Study On The Key Technology Of The Dynamics Solver Of Transfer Matrix Method For Multibody Systems

Rui method,namely transfer matrix method for multibody systems(MSTMM),is a new method for multibody system dynamics(MSD)proposed and developed in recent 20 years.It does not need global dynamics equations in studying MSD and has been widely used due to the following features:low-order system matrices,speedy computation,high stylization,automatic deduction of overall transfer equation,etc.The theory and applications of MSTMM are developing rapidly,where the transfer matrix method for linear multibody systems(linear MSTMM)owns perfect theory and has been most widely used.As an important part of the National Defense 973 Project achievements,this thesis presents a novel methodology with the advantages of highly stylized dynamic modeling,computation and programming for the dynamics analysis of mechanical systems.And an object-oriented universal software framework for the dynamics solver based on MSTMM is designed.Taking the dynamics of linear multibody systems as an example,the linear MSTMM and extended transfer matrix method for multibody systems(MSETMM)are improved,and a solver with wide application range is developed.The present work liberates the mechanical workers and engineers from the complicated deduction of dynamics equations and programming,and provides a powerful tool for the dynamics computation and performance optimization of mechanical systems.The main contributions of this thesis are as follows:(1)The direction cosine matrix representing the orientations of hinge or flexible body elements is introduced into element transfer matrices.Then,all element transfer equations and transfer matrices are expressed in the same global inertial coordinate system,which significantly simplifies the deduction of system overall transfer equation.The value of system external force and its position as well as direction are described separately,which makes system body dynamics equation more specific and facilitates the deduction of system dynamics control equation.These two improvements enhance the stylization of linear MSTMM and facilitate developing universal program.(2)A novel method for dynamics control design based on linear MSTMM is proposed.The state space representation of multi-rigid-flexible-body system is derived by adopting system body dynamics equation and the orthogonality of augmented eigenvectors.Then,the controllability and observability analysis,lodel reduction and controller design are achieved.(3)MSETMM is improved by expressing the extended state vector with complex numbers,the extended transfer and geoletric equations of some typical elements are derived.The dynamics analysis in frequency domain based on MSETMM is established,and the accurate computations of frequency response function,steady state response and random vibration response statistics for damped multi-rigid-fiexible-body systems are achieved.(4)Object-oriented technique is employed to describe MSTMM,and the element transfer matrix library is preliminarily built in computer.Binary tree is employed to describe multibody system topology,and a combined storing approach is proposed to store element data and system topology.A recursive formula of system main transfer matrix is established,and the automatic deduction of overall transfer matrix by computer is achieved.The dynamics solver of transfer matrix method for multibody systems(MSTMMDS)is developed,where the computations of vibration characteristics,transient response,state space representation,frequency response function,steady state response and random vibration response statistics for mechanical systems are achieved.(5)MSTMMDS is used to study the vibration characteristics of a diamond fly-cutting machine tool,and the computational results are verified by modal test.The present method is used to Study the vibration characteristics of missiles and the dynamics of laser gyro strapdown inertial measurement unit(LGSIMU).Then,a novel magnetorheological elastomer isolator working in shear-squeeze mode is proposed for the LGSIMU on missile.Furthermore,a variable stiffness strategy for the vibration reduction of LGSIMU on missile is presented and verified by shaking table test.