Approximate analysis of two-mass–spring systems and buckling of a column

Abstract

Single degree of freedom (SDOF) Two degrees of freedom (TDOF) Max-Min approach (MMA) a b s t r a c tMax-Min Approach (MMA) is applied to obtain an approximate solution of three practical cases in terms of a nonlinear oscillation system. After finding maximal and minimal solution thresholds of a nonlinear problem, an approximate solution of the nonlinear equation can be easily achieved using He Chengtian's interpolation. Numerical results indicate the effectiveness of the proposed method both in respect of the whole range of involved parameters as well as the excellent agreement with the approximate frequencies and periodic solutions with the exact ones. It is predicted that MMA can be found widely applicable in engineering.

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.…”

Using instability to reconfigure smart structures in a spring-mass model

“…Through using this qualitatively simple model, new insights can be obtained on the use of heteroclinic connections. This simple model can be used to introduce this new reconfiguration concept and provide insights for use in a more accurate high fidelity model [27].…”

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.…”