Sharif Digital Repository

In this paper, nonlinear vibration of a micro cantilever exposed to a constant velocity flow is studied. In order to obtain vibration frequency and time response of the micro beam the variational iteration method is used as a novel tool for solving nonlinear differential equations. Results of the analytical solution are compared with those obtained by Runge-Kutta method which shows very good agreement between them. Results confirm that frequency of vibration depends on the flow velocity. Also, the high sensitivity of the vibration frequency to the flow velocity means that it can be an effective indicator of velocity  

In this paper, we consider the solution of an nth order boundary-value problem. We solve this problem by changing the problem to a system of two integral-differential equations and using the variational iteration method. By giving three examples and comparing with the other methods, the efficiency of the method will be shown. © 2007 Elsevier Inc. All rights reserved  

In this paper, distributions of stress and strain components of rotating disks with non-uniform thickness and material properties subjected to thermo-elastic loading under different boundary conditions are obtained by semi-exact methods of Liao's homotopy analysis method (HAM), Adomian's decomposition method and He's variational iteration method (VIM). The materials are assumed to be perfectly elastic and isotropic. A two dimensional plane stress analysis is used. The distribution of temperature over the disk radius is assumed to have power forms with the higher temperature at the outer surface. The results of the three methods are compared with those obtained by Runge-Kutta's numerical... 

In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations. © 2009 Elsevier Ltd. All rights reserved  

The purpose of this paper is to present efficient and accurate analytical expressions for large amplitude free vibration analysis of single and double tapered beams on elastic foundation. Geometric nonlinearity is considered using the condition of inextensibility of neutral axis. Moreover, the elastic foundation consists of a linear and cubic nonlinear parts together with a shearing layer. The nonlinear governing equation is solved by employing the variational iteration method (VIM). This study shows that the second-order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. The effects of different parameters on the nonlinear... 

In this paper, employing the limit analysis theorem, critical loading on functionally graded (FG) circular plate with simply supported boundary conditions and subjected to an arbitrary rotationally symmetric loading is determined. The material behavior follows a rigid-perfectly plastic model and yielding obeys the von-Mises criterion. In the homogeneous case, the highly nonlinear ordinary differential equation governing the problem is analytically solved using a variational iteration method. In other cases, numerical results are reported. Finally, the results are compared with those of the FG plate with Tresca yield criterion and also in the homogeneous case with those of employing the... 

An analytical study using Variational Iteration Method (VIM) is carried out in order to investigate the vibrations of electro-statically actuated double-clamped and simply-supported microbeams. Effects of applied voltage and residual axial load on the nonlinear natural frequency and deflection of the microbeams are studied. It shows that pre-compression in microbeams increases the amplitude of deflections for a specific applied voltage. Also, an increase in pre-tension motivates the microbeam to show more nonlinear behavior in an applied voltage. Predicted results are compared with the experimental data available in the literature and also with numerical results which shows a good agreement.... 

In this paper, an analytical solution for the nonlinear free vibration of a conservative oscillator is presented. The nonlinear governing equation is solved by employing the Variational Iteration Method (VIM). This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a function. Obtained results reveal that the proposed method is very effective, simple and exact. In the present investigation, the results of this method are compared with those of the Homotopy Analysis Method (HAM), as well as those predicted by the Runge-Kutta method. The excellent accuracy of the obtained results is demonstrated by comparing them with available analytical... 

In this paper an analytical solution for size-dependent response of cantilever micro-beams is presented. Using the modified couple stress theory, the small scale effects are accounted for. Employing the Modified Variational Iteration Method, efficient and accurate analytical expressions for the deflection of the micro-beam are presented. Very good agreement is observed between the present work results and available experimental data. This study may be helpful to characterize the size-dependent mechanical properties of MEMS. Consequently, the proposed analytical solution can be used as an efficient tool for studying the effects of the material or geometrical parameters on small scale devices... 

The purpose of this paper is to present efficient and accurate analytical expressions for large amplitude free vibration and post-buckling analysis of unsymmetrically laminated composite beams on elastic foundation. Geometric nonlinearity is considered using Von Karman's strain-displacement relations. Besides, the elastic foundation has cubic nonlinearity with shearing layer. The nonlinear governing equation is solved by employing the variational iteration method (VIM). This study shows that the third-order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. The effects of different parameters on the ratio of nonlinear to...