Although the complex structure-preserving method presented in our previous studies can be used to investigate the orbit–attitude–vibration coupled dynamic behaviors of the spatial flexible damping beam,the simulatio...Although the complex structure-preserving method presented in our previous studies can be used to investigate the orbit–attitude–vibration coupled dynamic behaviors of the spatial flexible damping beam,the simulation speed still needs to be improved.In this paper,the infinite-dimensional dynamic model describing the orbit–attitude–vibration coupled dynamic problem of the spatial flexible damping beam is pretreated by the method of separation of variables,and the second-level fourth-order symplectic Runge–Kutta scheme is constructed to investigate the coupling dynamic behaviors of the spatial flexible damping beam quickly.Compared with the simulation speed of the complex structure-preserving method,the simulation speed of the symplectic Runge–Kutta method is faster,which benefits from the pretreatment step.The effect of the initial radial velocity on the transverse vibration as well as on the attitude evolution of the spatial flexible damping beam is presented in the numerical examples.From the numerical results about the effect of the initial radial velocity,it can be found that the appearance of the initial radial velocity can decrease the vibration frequency of the spatial beam and shorten the evolution interval for the attitude angle to tend towards a stable value significantly.In addition,the validity of the numerical results reported in this paper is verified by comparing with some numerical results presented in our previous studies.展开更多
This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink s...This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.展开更多
基金supported by the National Natural Science Foundation of China(12172281,11972284 and 11872303)Fund for Distinguished Young Scholars of Shaanxi Province(2019JC-29)+1 种基金Foundation Strengthening Programme Technical Area Fund(2021-JCJQ-JJ-0565)Fund of the Youth Innovation Team of Shaanxi Universities and the Open Foundation of State Key Laboratory of Structural Analysis of Industrial Equipment(GZ19103).
文摘Although the complex structure-preserving method presented in our previous studies can be used to investigate the orbit–attitude–vibration coupled dynamic behaviors of the spatial flexible damping beam,the simulation speed still needs to be improved.In this paper,the infinite-dimensional dynamic model describing the orbit–attitude–vibration coupled dynamic problem of the spatial flexible damping beam is pretreated by the method of separation of variables,and the second-level fourth-order symplectic Runge–Kutta scheme is constructed to investigate the coupling dynamic behaviors of the spatial flexible damping beam quickly.Compared with the simulation speed of the complex structure-preserving method,the simulation speed of the symplectic Runge–Kutta method is faster,which benefits from the pretreatment step.The effect of the initial radial velocity on the transverse vibration as well as on the attitude evolution of the spatial flexible damping beam is presented in the numerical examples.From the numerical results about the effect of the initial radial velocity,it can be found that the appearance of the initial radial velocity can decrease the vibration frequency of the spatial beam and shorten the evolution interval for the attitude angle to tend towards a stable value significantly.In addition,the validity of the numerical results reported in this paper is verified by comparing with some numerical results presented in our previous studies.
基金Supported by the National Natural Science Foundation of China under Grant No.11261037the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No.2014MS0111+1 种基金the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No.CYYC2011050the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT14A04
文摘This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.
