Mote, Classical vibration analysis of axially moving continua. Chen, Steady-state responses and their stability of nonlinear vibration of an axially accelerating string. Pakdemirli, Lie group theory and analytical solutions for the axially accelerating string problem. Department of Vehicle Engineering, School of Rail Transportation, Soochow University, Suzhou 215131, Jiangsu, China. Ulsoy, Stability analysis of an axially accelerating string. Nonlinear transverse vibration of nano-strings based on the differential type of nonlocal theory. Ceranoglu, Transverse vibration of an axially accelerating string. Batan, Dynamic stability of a constantly accelerating string. Miranker, The wave equation in a medium of motion. Ulsoy, Stability and limit cycles of parametrically excited, axially moving strings. Lin, Dynamic stability of a moving string undergoing three-dimensional vibration. Chen, A numerical algorithm for non-linear parametric vibration analysis of a viscoelastic moving belt. Wu, Dynamic response of the parametrically excited axially moving string constituted by the Boltzmann superposition principle. In order to control the transverse waves in a vibrating string. Zu, Nonlinear vibration of parametrically excited moving belts, part 2: stability analysis. explain the theory behind band pass filter control and PID control as applied to a. Zu, Nonlinear vibration of parametrically excited moving belts, part 1: dynamic response. Zu, Non-linear vibrations of viscoelastic moving belts, part 2: forced vibration analysis.
#Transverse vibration of strings theory free
Zu, Non-linear vibrations of viscoelastic moving belts, part 1: free vibration analysis. Chen, The transient amplitude of the viscoelastic travelling string: an integral constitutive law. Zu, Transverse vibration of axially moving strings and its control. Abrate, Vibration of belts and belt drives. Mote, Current research on the vibration and stability of axially-moving materials. Mote, Dynamic stability of axially moving materials. Some numerical examples highlighting the effects of the related parameters on the stability conditions are presented.Ĭ.D. Lyapunov's linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions for two-to-one parametric resonance. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation are presented. Closed-form solutions for the amplitude of the vibration and the existence conditions of nontrivial steady-state response in two-to-one parametric resonance are obtained. The method of multiple scales is applied directly to the equation, and the solvability condition of eliminating secular terms is established. The nonlinear partial differential equation that governs transverse vibration of the string is derived from Newton's second law. The transport speed is assumed to be a constant mean speed with small harmonic variations.
Two-to-one parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated.
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