Structure-preserving approach for infinite dimensional nonconservative system  

作　　者：Weipeng Hu 

机构地区：[1]School of Civil Engineering and Architecture, Xi'an University of Technology

出　　处：《Theoretical & Applied Mechanics Letters》2018年第6期404-407,I0005,共5页力学快报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant 11672241);the Seed Foundation of Qian Xuesen Laboratory of Space Technology;the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment (Grant GZ1605)

摘　　要：The current structure-preserving theory, including the symplectic method and the multisymplectic method, pays most attention on the conservative properties of the continuous systems because that the conservative properties of the conservative systems can be formulated in the mathematical form. But, the nonconservative characteristics are the nature of the systems existing in engineering. In this letter, the structure-preserving approach for the infinite dimensional nonconservative systems is proposed based on the generalized multi-symplectic method to broaden the application fields of the current structure-preserving idea. In the numerical examples,two nonconservative factors, including the strong excitation on the string and the impact on the cantilever, are considered respectively. The vibrations of the string and the cantilever are investigated by the structure-preserving approach and the good long-time numerical behaviors as well as the high numerical precision of which are illustrated by the numerical results presented.The current structure-preserving theory, including the symplectic method and the multisymplectic method, pays most attention on the conservative properties of the continuous systems because that the conservative properties of the conservative systems can be formulated in the mathematical form. But, the nonconservative characteristics are the nature of the systems existing in engineering. In this letter, the structure-preserving approach for the infinite dimensional nonconservative systems is proposed based on the generalized multi-symplectic method to broaden the application fields of the current structure-preserving idea. In the numerical examples,two nonconservative factors, including the strong excitation on the string and the impact on the cantilever, are considered respectively. The vibrations of the string and the cantilever are investigated by the structure-preserving approach and the good long-time numerical behaviors as well as the high numerical precision of which are illustrated by the numerical results presented.

关 键 词：Structure-preserving approach Generalized multi-symplectic HAMILTONIAN Nonconservative system Non-smooth model 

分 类 号：O3[理学—力学]