Transverse Parametric Vibration Analysis Of Axially Moving Beams And In-plane Transporting Plates With Internal Resonance

A variety of engineering systems,such as lifting cable,band saw,conveyor belt,power conveyor belt,textile fiber and strip steel,may be simulated as moving structures.Due to variations in moving speed,the moving structures suffer from the occurrence of large transverse vibrations.In most cases,these transverse vibrations are harmful and seriously affect the production and processing.On the other hand,the moving structure is a typical gyroscopic continuum.The theoretical analysis is difficult due to the existence of gyroscopic terms.Thus,the study of the transverse vibration of moving structures has very broad engineering application prospects and important theoretical significance.In this dissertation,the vibration characteristics of moving structures are investigated.The dissertation is organized as follows:Chapter 1 clarifies the purpose and significance of this thesis and introduces the research background and current situation of moving structures in detail.Finallly,the main contents and innovations of this dissertation are presented.In Chapter 2,the dynamic stability of an axially accelerating viscoelastic Euler beam is revisited.The variable tension caused by the axial acceleration is introduced.The effects of the nonhomogeneous boundary conditions are emphasized.The governing equations and the corresponding nonhomogeneous boundary conditions of the beam are derived from the generalized Hamilton principle.The method of multiple scales is applied to analyze the parametric stabilities of the beam with 1:3 internal resonance under one-and two-frequency parametric excitation.More accurate stability boundaries are obtained by introducing nonhomogeneous boundary conditions.The approximate analytical results are numerically verified by the differential quadrature scheme.In Chapter 3,nonlinear parametric vibrations are investigated in the case of the 1:2 principal parametric and 1:3 internal resonance of an axially accelerating viscoelastic Euler beam subjected to nonhomogeneous boundary conditions.The relation between the acceleration and the longitudinally varying tensions is introduced.A nonlinear integro-partial-differential equation and corresponding nonhomogeneous boundary conditions are presented.The method of multiple scales is applied to analyze the principal parametric and internal resonances of the beam under one-and two-frequency parametric excitation.The effects of some system parameters on the steady-state responses are investigated.The steady-state responses under homogeneous and nonhomogeneous boundary conditions are compared.The differential quadrature scheme is applied to verify the approximate analytical results.In Chapter 4,the generalized Hamilton principle and Kelvin viscoelastic constitutive relation are introduced to establish the nonlinear partial differential equation and the nonhomogeneous boundary conditions of an in-plane accelerating viscoelastic plate.The effects of the nonhomogeneous boundary conditions are emphasized.Ignoring the nonlinearity,the modified solvability conditions in principal parametric and internal resonances are established by the method of multiple scales.The Routh-Hurwitz criterion is introduced to determine the instability boundaries.The differential quadrature scheme is developed to verify the approximate analytical results obtained by the method of multiple scales.In Chapter 5,nonlinear transverse vibrations of an in-plane accelerating viscoelastic plate are investigated in the presence of principal parametric and 1:3 internal resonance.The method of multiple scales is applied to establish the solvability conditions to obtain the steady-state responses in the parametric and internal resonance.The stability of the response is determined by the Routh-Hurvitz criterion.The steady-state responses under homogeneous and nonhomogeneous boundary conditions are compared.A differential quadrature scheme is developed to solve numerically the governing equation under the given boundary conditions.