The modal characteristics of the transverse vibration of an axially moving roller chain coupled with lumped mass were analyzed.The chain system was modeled by using the multi-body dynamics theory and the governing equ...The modal characteristics of the transverse vibration of an axially moving roller chain coupled with lumped mass were analyzed.The chain system was modeled by using the multi-body dynamics theory and the governing equations were derived by means of Lagrange's equations.The effects of the parameters,such as the axially moving velocity of the chain,the tension force,the weight of lumped mass and its time-variable assign position in chain span,on the modal characteristics of transverse vibration for roller chain were investigated.The numerical examples were given.It is found that the natural frequencies and the corresponding mode shapes of the transverse vibration for roller chain coupled with lumped mass change significantly when the variations of above parameters are considered.With the movement of the chain strand,the natural frequencies present a fluctuating phenomenon,which is different from the uniform chain.The higher the order of mode is,the greater the fluctuating magnitude and frequency are.展开更多
A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established ...A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established using Lagrange's equation. In order to obtain approximate solution, multiple time scales method, one of perturbation technique, was applied. Cases of non-resonant and 1:1:2:2 internal resonant were discussed. In the non-resonant case, the validity of multiple time scales method is confirmed, comparing numerical results derived from fourth order Runge-Kutta method with analytical results derived from first order approximate expression. In the 1:1:2:2 internal resonant case, modal amplitudes of Aa1 and Ab2 increase, respectively, from 0.38 to 0.63 and from 0.19 to 0.32, while the corresponding frequencies have an increase of almost 1.6 times with changes of initial conditions, indicating the existence of typical nonlinear phenomenon. In addition, the chaotic motion is found under this condition.展开更多
基金Project(50605060) supported by the National Natural Science Foundation of ChinaProject(20050056058) supported by the Research Fund for the Doctoral Program of Higher Education of ChinaProject(06YFJMJC03300) supported by the National Science Foundation of Tianjin,China
文摘The modal characteristics of the transverse vibration of an axially moving roller chain coupled with lumped mass were analyzed.The chain system was modeled by using the multi-body dynamics theory and the governing equations were derived by means of Lagrange's equations.The effects of the parameters,such as the axially moving velocity of the chain,the tension force,the weight of lumped mass and its time-variable assign position in chain span,on the modal characteristics of transverse vibration for roller chain were investigated.The numerical examples were given.It is found that the natural frequencies and the corresponding mode shapes of the transverse vibration for roller chain coupled with lumped mass change significantly when the variations of above parameters are considered.With the movement of the chain strand,the natural frequencies present a fluctuating phenomenon,which is different from the uniform chain.The higher the order of mode is,the greater the fluctuating magnitude and frequency are.
基金Projects(50574091, 50774084) supported by the National Natural Science Foundation of ChinaProject supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions+1 种基金Project(CXLX12_0949) supported by Research and Innovation Project for College Graduates of Jiangsu Province, ChinaProject(2013DXS03) supported by the Fundamental Research Funds for the Central Universities, China
文摘A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established using Lagrange's equation. In order to obtain approximate solution, multiple time scales method, one of perturbation technique, was applied. Cases of non-resonant and 1:1:2:2 internal resonant were discussed. In the non-resonant case, the validity of multiple time scales method is confirmed, comparing numerical results derived from fourth order Runge-Kutta method with analytical results derived from first order approximate expression. In the 1:1:2:2 internal resonant case, modal amplitudes of Aa1 and Ab2 increase, respectively, from 0.38 to 0.63 and from 0.19 to 0.32, while the corresponding frequencies have an increase of almost 1.6 times with changes of initial conditions, indicating the existence of typical nonlinear phenomenon. In addition, the chaotic motion is found under this condition.
