Analytical approximation of nonlinear vibration of string with large amplitudes

Abstract

Study of nonlinear problems in strings with large amplitude is a very important research area in many fields of physics and engineering. variational approach method (VAM) is in particular selected because the method is appropriate to solve nonlinear vibration of a constanttension string. VAM is an explicit method with high capability for resolving strong nonlinear oscillation system problems. It has been found that VAM is well suited for a range of parameters and the approximate frequencies and periodic solutions show a good agreement with the exact ones. This paper compares the various aspects of VAM in relative to exact approaches and higher-order approximate solutions for the constant-tension string. The comparison indicates that VAM is very fast, effective and convenient. The method does not require any linearization or small perturbation, and it leads to high accuracy of the solutions in a single iteration.