Analyzing dynamic response of non-homogeneous string fixed at both ends

• Published in: International journal of non-linear mechanics 2012-12, Vol.47 (10), p.1111-1115
• Main Authors: Hu, W.P., Han, S.M., Deng, Z.C.
• Format: Article
• Language: English
• Subjects: Conservation; Conservation law; Dynamic mechanical properties; Dynamic response; Dynamic structural analysis; Dynamical systems; Generalized multi-symplectic; Mathematical analysis; Non-homogeneous string; Strings; Vibration
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2011.09.008

To survey the local conservation properties of complex dynamic problems, a structure-preserving numerical method, named as generalized multi-symplectic method, is proposed to analyze the dynamic response of a non-homogeneous string fixed at both ends. Firstly, based on the multi-symplectic idea, a generalized multi-symplectic form derived from the vibration equation of a non-homogeneous string is presented. Secondly, several conservation laws are deduced from the generalized multi-symplectic form to illustrate the local properties of the system. Thirdly, a centered box difference scheme satisfying the discrete local momentum conservation law exactly, named as a generalized multi-symplectic scheme, is constructed to analyze the dynamic response of the non-homogeneous string fixed at both ends. Finally, numerical experiments on the generalized multi-symplectic scheme are reported. The results illustrate the high accuracy, the good local conservation properties as well as the excellent long-time numerical behavior of the generalized multi-symplectic scheme well. ► We propose a generalized multi-symplectic method to analyze the dynamic response of a non-homogeneous string. ► A generalized multi-symplectic form with several conservation laws derived from the vibration equation of the string is presented. ► And then, a box scheme is constructed to analyze the dynamic response of the string. ► The results illustrate some good numerical behaviors of the scheme.