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Bo Pan [1] and Jingda Tang [2] and Ryuichi Tarumi [3] and Fulin Shang [2] and Yanbo Wang [1] and Weijun Zhang [1] and Xueyan Zhang [1]

Academic Editor: Chao Tao

1, Xi’an Thermal Power Research Institute Co., Ltd., Xi’an, Shaanxi 710032, China, tpri.com.cn

2, State Key Lab for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, Xi’an Jiaotong University, Xi’an 710049, China, xjtu.edu.cn

3, Department of Mechanical Engineering, Osaka University, Suita, Osaka 565-0871, Japan, osaka-u.ac.jp

Received Jul 9, 2017; Accepted Oct 16, 2017

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Recently, we have analyzed the nonlinear dynamic response of the cross string, the simplest net structure of strings such as the space antennas, using Hamilton’s principle and the perturbation method [1]. Tri-cross string is another simplest net structure with odd constituent strings among all the multi-cross strings, except for the cross string. It is difficult to discuss their oscillation characteristics (such as natural frequency) by a theoretical analysis because of the complex nonlinearity. However, it is necessary to provide an analytical result to compare with experiments to obtain insight on the motion law of the structure and guide the structural design.

Natural vibration of an initially stressed and linearly elastic string with small amplitudes has been extensively investigated by theoretical analysis, simulations, and experimental researches. However, the relevant researches on the initially stretched string with finite amplitudes are still rare, despite they are quite important for the engineering problems. The Kirchhoff string equation is accepted as a good first approximation of the nonlinear behavior in the transverse direction of a string [2]. Molteno and Tufillaro studied qualitatively the agreement between the analytical results obtained via the truncated Kirchhoff string equation and the experimental results [3]. Various numerical schemes, such as the Galerkin method, were developed to simulate the large-amplitude vibrating problem of the elastic strings based on the nonlinear Kirchhoff string model [4]. Xiong and Hutton used Hamilton’s principle to obtain the governing equation and the boundary conditions of a multi-guided rotating string [5], and they proved that Hamilton’s principle could be used for the derivation of...

 

 

         

  

                   

                                                                        

  

 

 

  

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