Based on the linear viscoelastic differential constitutive law andcable structural model, the coupled longitudinal-transverse wavesthat propagate along a viscoelastic cable with small curvature isinvesti- gated. A mat...Based on the linear viscoelastic differential constitutive law andcable structural model, the coupled longitudinal-transverse wavesthat propagate along a viscoelastic cable with small curvature isinvesti- gated. A mathematical model is presented that describes thethree-dimensional nonlinear response of a vis- coelastic cable. Anasymptotic form of this model is obtained for the linear response ofcables having small equilibrium curvature.展开更多
Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to...Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to be of the hereditary integral type.The partial differential -integral equations of motion are derivedfirst. Then by applying Galerkin's method, the governing equationsare reduced to a set of second-order non- linear differential-integral equations which are solved by finite difference numericalintegration procedures. Finally, the effects of the viscosityparameter and the elastic parameter on the transient amplitudes ofthe first Mode are investigated by numerical simulation.展开更多
The problem considered is an initially stressed viscoelastic cable with small sag. The cable material is assumed to be constituted by the hereditary differential type. The partial differential equations of motion is d...The problem considered is an initially stressed viscoelastic cable with small sag. The cable material is assumed to be constituted by the hereditary differential type. The partial differential equations of motion is derived first. Then by applying Galerkin's method, the governing equations are reduced to a set of third order nonlinear ordinary differential equations which are solved by Runge-Kutta numerical integration procedures. Only after the transverse vibration of the plane is considered and the nonlinear terms are neglected, can the nonlinear ordinary differential equations be expressed as a continuous state equation in the state space. The matrix of state transition is approximated stepwise by the matrix exponential; in addition, the state equation is discretized to a difference equation to improve the computing efficiency. Furthermore, an optimal control of procedure system based on the minimization of a quadratic performance index for state vector and control forces is developed. Finally, the effect of dynamic response of the cable, which is produced by viscoelastic parameters, is testified by the research of digital simulation.展开更多
The coupled longitudinal-transverse waves propagating freely along a viscoelastic cable was studied. The frequency-spectrum equation governing propagating waves and the formulations of the phase velocities and the gro...The coupled longitudinal-transverse waves propagating freely along a viscoelastic cable was studied. The frequency-spectrum equation governing propagating waves and the formulations of the phase velocities and the group velocities characterizing propagating waves were derived. The effects of viscosity parameters on the phase velocities and the group velocities were investigated with numerical simulation. The analyses show that viscosity has a strong influence on the phase velocity and the group velocity of propagating waves and attenuation waves for longitudinal-dominant waves, but the phase velocities of propagating waves of transverse-dominant waves do not change with viscosity.展开更多
基金the National Natural Science Foundation of China(No.59635140)
文摘Based on the linear viscoelastic differential constitutive law andcable structural model, the coupled longitudinal-transverse wavesthat propagate along a viscoelastic cable with small curvature isinvesti- gated. A mathematical model is presented that describes thethree-dimensional nonlinear response of a vis- coelastic cable. Anasymptotic form of this model is obtained for the linear response ofcables having small equilibrium curvature.
基金the National Natural Science Foundation of China (No.59635140)the National Postdoctoral Foundation of China.
文摘Both the inplane and out-of-plane transverse vibrations of aviscoelastic cable subjected to an initial stress distributinguniform on the cross section are studied. The constitution of thecable material is as- sumed to be of the hereditary integral type.The partial differential -integral equations of motion are derivedfirst. Then by applying Galerkin's method, the governing equationsare reduced to a set of second-order non- linear differential-integral equations which are solved by finite difference numericalintegration procedures. Finally, the effects of the viscosityparameter and the elastic parameter on the transient amplitudes ofthe first Mode are investigated by numerical simulation.
文摘The problem considered is an initially stressed viscoelastic cable with small sag. The cable material is assumed to be constituted by the hereditary differential type. The partial differential equations of motion is derived first. Then by applying Galerkin's method, the governing equations are reduced to a set of third order nonlinear ordinary differential equations which are solved by Runge-Kutta numerical integration procedures. Only after the transverse vibration of the plane is considered and the nonlinear terms are neglected, can the nonlinear ordinary differential equations be expressed as a continuous state equation in the state space. The matrix of state transition is approximated stepwise by the matrix exponential; in addition, the state equation is discretized to a difference equation to improve the computing efficiency. Furthermore, an optimal control of procedure system based on the minimization of a quadratic performance index for state vector and control forces is developed. Finally, the effect of dynamic response of the cable, which is produced by viscoelastic parameters, is testified by the research of digital simulation.
文摘The coupled longitudinal-transverse waves propagating freely along a viscoelastic cable was studied. The frequency-spectrum equation governing propagating waves and the formulations of the phase velocities and the group velocities characterizing propagating waves were derived. The effects of viscosity parameters on the phase velocities and the group velocities were investigated with numerical simulation. The analyses show that viscosity has a strong influence on the phase velocity and the group velocity of propagating waves and attenuation waves for longitudinal-dominant waves, but the phase velocities of propagating waves of transverse-dominant waves do not change with viscosity.
