Complex Modal Analysis Of Generalized Damping Gyroscopic Continuous System

The coexistence of the distributed transverse vibration and gyroscopic effect,bring the gyroscopic continuous system both the particular dynamic behavior and the great challenge in theoretical analysis.Meanwhile,as the mechanics model of band saws,axially moving string/beam/membrane/planet/shell,convey fluid and rotating structure,the vibration analysis of the gyroscopic continuous system has an important engineering significance.This dissertation mainly investigates the dynamic characteristic of the generalized damped gyroscopic continuous system,including the natural frequency,natural formation and the dynamic response by using the complex modal analysis method.The dissertation is organized as following:Chapter 1 surveys the development of the gyroscopic continuous system and the axially moving continua with viscoelastic foundation in the corresponding theories,and presents the significance,main contents,and main innovations of this dissertation.In Chapter 2,based on the governing equation of the gyroscopic continuous system and its specific representatives,the generalized damped gyroscopic continuous system is introduced and the governing equation is presented.What the generalized damped gyroscopic continuous system standards for is discussed when different operators are selected.Chapter 3 presents the eigenvalues and eigenfunctions of the generalized damped gyroscopic continuous system.The orthogonality of the eigenfunctions are deduced based on the relationship of the original equation and the adjoint equation.At last,the orthogonalitys of the degenerate forms of generalized damped gyroscopic continuous system are discussed.In Chapter 4,the orthogonality of the generalized damped gyroscopic continuous system is applied to decouple the governing equation,and exact closed-form solution of the response is obtained to arbitrary initial condition and external excitation.In Chapter 5,the dynamic characteristics of the axially moving string supported by a viscoelastic foundation are analysed.Firstly,the equation of motion and boundary condition are developed using generalized Hamilton principle.Exact closed-form solution of eigenvalues and eigenfunctions are obtained.The adjoint eigenfunctions of an auxiliary system are introduced to analyse the corresponding non-self-adjoint system.The response to arbitrary external excitation and initial conditions can be expressed in the modal expansion expression.Numerical examples are presented to validate the proposed approach.At last,the critical speed,critical damping,the cut frequency,the frequency response curve and the effects of damping on free vibration and forced vibration are discussed.In chapter 6,the dynamic characteristics of the axially moving beam supported by a viscoelastic foundation are analysed.The equation of motion and boundary condition are developed using generalized Hamilton principle.Semi-closed-form solution of eigenvalues and eigenfunctions are obtained.The response to arbitrary external excitation and initial conditions can be expressed in the modal expansion expression.Numerical examples are presented to illustrate the proposed approach.The critical speed,critical damping,the effects of damping on free vibration and forced vibration are discussed.In chapter 7,the dynamic characteristics of the axially moving beam supported by a partially viscoelastic foundation are analysed.The equation of motion is developed using generalized Hamilton principle,eigenvalues and eigenfunctions are obtained.The effects of damping on natural frequency and natural formation are discussed.The critical damping are discussed.