Nonlinear vibration of an electrostatically actuated microbeam

Abstract

In this paper, we have considered a new class of critical technique that called the He's Variational Approach (VA) to solve the nonlinear vibration of an electrostatically actuated microbeam. It has been indicated that the Variational Approach (VA) is quickly convergence and does not demand small perturbation and also sufficiently accurate to both linear and nonlinear problems in engineering. The obtained results show that the approximate solutions are uniformly legitimate on the whole solution field.

Application of Higher Order Hamiltonian Approach to the Nonlinear Vibration of Micro Electro Mechanical Systems

“…Contrarily to some recent researches such as (Bayat, Bayat et al 2014), we showed that the second order is extremely close to the EBM solution and exact solution. The methodology of the higher order Hamiltonian for solving an ordinary differential equation with strong power nonlinearity is presented.…”

“…The variational approach (Bayat, Bayat et al 2014) and analytical approximate solution (Rafieipour, Lotfavar et al 2013) resulted the same response for this problem.…”

“…Bayat et al (Bayat, Bayat et al 2014) investigated He's Variational Approach (VA) to solve nonlinear vibration of an electro statically actuated clamped-clamped micro beam that was equivalent to the first order of higher Hamiltonian method (Yildirim, Askari et al 2012 This research investigated high order approximate solutions by using higher order Hamiltonian method (He 2010) for solving a non-linear dynamic problem, in order to have a highly accurate numerical approximation. Contrarily to some recent researches such as (Bayat, Bayat et al 2014), we showed that the second order is extremely close to the EBM solution and exact solution.…”

Fuzzy Semiactive Vibration Control of Structures Using Magnetorheological Elastomer

“…Solving nonlinear vibration equations is always a difficult problem. In recent years, there are many analytical and numerical approaches which have been investigated, such as variational iteration method [15,16] and He's energy balance method [17,18]. In our research, the mass displacement, ( ) in (7), was determined by the application of He's energy balance method.…”

Nonlinearities distribution Laplace transform-homotopy perturbation method

“…As it is widely known, the importance of research on nonlinear differential equations is that many phenomena, practical or theoretical, are of nonlinear nature. In recent years, several methods focused to find approximate solutions to nonlinear differential equations, as an alternative to classical methods, have been reported, such those based on: variational approaches (Assas 2007; He 2007; Kazemnia et al 2008; Noorzad et al 2008), tanh method (Evans & Raslan 2005), exp-function (Xu 2007; Mahmoudi et al 2008), Adomian’s Decomposition Method (ADM) (Adomian 1988; Babolian & Biazar 2002; Kooch & Abadyan 2012; Kooch & Abadyan 2011; Vanani et al 2011; Chowdhury 2011; Elias et al 2000), parameter expansion (Zhang & Xu 2007), HPM (Aminikhan & Hemmatnezhad 2012; Aminikhah 2012; Filobello-Nino et al 2013; Aminikhah 2011; Khan et al 2011; Marinca & Herisanu 2011; He 1998; He 1999; He 2006a; Vazquez-Leal et al 2014; Belendez et al 2009; He 2000; El-Shaed 2005; He 2006b; Vazquez-Leal et al 2012a; Ganji et al 2008; Fereidon et al 2010; Sharma & Methi 2011; Biazar & Ghanbari 2012; Biazar & Eslami 2012; Araghi & Sotoodeh 2012; Araghi & Rezapour 2011; Bayat et al 2014; Bayat et al 2013; Vazquez-Leal et al 2012b; Vazquez-Leal et al 2012c; Filobello-Niño et al 2012; Biazar & Aminikhan 2009; Biazar & Ghazvini 2009; Filobello-Nino et al 2012; Khan & Qingbiao 2011; Madani et al 2011; Ji Huan 2006; Feng et al 2007; Mirmoradia et al 2009; Vazquez-Leal et al 2012; Vazquez-Leal et al 2013), Homotopy Analysis Method (HAM) (Rashidi et al 2012a; Rashidi et al 2012b; Patel et al 2012; Hassana & El-Tawil 2011), and perturbation method (Filobello-Nino et al 2013; Holmes 1995; Filobello-Niño et al 2013b; Filobello-Nino et al 2014) among many others. Also, a ...…”