| In practical engineering,a lot of structure mechanics model can be simplified as gyroscopic continua,it includes the spinning continuum and axially moving continuum,such as: both beam and pole with spinning motion,and the string,beam,plate,shell,pipeline with axially moving motion,etc.The structure with axially moving motion,the body of revolution and the flow duct is a typical representative of the gyroscopic continuum,it’s application is very extensive,such as the transmission of the belt,high-rise elevator rope,scalable wing,the oil pipeline in deep-sea drilling,etc.,and as the main shaft of the turbine,the drive shaft of a car,the blades of an aero engine,etc.the dynamics analysis of it has important research significance.In dynamic analysis,gyroscopic effects occur in gyro systems.The gyroscopic effect of the axially moving material is pronounced via the gyroscopic coupling among the basis functions in the same motional direction.On the other hand,the gyroscopic coupling of the spinning structure acts in the two different directions of motion.This paper introduced the concept of bi-gyroscopic effect,considering the bi-gyroscopic effect co-exist,such as the drill string used in oil drilling and the drill in machine tool processing,it is the combination of axially moving motion and spinning motion,and like a revolving missile in the military war and the spin satellite,it is the spinning motion and rotating motion,To study the vibration characteristics of the structures with bi-gyroscopic effect.The bi-gyroscopic effect makes the gyroscopic system have unique dynamic behavior,which also brings some challenges to its theoretical analysis.The main contents of this thesis can be summarized as follows:(1)On the basis of the single gyroscopic system,we study the dynamic characteristic of bi-gyroscopic continua by introducing bi-gyroscopic effect,the bigyroscopic system is divided into two types: the combinations of different types of bigyroscopic effect and the combinations of same type of bi-gyroscopic effect.(2)For the bi-gyroscopic system of the combinations of different types of bigyroscopic effect,the beam model with axially moving motion and spinning motion is used as the object of study,and the nonlinear vibration differential equations of beam with axially moving motion and spinning motion are derived by using Hamilton’s principle,and the equation is discretized by Galerkin method.The linear analysis of the dynamic equation is carried out: the influence of bi-gyroscopic effects on the natural frequencies,modes,and stability is investigated by an analytical method applied to the discretized equations,and the complex modes describing both whirling motions and traveling waves are investigated in detail for such bi-gyroscopic system.(3)For the bi-gyroscopic system of the combinations of same types of bi-gyroscopic effect,the beam model with rotating motion and spinning motion is used as the object of study,and the nonlinear vibration differential equations of beam with rotating motion and spinning motion are derived by using Hamilton’s principle,and the equation is discretized by Galerkin method.The linear analysis of the dynamic equation is carried out: the influence of bi-gyroscopic effects on the natural frequencies,modes,and stability is investigated by an analytical method applied to the discretized equations,and the complex modes describing both whirling motions and waving motions are investigated in detail for such bi-gyroscopic system.(4)The nonlinear analysis of the dynamic equations of the two types of beams are carried out: the motion equations are solved by using the multiscale method,the modal and energy transfer problems of the undamped free vibration of the gyroscopic system are studied.It is found that: the center of the cross section of the midpoint of the beam will become a four-leaf grassy trajectory when the two types of beams are in inner resonance,and the energy of the system is always going back and forth between two modes when the beam is undamped free vibration. |
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