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Variational iterational method in stability analysis of beams under nonconservative forces

Glabisz W., Jarczewska K., Zielichowski-Haber W.

Archives of Civil and Mechanical Engineering

2013

Vol. 13, no. 1

82--87

The aim of this paper is to demonstrate the effectiveness of VIM in the analysis of the stability of prismatic and nonprismatic (multisegmental) Euler–Bernoulli beams under static nonconservative loads. The application of VIM to the analysis of beam problems may lead to solutions which can form the basis for the evaluation of the quality of the numerical methods used in the problems. The general Lagrange multipliers for the Euler–Bernoulli beam equation are presented. The convergence of VIM for the multipliers is discussed and an exemplary solution to the problem of the stability of the multisegmental beam under nonconservative loads is presented.

Periodic solutions for highly nonlinear oscillation systems

Ghadimi M., Barari A., Kaliji H. D., Domairry G.

Archives of Civil and Mechanical Engineering

2012

Vol. 12, no. 3

389--395

In this paper, Frequency-Amplitude Formulation is used to analyze the periodic behavior of tapered beam as well as two complex nonlinear systems. Many engineering structures, such as offshore foundations, oil platform supports, tower structures and moving arms, are modeled as tapered beams. The results obtained are compared with Variational Iteration Method (VIM) and other analytical methods as well as time marching solution. The results given show the effectiveness and accuracy of the proposed techniques.