In this paper, the homotopy analysis method (HAM) has been employed to obtain the approximate analytical solution of the nonlinear Harry-Dym (HD) equation, which is one of the most important soliton equations. Utilizi...In this paper, the homotopy analysis method (HAM) has been employed to obtain the approximate analytical solution of the nonlinear Harry-Dym (HD) equation, which is one of the most important soliton equations. Utilizing the HAM, thereby employing the initial approximation, variations of the 7th-order approximation of the Harry-Dym equation is obtained. It is found that effect of the nonzero auxiliary parameter on convergence rate of the series solution is undeniable. It is also shown that, to some extent, order of the fractional derivative plays a fundamental role in the prediction of convergence. The final results reported by the HAM have been compared with the exact solution as well as those obtained through the other methods.展开更多
This paper shows an analysis ofMEM S （micro electro mechanical systems） due to Lorentz force and mechanical shock. The formulation is based on a modified couple stress theory, the von Karman geometric nonlinearity a...This paper shows an analysis ofMEM S （micro electro mechanical systems） due to Lorentz force and mechanical shock. The formulation is based on a modified couple stress theory, the von Karman geometric nonlinearity and Reynolds equation as well. The model contains a silicon microbeam, which is encircled by a stationary plate. The non-dimensional governing equations and associated boundary conditions are then solved iteratively through the Galerkin weighted method. The results show that pull-in voltage is dependent on the geometry nonlinearity. It is also demonstrated that by increasing voltage between the silicon microbeam and stationary plate, the pull-in instability happens.展开更多
文摘In this paper, the homotopy analysis method (HAM) has been employed to obtain the approximate analytical solution of the nonlinear Harry-Dym (HD) equation, which is one of the most important soliton equations. Utilizing the HAM, thereby employing the initial approximation, variations of the 7th-order approximation of the Harry-Dym equation is obtained. It is found that effect of the nonzero auxiliary parameter on convergence rate of the series solution is undeniable. It is also shown that, to some extent, order of the fractional derivative plays a fundamental role in the prediction of convergence. The final results reported by the HAM have been compared with the exact solution as well as those obtained through the other methods.
文摘This paper shows an analysis ofMEM S （micro electro mechanical systems） due to Lorentz force and mechanical shock. The formulation is based on a modified couple stress theory, the von Karman geometric nonlinearity and Reynolds equation as well. The model contains a silicon microbeam, which is encircled by a stationary plate. The non-dimensional governing equations and associated boundary conditions are then solved iteratively through the Galerkin weighted method. The results show that pull-in voltage is dependent on the geometry nonlinearity. It is also demonstrated that by increasing voltage between the silicon microbeam and stationary plate, the pull-in instability happens.
