New analytical approach to nonlinear behavior study of asymmetrically LCBs on nonlinear elastic foundation under steady axial and thermal loading

Abstract

In this paper, nonlinear behavior analysis of an asymmetrically laminated composite beam (LCB) on nonlinear foundation under axial and in-plane thermal loading is considered. To solve the obtained governing equation, a novel method based on Laplace transform is used. The resulted approximate analytical solution allows us the parametric study of different parameters which influence the nonlinear behavior of the system. The numerical results illustrate that proposed technique yields a very rapid convergence of the solution as well as low computational effort. The accuracy of the proposed method is verified by those available in literatures.

Dynamic model of large amplitude vibration of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

“…So, many new techniques have appeared in the open literature such as: variational iteration method (He, 2007a;Barari et al, 2011), homotopy perturbation method Saravi et al, 2013), homotopy analysis method (Liao, 2003;Khan et al, 2012)and some other methods Ghasempoor et al, 2102;Akbarzade and Khan, 2012;Alinia et al, 2011;Ganji, 2012;Torabi et al, 2012;Sheikholeslami et al, 2012a;2012b;Bayat et al, 2011;Rafieipour et al, 2012;Marinca and Herisanu, 2010;Salehi et al, 2012;Hamidi et al, 2012) The variational iteration method (VIM) and variational approach (VA) which were introduced by 2007a;2007b) are very powerful methods in solving non-linear differential equations and studying nonlinear vibration of beams. The Variational Approach which is also called He's variational approach, as well as the variational iteration method, was utilized here to obtain the analytical expression for the following model of nonlinear oscillations in the structural engineering problems:…”

Study of nonlinear vibration of Euler-Bernoulli beams by using analytical approximate techniques

“…The Laplace Iteration Method (LIM) and Variational Approach (VA) which were introduced by Rafieipour et al (2012) and He (2007) are very powerful methods in solving non-linear differential equations and studying nonlinear vibration of beams. The Variational Approach which is also called He's Variational Approach, as well as the Laplace Iteration Method, was utilized here to obtain the analytical expression for geometrically non-linear vibration of clamped-clamped Euler-Bernoulli beams fixed at one end.…”

Dynamic pull-in instability of geometrically nonlinear actuated micro-beams based on the modified couple stress theory

“…Recently, considerable progresses had been made in asymptotic approximate solutionsof nonlinear differential equations . There have been several approaches employed to solve the governing nonlinear differential equations to study the nonlinear vibrations such as Parametrized Perturbation Method (PPM) (Barari et al, 2011), Energy Balance Method (Ghadimi et al, 2012), Variational Iteration Method and Hamiltonian Approach (HA) , Laplace Transform Method (Rafieipour et al, 2012), Max-Min Approach (He, 2008), Homotopy Analysis Method (HAM) , Parameter Expansion Method , Iteration Perturbation Method (IPM) (He, 2001) and Homotopy Perturbation Method (HPM) (He, 1999). It is well known that while the perturbation methods provide the most versatile tools for the nonlinear analysis of engineering problems, they have also some limitations.…”