Studying Dynamic Pull-In Behavior of Microbeams by Means of the Homotopy Analysis Method

2008 ◽  
Author(s):  
Mahdi Moghimi Zand ◽  
S. Ahmad Tajalli ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Differential Equation ◽  
Homotopy Analysis Method ◽  
Nonlinear Partial Differential Equation ◽  
Nonlinear Ordinary Differential Equation ◽  
Strong Nonlinearity ◽  
Analysis Method ◽  
Solution Methods ◽  
Homotopy Analysis ◽  
Fringing Field ◽  
Fringing Field Effect

In this study, the homotopy analysis method (HAM) is used to study dynamic pull-in instability in microbeams considering different sources of nonlinearity. Electrostatic actuation, fringing field effect and midplane stretching causes strong nonlinearity in microbeams. In order to investigate dynamic pull-in behavior, using Galerkin’s decomposition method, the nonlinear partial differential equation of motion is reduced to a single nonlinear ordinary differential equation. The obtained equation is solved analytically in time domain using HAM. The problem is studied by two separate manners: direct use of HAM and indirect use of HAM in conjunction with He’s Modified Lindstedt-Poincare´ Method. To demonstrate the effectiveness of the solution methods, results are compared with those in literature. The comparison between obtained results and those available in literature shows good agreement.

scholarly journals Application of Homotopy Analysis Method to the Unsteady Squeezing Flow of a Second-Grade Fluid between Circular Plates

2010 ◽  
Vol 2010 ◽  
pp. 1-18 ◽  
Author(s):  
Mohammad Mehdi Rashidi ◽  
Abdul Majid Siddiqui ◽  
Mostafa Asadi
Keyword(s):  
Differential Equation ◽  
Homotopy Analysis Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Second Grade ◽  
Squeezing Flow ◽  
Circular Plates ◽  
Analysis Method ◽  
Second Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid

We investigated an axisymmetric unsteady two-dimensional flow of nonconducting, incompressible second grade fluid between two circular plates. The similarity transformation is applied to reduce governing partial differential equation (PDE) to a nonlinear ordinary differential equation (ODE) in dimensionless form. The resulting nonlinear boundary value problem is solved using homotopy analysis method and numerical method. The effects of appropriate dimensionless parameters on the velocity profiles are studied. The total resistance to the upper plate has been calculated.

Investigation of the Oscillatory Behavior of Electrostatically-Actuated Microbeams

2010 ◽  
Author(s):  
Mahdi Mojahedi ◽  
Mahdi Moghimi Zand ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Differential Equation ◽  
Homotopy Perturbation Method ◽  
Axial Stress ◽  
Nonlinear Partial Differential Equation ◽  
Nonlinear Ordinary Differential Equation ◽  
Oscillatory Behavior ◽  
Electrostatically Actuated ◽  
Homotopy Analysis ◽  
Analytic Expressions ◽  
Good Agreement

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 numerical results in the literature.

One Dimensional Model of Martensitic Transformation Solved by Homotopy Analysis Method

2012 ◽  
Vol 67 (5) ◽  
pp. 230-238 ◽  
Author(s):  
Chen Xuan ◽  
Cheng Peng ◽  
Yongzhong Huo
Keyword(s):  
Phase Transition ◽  
Martensitic Transformation ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Lagrange Equation ◽  
Nonlinear Ordinary Differential Equation ◽  
Physical Parameters ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The One

The homotopy analysis method (HAM) is applied to solve a nonlinear ordinary differential equation describing certain phase transition problem in solids. Both bifurcation conditions and analytical solutions are obtained simultaneously for the Euler-Lagrange equation of the martensitic transformation. HAM is capable of providing an analytical expression for the bifurcation condition to judge the occurrence of the phase transition, while other numerical techniques have difficulties in bifurcation analysis. The convergence of the analytical solutions on the one hand can be adjusted by the auxiliary parameter and on the other hand is always obtainable for all relevant physical parameters satisfying the bifurcation condition.

scholarly journals On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative

2018 ◽  
Vol 22 ◽  
pp. 01045 ◽  
Author(s):  
Mehmet Yavuz ◽  
Necati Özdemir
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Exact Solutions ◽  
Detailed Analysis ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Conformable Derivative ◽  
Homotopy Analysis ◽  
Fractional Cauchy Problem

In this study, we have obtained analytical solutions of fractional Cauchy problem by using q-Homotopy Analysis Method (q-HAM) featuring conformable derivative. We have considered different situations according to the homogeneity and linearity of the fractional Cauchy differential equation. A detailed analysis of the results obtained in the study has been reported. According to the results, we have found out that our obtained solutions approach very speedily to the exact solutions.

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