Non-linear Dynamics On Transverse Vibrations Of Moving Belts By Theoretical And Experimental Methods

Axially moving belt is very important in the mechanism energy transmission system.Ignoring bending stiffness the transmission belt can be modeled as an axially moving string.In engineering,understanding the transverse vibrations of axially moving strings is import for the safe design and operation of a variety of machines and structures.The research of the transverse vibration in that case may pay contribution to the context of continuous gyroscopic systems.In this paper,firstly,the partial-differential equation is derived from considering the transverse displacement only,and considering viscoelastic of material and the periodic fluctuation of the tension.By using the Galerkin method,we transformed partial differential equations into ordinary differential equations,and we get the general formula.The string model governed by partial differential equations(PDEs)as well as the discretized model governed by ordinary differential equations(ODEs)are used in the dynamical study of the string.The invariant manifold method is employed to derive the complex mode functions of the discretized models,which are compared to the mode functions derived from the continuous model.It is found that the complex mode functions constituted by trial functions of the discretized system yield good agreement with that derived by the continuous system.This discretization method is compared with the original continuous system to validate its efficiency.In this paper,we propose a noval gyroscopic decoupled method,and in resonance response we use gyroscopic decoupled method and multiple scale method to obtain response of nonlinear system,and we discussed the relationship between nonlinear frequency and initial amplitude.The method of multiple scales is subsequently applied to investigate the 1:3 internal resonance based on the gyroscopic decoupled nonlinear system.The classic procedure is apply the multiple scale method directly to the gyroscopic coupled system.The results of the multiple scale analysis to both classical,gyroscopic coupled system and the decoupled system introduced in this paper are further compared and discussed with a numerical example.We found that the gyroscopic decoupled system is much better in frequency and the classic method is better in amplitude.Gyroscopic decoupled method is a novel procedure for solve the nonlinear gyroscopic system.The tension is a constant mean value with small periodic fluctuations,based on this,we use multiple scales method and number iteration method to handle those governing equations.The amplitude response and stability could be discussed for parametric and combination resonance in disturbed systems at near exact-resonance.Numerical examples are presented to highlight the effects of speed and nonlinearity.At last,we set up an experimental platform for testing the transverse and introduce its working principle.The experimental system consists of three parts,machinery part,measurement part and control part.We researched the relationship between axially moving speed and vibration frequency,the relationship between axially moving speed with tension.The vibration of the system is observed by the high-speed camera.