Sharif Digital Repository

The steady 2-D boundary layer flow over a flat plate is studied analytically by homotopy perturbation method to analyze the entropy generation inside the boundary layer with constant wall temperature. By the transformations of go-verning equations including continuity, momentum, and energy by similarity va-riables, a dimensionless equation for entropy generation inside the boundary layer is obtained. The effects of important parameters such as Reynolds and Eck-ert numbers are investigated and the physical interpretations of the results are explained in details  

In the current paper, the effect of van der Waals (vdW) force on the static behavior and pull-in characteristics of nano/micromirrors under capillary force is investigated. At first, the dimensionless equation governing the static behavior of nano/micromirrors is obtained. The dependence of the critical tilting angle on the physical and geometrical parameters of the nano/micromirror and its supporting torsional beams is investigated. It is found that the existence of vdW force can considerably reduce the stability limits of the nano/micromirror. It is also found that rotation angle of the mirror due to capillary force highly depends on the vdW force applied to the mirror. Finally, analytical... 

This paper presents analytical soltions for the nonlinear problem of electrostatically actuated torsional micromirrors considering the bending of the torsional beams. First the energy method is used for finding the equilibrium equations. Then the explicit function theorem is utilized for finding the equations governing the instability mode of the mirror. These equations are then solved using Homotopy Perturbation Method (HPM) for the especial case of α = 0 where α is a small nondimensional geometrical parameter defining the starting point of the underneath electrodes. Then straight forward perturbation method is applied for finding the pull-in angle and pull-in displacement of the... 

The objective of this paper is to apply He's homotopy perturbation method (HPM) to analyze nonlinear free vibration of simply supported Timoshenko beams considering the effects of rotary inertia and shear deformation. First, the equation governing the nonlinear free vibration of a Timoshinko beam is nondimensionalized. Galerkin's projection method is utilized to reduce the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. HPM is then used to find analytic expressions for nonlinear natural frequencies of the pre-stretched beam. A parametric study has also been applied in order to investigate the effects of design parameters such as applied axial... 

The performance of perturbation method in nonlinear analyses of plates subjected to mechanical, thermal, and thermo-mechanical loadings is investigated. To this end, cylindrical bending of FG plates with clamped and simply-supported edges is considered. The governing equations of Mindlin's first-order shear deformation theory with von Kármán's geometric nonlinearity are solved using one- and two-parameter perturbation methods and the results are compared with the results of an analytical solution. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. It is shown that the... 

The performance of perturbation method in nonlinear analyses of plates subjected to mechanical, thermal, and thermo-mechanical loadings is investigated. To this end, cylindrical bending of FG plates with clamped and simply-supported edges is considered. The governing equations of Mindlin's first-order shear deformation theory with von Kármán's geometric nonlinearity are solved using one- and two-parameter perturbation methods and the results are compared with the results of an analytical solution. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. It is shown that the... 

In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions are valid for a wide range of... 

In this work, we use a powerful analytical method called homotopy analysis method (HAM) to derive the frequency of a nonlinear oscillating system. Unlike the perturbation method, the HAM does not require the addition of a small physically parameter to the differential equation. It is applicable to strongly and weakly nonlinear problems. Moreover, the HAM involves an auxiliary parameter, h, which renders the convergence parameter of series solutions Controllable, and increases the convergence, and increases the convergence significantly. This article depicts that the HAM is an efficient and powerful method for solving oscillating systems  

Vibrations of electrostatically-Actuated microbeams are investigated. Effects of electrostatic actuation, axial stress and midplane stretching are considered in the model. Galerkin's decomposition method is utilized to convert the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. Homotopy perturbation method (i.e. a special and simpler case of homotopy analysis method) is utilized to find analytic expressions for natural frequencies of predeformed microbeam. Effects of increasing the voltage, midplane stretching, axial force and higher modes contribution on natural frequency are also studied. The anayltical results are in good agreement with the... 

Marton’s inner bound is the best known achievable rate region for a general two-receiver discrete memoryless broadcast channel. In this paper, we establish improved bounds on the cardinalities of the auxiliary random variables appearing in this inner bound to the true rate region. We combine a perturbation technique, along with a representation using concave envelopes of information-theoretic functions that involve the use of auxiliary random variables, to achieve this improvement. The new cardinality bounds lead to a proof that a randomized time-division strategy achieves every rate triple in Marton’s region for binary input broadcast channels. This extends the result by Hajek and Pursley... 

In this article, the static behavior of micromirrors under the effect of capillary force is studied. The dimensionless equations governing the static behavior and the pull-in state of the micromirror under capillary force are obtained, and the effects of different geometrical parameters on the pull-in angle of micromirrors are investigated. The static behavior of micromirrors is studied both numerically and analytically using the homotopy perturbation method. It is observed that with increasing the instability number defined in this article, the rotation angle of the micromirror is increased and suddenly the pull-in occurs. The results of the presented model are then verified by comparing... 

In this paper, the effect of van der Waals (vdW) force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum potential energy principle is utilized to find the equation governing the static behavior of nano/micromirror under electrostatic and vdW forces. Then, the stability of static equilibrium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of different design parameters on the mirror's pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the...