Explicit solution of the large amplitude transverse vibrations of a flexible string under constant tension

Reza Taghipour,Ali Nikkar,Tohid Akhlaghi

doi:10.1590/s1679-78252014000300010

Reza Taghipour, Ali Nikkar + Show 1 more

Open Access

https://doi.org/10.1590/s1679-78252014000300010

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Abstract

This paper presents the analytical simulation of string with large amplitudes using the Variational Iteration Method (VIM) and Hamiltonian Approach (HA). In order to verify the precision of the presented methods, current results were compared with He's Variational Approach and Runge-Kutta 4th order. It has been found that these methods are well suited for a range of parameters and the approximate frequencies and periodic solutions show a good agreement with other techniques. The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering.

Highlights

Study of nonlinear problems in strings with large amplitude is a very important research area in many fields of physics and engineering
The main objective of the present study is to propose two analytical methods, namely the Variational Iteration Method (VIM) and Hamiltonian Approach (HA) which were introduced by He (He, 1999; 2010) to solve the nonlinear differential equation of the large deformation of string with large amplitudes
The results reveal that these methods are very effective and convenient in predicting the solution of such problems, and it is predicted that the VIM and Hamiltonian Approach (HA) can find a wide application in new engineering problems

Summary

Introduction

Study of nonlinear problems in strings with large amplitude is a very important research area in many fields of physics and engineering. Long cables and wires are extensively used in many mechanical systems and structures such as cranes, ships, offshore platforms and bridges. The study of nonlinear vibration of strings (cables and wires) with large amplitude is in practice very complicated. The force data like air flow speed, direction and turbulence characteristic is, as a rule, difficult to definitely specify. The mechanical characteristic of cables like bending stiffness and damping effects depend on a number of parameters (Omran et al, 2013). Nikkar et al / Explicit solution of the large amplitude transverse vibrations of a flexible string under constant tension

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