Investigation of Casimir and Van der Waals Forces for a Nonlinear Double-Clamped Beam Using Homotopy Perturbation Method

2009 ◽  
Author(s):  
Mahdi Mojahedi ◽  
Hamid Moeenfard ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Axial Loading ◽  
Design Parameters ◽  
Electric Force ◽  
Homotopy Perturbation ◽  
Static Responses ◽  
Fringing Field ◽  
Fringing Field Effect ◽  
Good Agreement

In this study, static deflection and Instability of double-clamped nanobeams actuated by electrostatic field and intermolecular force, are investigated. The model accounts for the electric force nonlinearity of the excitation and for the fringing field effect. Effects of mid-plane stretching and axial loading are considered. Galerkin’s decomposition method is utilized to convert the nonlinear differential equation of motion to a nonlinear algebraic equation which is solved using the homotopy perturbation method. The effect of the design parameters such as axial load and mid-plane stretching on the static responses and pull-in instability is discussed. Results are in good agreement with presented in the literature.

Numerical inversion method for the Laplace transform based on Boubaker polynomials operational matrix

2021 ◽  
Author(s):  
Rachid Belgacem ◽  
Ahmed Bokhari ◽  
Salih Djilali ◽  
Sunil Kumar
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Operational Matrix ◽  
Inversion Method ◽  
Numerical Inversion ◽  
Homotopy Perturbation ◽  
Boubaker Polynomials ◽  
The Laplace Transform ◽  
Good Agreement

We investigate through this research the numerical inversion technique for the Laplace transforms cooperated by the integration Boubaker polynomials operational matrix. The efficiency of the presented approach is demonstrated by solving some differential equations. Also, this technique is combined with the standard Laplace Homotopy Perturbation Method. The numerical results highlight that there is a very good agreement between the estimated solutions with exact solutions.

scholarly journals Homotopy perturbation method for a Stefan problem with variable latent heat

2014 ◽  
Vol 18 (2) ◽  
pp. 391-398 ◽  
Author(s):  
R Rajeev
Keyword(s):  
Approximate Solution ◽  
Analytical Solution ◽  
Perturbation Method ◽  
Latent Heat ◽  
Stefan Problem ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Variable Latent Heat ◽  
Good Agreement

In this paper, homotopy perturbation method is successfully applied to find an approximate solution of one phase Stefan problem with variable latent heat. The results thus obtained are compared graphically with a published analytical solution and are in good agreement.

A NEW EFFICIENT APPROACH FOR MODELING AND SIMULATION OF NANO-SWITCHES UNDER THE COMBINED EFFECTS OF INTERMOLECULAR SURFACE FORCES AND ELECTROSTATIC ACTUATION

2009 ◽  
Vol 01 (02) ◽  
pp. 349-365 ◽  
Author(s):  
MAHDI MOJAHEDI ◽  
HAMID MOEENFARD ◽  
MOHAMMAD TAGHI AHMADIAN
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Electrostatic Force ◽  
Perturbation Expansion ◽  
Electrostatic Actuation ◽  
Surface Forces ◽  
Design Tool ◽  
Galerkin Projection ◽  
Homotopy Perturbation ◽  
Fringing Field Effect

This paper applies the homotopy perturbation method to the simulation of the static response of nano-switches to electrostatic actuation and intermolecular surface forces. The model accounts for the electric force nonlinearity of the excitation and for the fringing field effect. Using a mode approximation in the Galerkin projection method, the nonlinear boundary value differential equation describing the statical behavior of nano-switch is reduced to a nonlinear algebraic equation which is solved using the homotopy perturbation method. The number of included terms in the perturbation expansion for achieving a reasonable response has been investigated. Three cases have been specifically studied. These cases correspond to when the effective external force is the electrostatic force, the combined electrostatic and Casimir force and the combined electrostatic and van der Waals force. In all three cases the pull-in characteristics has been investigated thoroughly. Results have been compared with numerical results and also analytical results available in the literature. It was found that HPM modifies the overestimation of N/MEMS instability limits reported in the literature and can be used as an effective and accurate design tool in the analysis of N/MEMS.

scholarly journals A Simple Modification of Homotopy Perturbation Method for the Solution of Blasius Equation in Semi-Infinite Domains

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
M. Aghakhani ◽  
M. Suhatril ◽  
M. Mohammadhassani ◽  
M. Daie ◽  
A. Toghroli
Keyword(s):  
Boundary Condition ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Modification ◽  
Infinite Domains ◽  
Homotopy Perturbation ◽  
Blasius Equation ◽  
Fifth Order ◽  
Adomian’S Polynomials ◽  
Good Agreement

A simple modification of the homotopy perturbation method is proposed for the solution of the Blasius equation with two different boundary conditions. Padé approximate is used to deal with the boundary condition at infinity. The results obtained from the analytical method are compared to Howarth’s numerical solution and fifth order Runge-Kutta Fehlberg method indicating a very good agreement. The proposed method is a simple and reliable modification of homotopy perturbation method, which does not require the existence of a small parameter, linearization of the equation, or computation of Adomian’s polynomials.

scholarly journals Application of Local Fractional Homotopy Perturbation Method in Physical Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Nabard Habibi ◽  
Zohre Nouri
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Models ◽  
Applied Mathematics ◽  
Nonlinear Phenomena ◽  
Homotopy Perturbation ◽  
Physical Problems ◽  
Fourier Series Method ◽  
Physical Phenomena ◽  
Good Agreement

Nonlinear phenomena have important effects on applied mathematics, physics, and issues related to engineering. Most physical phenomena are modeled according to partial differential equations. It is difficult for nonlinear models to obtain the closed form of the solution, and in many cases, only an approximation of the real solution can be obtained. The perturbation method is a wave equation solution using HPM compared with the Fourier series method, and both methods results are good agreement. The percentage of error of ux,t with α=1 and 0.33, t =0.1 sec, between the present research and Yong-Ju Yang study for x≥0.6 is less than 10. Also, the % error for x≥0.5 in α=1 and 0.33, t =0.3 sec, is less than 5, whereas for α=1 and 0.33, t =0.8 and 0.7 sec, the % error for x≥0.4 is less than 8.

scholarly journals Analytical Solution of Liénard Differential Equation using Homotopy Perturbation Method

2019 ◽  
Vol 39 ◽  
pp. 87-100
Author(s):  
Md Mamun Ur Rashid Khan ◽  
Goutam Saha
Keyword(s):  
Differential Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Research Work ◽  
Approximate Solutions ◽  
Homotopy Perturbation ◽  
Actual Solution ◽  
Different Types ◽  
Taylor’S Series ◽  
Good Agreement

In this research work, the well-known Homotopy perturbation method (HPM) is used to find the approximate solutions of the nonlinear Liénard differential equation (LDE) using different types of boundary conditions. In order to find the accuracy of the approximate solution, one term, two terms and three terms HPM approximations are considered. This idea is actually based on the idea of Taylor’s series polynomials. It is found that solution converges to the actual solution with the increase of the terms in the guess solution. Moreover, in each of the new HPM solution, previously obtained solutions are added to it in order to find the exactness of HPM solutions. However, the nature of the solution seems to be complicated. In addition, comparisons are made with the previously published results and a good agreement is observed. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 87-100

Homotopy perturbation method for predicting tsunami wave propagation with crisp and uncertain parameters

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Perumandla Karunakar ◽  
Snehashish Chakraverty
Keyword(s):  
Wave Propagation ◽  
Perturbation Method ◽  
Water Wave ◽  
Design Methodology ◽  
Homotopy Perturbation Method ◽  
Tsunami Wave ◽  
Uncertain Parameters ◽  
Content Type ◽  
Homotopy Perturbation ◽  
Good Agreement

Purpose The purpose of this paper is to find the solution of classical nonlinear shallow-water wave (SWW) equations in particular to the tsunami wave propagation in crisp and interval environment. Design/methodology/approach Homotopy perturbation method (HPM) has been used for handling crisp and uncertain differential equations governing SWW equations. Findings The wave height and depth-averaged velocity of a tsunami wave in crisp and interval cases have been obtained. Originality/value Present results by HPM are compared with the existing solution (in crisp case), and they are found to be in good agreement. Also, the residual error of the solutions is found for the convergence conformation and reliability of the present results.

scholarly journals Solution of the Davey–Stewardson equation using homotopuy analysis method

2010 ◽  
Vol 15 (4) ◽  
pp. 423-433 ◽  
Author(s):  
H. Jafari ◽  
M. Alipour
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Analysis Method ◽  
Homotopy Perturbation Method ◽  
Analysis Method ◽  
Nls Equation ◽  
Homotopy Perturbation ◽  
Higher Dimensional ◽  
Homotopy Analysis ◽  
Good Agreement

In this paper, the homotopy analysis method (HAM) proposed by Liao is adopted for solving Davey–Stewartson (DS) equations which arise as higher dimensional generalizations of the nonlinear Schrödinger (NLS) equation. The results obtained by HAM have been compared with the exact solutions and homotopy perturbation method (HPM) to show the accuracy of the method. Comparisons indicate that there is a very good agreement between the HAM solutions and the exact solutions in terms of accuracy.

On the Primary Resonance of an Electrostatically Actuated MEMS Using the Homotopy Perturbation Method

2009 ◽  
Author(s):  
Mahdi Mojahedi ◽  
Mahdi Moghimi Zand ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Differential Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Multiple Scales ◽  
Electrostatic Force ◽  
Nonlinear Partial Differential Equation ◽  
Primary Resonance ◽  
Analytic Solutions ◽  
Design Parameters ◽  
Homotopy Perturbation

In this paper, primary resonance of a double-clamped microbeam has been investigated. The Microbeam is predeformed by a DC electrostatic force and then driven to vibrate by an AC harmonic electrostatic force. Effects of midplane stretching, axial loads and damping are considered in modeling. Galerkin’s approximation is utilized to convert the nonlinear partial differential equation of motion to a nonlinear ordinary differential equation. Afterward, a combination of homotopy perturbation method and the method of multiple scales are utilized to find analytic solutions to the steady-state motion of the microbeam, far from pull-in. The effects of different design parameters on dynamic behavior are discussed. The results obtained by the presented method are validated by comparing with literature.

Sign in / Sign up

Export Citation Format

Share Document