A new approach to modified regularized long wave equation

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; …”

“…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:…”

Nonlinear Vibration Analysis of Euler-Bernoulli Beams by Using Continuous Galerkin-Petrov Time-Discretization Method

“…To study their behavior it is therefore important to design methods for the numerical solutions of these partial differential equations. In this respect, recently some approximate analytical techniques (see for instance, Bayat et al, 2010;Baghari et al, 2014;Jafari et al, 2014;Bayat et al, 2011;, Ganji, 2012;He, 1999;He, 2006;Khan et al, 2012;Liu and Gurram, 2009;Mirgolbabaei et al, 2010;Sfahani et al, 2011) as well as numerical methods by Lai et al (2008) (see also, Boukhalfa et al, 2010 Ganji et al, 2011) and references therein, have been proposed to investigate the nonlinear vibrations of beams for designing and fabrication purpose.…”

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

“…The vibration problems of uniform Euler-Bernoulli beams can be solved by analytical or approximate approaches. In this respect, several methods have been developed recently for finding approximate solutions to nonlinear problems; see (Boukhalfa and Hadjoui, 2010;Da Silva et al, 2009;He, 2006;Ganji et al, 2011;Ganji, 2012;Bayat et al, 2011;Khan et al, 2012;Nikkar et al, 2012;Ghasempoor et al, 2102;Ghotbi et al, 2012;Fereidoon et al, 2010) and the references therein. Lai et al (2008) utilized Adomian Decomposition Method to obtain the natural frequencies and mode shapes for the Euler-Bernoulli beam under various supporting conditions.…”