Authors: Xiao Ping Gao, Yi Ze Sun, Zhuo Meng, Zhi Jun Sun

Abstract: In this paper, the non-linear tranverse vibration of an axially moving pile-yarn with time-dependent tension are investigated. The pile-yarn material is modeled as Kelvin-Voigt element. A partial-differential equation governing the transverse vibration is derived from the Newton’s second law. The Galerkin method and the fourth order Runge-Kutta method are used to solve the governing non-linear differential equation. The effects of the transport speed, the tension perturbation amplitude and the damping coefficient on the dynamic behaviour of the system are numerically investigated.

1517

Authors: Li Wang, Huai Hai Chen, Xu Dong He

Abstract: The transverse vibration equation of an axially moving cantilever beam with tip mass is given. The instant linearized equations are set up based on Galerkin’s method. The tip mass influences to the first three order modes of the beam are computed. The calculated responses using the modes with tip mass are compared with the results using the modes without tip mass. Modes without tip mass can replace the modes with tip mass while the tip mass is small. The heavier the tip mass is, the bigger the difference of using the replacement is. It is found that the experimental result is fit well with the theoretical result using the modes with tip mass.

200

Authors: Zhi Xin Zhang, Zhen Dong Hu

Abstract: From the view of flexible multibody dynamics, this paper considers not only Euler-Bernoulli beam assumption but also the effects of rotary inertia and beam’s inner tension, the equation of motion and associated boundary conditions of the dynamic model are derived by using the extended Hamilton’s principle. Converting the varying-time equation into a varying-coefficient differential equation in fixed region by substituting argument. And truncating the equation to a set of varying-time ordinary equations expressed by modal coordinates based on Assumption Modal Method and Galerkin Discrete Method. Then the equations were solved by using Newmark time integration method. The results show that moving mass excites mainly the first order mode vibration of beam. Before the moving mass disengages the beam, the dynamic effect of mass is so small that cantilever beam is lacked of obvious vibration. Its transverse displacement was mainly driven by static load. After the moving mass disengages the beam, the shorten length and shrinking movement of beam make the instantaneous vibration frequency continuously reduce and the vibration displacement gradually decrease too. While, at the same time, its total mechanical energy is increasing, so the beam is in unsteady vibration state.

934

Authors: Feng Qun Zhao, Miao Miao Wang

Abstract: Assumed that the viscoelastic material of the beam obeys the Kelvin-Voigt fractional derivative constitutive relationship, the governing equation of the axially moving viscoelastic beam is established by the D ' Alembert principle. Based on Galerkin method, the fractional ordinary differential equations of simply supported beam are obtained. Then, Haar wavelet algorithm based on fractional integral operator matrix is employed to numerically solve the resulting equations. The effects of moving speed on the vibration behaviors of moving viscoelastic beams are investigated.

1177

Authors: Jin Mei Wang, Ying Hui Li, E Chuan Yang

Abstract: The transverse vibration characteristic of the viscoelastic sandwich beam with axial speed is studied under the coupled temperature field and displacement field. Based on the theory of Euler - Bernouli beam and the constitutive relation of Kelvin viscoelastic material model, the transverse vibration equation of the axially moving beam is established ; considering the interaction of the material deformation and the heat conduction, the coupled governing equation of the beam is obtained. and the coupled thermoelastic dynamics system are obtained by Galerkin method. The related thermal parameters on the vibration frequency are analyzed by using numerical method.

301