas, geometric parameters, length scale parameter, fiber orientation angle, the parameter of elastic medium on critical buckling loads of laminated micro beams are investigated.

This study deals with the vibration and stability analysis of double-graphene nanoribbon system (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and Modified couple Stress within the framework of Rayleigh beam Theory. In this system, two graphene nanoribbons (GNRs) are bonded by Pasternak medium which characterized by Winkler modulus and shear modulus. An analytical approach is utilized to determine the frequency and critical buckling load of the Coupled system. The three vibrational states including out-of-phase vibration, in-phase vibration and one GNR being stationary are discussed. A detailed parametric study is conducted to elucidate the influences of the small scale coefficients, stiffness of the internal elastic medium, mode number and axial load on the vibration of the DGNRS. The results reveal that the dimensionless frequency and critical buckling load obtained by the strain gradient Theory is higher than the Eringen's and Modified couple Stress theories. Moreover, the small scale effect in the case of in-phase vibration is higher than that in the other cases. This study might be useful for the design of nano-devices in which GNRs act as basic elements.

In this paper, a new viscoelastic size-depended model developed based on a Modified couple Stress Theory and the for nonlinear viscoelastic material in order to vibration analysis of a viscoelastic nanoplate. The material of the nanoplate is assumed to obey the Leaderman nonlinear constitutive relation and the von Ká rmá n plate Theory is employed to model the system. The viscous parts of the classical and nonclassical Stress tensors are obtained based on the Leaderman integral and the corresponding work terms are calculated. The viscous work equations are balanced by the terms of size-dependent potential energy, kinetic energy. Then the equations of motion are derived from Hamilton’ s principle. The governing nonlinear integro-differential equations with Coupled terms are solved by using the fourth-order Runge-Kutta method and Galerkin approach. The results are validated by carrying out the comparison with existing results in the literature when our model is reduced into an elastic case. In order to explore the vibrational characteristics, the influences of the thickness ratio, relaxation coefficient, and aspect ratio on the frequency and damping ratio were also examined. The results revealed that the frequency, vibration amplitude and damping ratio of viscoelastic nanoplate were significantly influenced by the relaxation coefficient of nanoplate material, and length scale parameter. Also, it was found that with increasing (h/l) the vibration frequency decreases and its amplitude and damping ratio increase.

In this paper, the coupling coefficient of two waveguides with conducting interfaces is calculated analytically. It is shown that the control of interface charge densities via a transverse voltage leads to the control of the coupling. To derive the coupling coefficient, the basic Coupled Mode Theory (CMT) with paraxial approximation is improved to include the effect of conducting interfaces. The analysis is performed independently for TE and TM polarizations. Several direct applications of this effect including a multiplexer, a coupler and a modulator/switch and programmable grating are introduced.

The main aim is to study the two dimensional axisymmetric problem of thick circular plate in Modified couple Stress Theory with heat and mass diffusive sources. The thermoelastic theories with mass diffusion developed by Sherief et al. [1] and kumar and Kansal [2] have been used to investigate the problem. Laplace and Hankel transforms technique is applied to obtain the solutions of the governing equations. The displacements, Stress components, temperature change and chemical potential are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of couple Stress on the resulting quantities are shown graphically. Some particular cases of interest are also deduced.

In this article, the size effect on the dynamic behavior of a simply supported multi-cracked microbeam is studied based on Modified Couple Stress Theory (MCST). At first, based on MCST, the equivalent torsional stiffness spring for every open edge crack at its location is calculated; in this regard, the Stress Intensity Factor (SIF) is also considered for all open edge cracks. Hamilton’ s principle has been used in order to achieve the governing equations of motion of the system and associated boundary conditions are derived based on MCST. Then the natural frequencies of multi-cracked microbeam are analytically determined. After that, the Numerical solutions have been presented for the microbeam with two open edge cracks. Finally, the variation of the first three natural frequencies of the system is investigated versus different values of the depth and the location of two cracks and the material length scale parameter. The obtained results express that the natural frequencies of the system increase by increasing the material length scale parameter and decrease by moving away from the simply supported of the beam and node points, in addition to increasing the number of cracks and cracks depth.