Transfer Matrix Method for Multibody Systems: Theory and Applications

ISBN-13: 9781118724804 / Angielski / Twarda / 2018 / 768 str.

Xiaoting Rui; Laifeng Yun; Yuqi Lu

Opis

TRANSFER MATRIX METHOD FOR MULTIBODY SYSTEMS: THEORY AND APPLICATIONS Xiaoting Rui, Guoping Wang and Jianshu Zhang - Nanjing University of Science and Technology, China Featuring a new method of multibody system dynamics, this book introduces the transfer matrix method systematically for the first time.

Spis treści

Introduction xiAbout the Author xiiiForeword One for the Chinese Edition xvForeword Two for the Chinese Edition xviiForeword Three for the Chinese Edition xixForeword Four for the Chinese Edition xxiProfessor Rui's Method--Discrete Time Transfer Matrix Method for Multibody System Dynamics xxiiiPreface xxv1 Introduction 11.1 The Status of the Multibody System Dynamics Method 11.2 The Transfer Matrix Method and the Finite Element Method 31.3 The Status of the Transfer Matrix Method for a Multibody System 51.4 Features of the Transfer Matrix Method for Multibody Systems 71.5 Launch Dynamics 121.6 Features of this Book 131.7 Sign Conventions 14Part I Transfer Matrix Method for Linear Multibody Systems 192 Transfer Matrix Method for Linear Multibody Systems 212.1 Introduction 212.2 State Vector, Transfer Equation and Transfer Matrix 222.3 Overall Transfer Equation, Overall Transfer Matrix and Boundary Conditions 312.4 Characteristic Equation 322.5 Computation for State Vector and Vibration Characteristics 362.6 Vibration Characteristics of Multibody Systems 412.7 Eigenvalues of Damped Vibration 562.8 Steady-state Response to Forced Vibration 632.9 Steady-state Response of Forced Damped Vibration 703 Augmented Eigenvector and System Response 793.1 Introduction 793.2 Body Dynamics Equation and Parameter Matrices 803.3 Basic Theory of the Orthogonality of Eigenvectors 833.4 Augmented Eigenvectors and their Orthogonality 863.5 Examples of the Orthogonality of Augmented Eigenvectors 963.6 Transient Response of a Multibody System 1023.7 Steady-state Response of a Damped Multibody System 1113.8 Steady-state Response of a Multibody System 1173.9 Static Response of a Multibody System 1244 Transfer Matrix Method for Nonlinear and Multidimensional Multibody Systems 1294.1 Introduction 1294.2 Incremental Transfer Matrix Method for Nonlinear Systems 1294.3 Finite Element Transfer Matrix Method for Two-dimensional Systems 1404.4 Finite Element Riccati Transfer Matrix Method for Two-dimensional Nonlinear Systems 1544.5 Fourier Series Transfer Matrix Method for Two-dimensional Systems 1624.6 Finite Difference Transfer Matrix Method for Two-dimensional Systems 1674.7 Transfer Matrix Method for Two-dimensional Systems 170Part II Transfer Matrix Method for Multibody Systems 1815 Transfer Matrix Method for Multi-rigid-body Systems 1835.1 Introduction 1835.2 State Vectors, Transfer Equations and Transfer Matrices 1845.3 Overall Transfer Equation and Overall Transfer Matrix 1855.4 Transfer Matrix of a Planar Rigid Body 1855.5 Transfer Matrix of a Spatial Rigid Body 1875.6 Transfer Matrix of a Planar Hinge 1885.7 Transfer Matrix of a Spatial Hinge 1895.8 Transfer Matrix of an Acceleration Hinge 1925.9 Algorithm of the Transfer Matrix Method for Multibody Systems 1935.10 Numerical Examples of Multibody System Dynamics 1946 Transfer Matrix Method for Multi-flexible-body Systems 1996.1 Introduction 1996.2 State Vector, Transfer Equation and Transfer Matrix 2006.3 Overall Transfer Equation and Overall Transfer Matrix 2016.4 Transfer Matrix of a Planar Beam 2016.5 Transfer Matrix of a Spatial Beam 2056.6 Numerical Examples of Multi-flexible-body System Dynamics 211Part III Discrete Time Transfer Matrix Method for Multibody Systems 2177 Discrete Time Transfer Matrix Method for Multibody Systems 2197.1 Introduction 2197.2 State Vector, Transfer Equation and Transfer Matrix 2217.3 Step-by-step Time Integration Method and Linearization 2257.4 Transfer Matrix of a Planar Rigid Body 2357.5 Transfer Matrices of Spatial Rigid Bodies 2427.6 Transfer Matrices of Planar Hinges 2517.7 Transfer Matrices of Spatial Hinges 2567.8 Algorithm of the Discrete Time Transfer Matrix Method for Multibody Systems 2597.9 Numerical Examples of Multibody System Dynamics 2598 Discrete Time Transfer Matrix Method for Multi-flexible-body Systems 2658.1 Introduction 2658.2 Dynamics of a Flexible Body with Large Motion 2668.3 State Vector, Transfer Equation and Transfer Matrix 2768.4 Transfer Matrix of a Beam with Large Planar Motion 2778.5 Transfer Matrices of Smooth Hinges Connected to a Beam with Large Planar Motion 2828.6 Transfer Matrices of Spring Hinges Connected to a Beam with Large Planar Motion 2868.7 Transfer Matrix of a Fixed Hinge Connected to a Beam 2928.8 Dynamics Equation of a Spatial Large Motion Beam 2968.9 Transfer Matrix of a Spatial Large Motion Beam 3008.10 Transfer Matrices of Fixed Hinges Connected to a Beam with Large Spatial Motion 3058.11 Transfer Matrices of Smooth Hinges Connected to a Beam with Large Spatial Motion 3098.12 Transfer Matrices of Spring Hinges Connected to a Beam with Large Spatial Motion 3138.13 Algorithm of the Discrete Time Transfer Matrix Method for Multi-flexible-body Systems 3188.14 Planar Multi-flexible-body System Dynamics 3188.15 Spatial Multi-flexible-body System Dynamics 3229 Transfer Matrix Method for Controlled Multibody Systems 3279.1 Introduction 3279.2 Mixed Transfer Matrix Method for Multibody Systems 3289.3 Finite Element Transfer Matrix Method for Multibody Systems 3389.4 Finite Segment Transfer Matrix Method for Multibody Systems 3419.5 Transfer Matrix Method for Controlled Multibody Systems I 3489.6 Transfer Matrix Method for Controlled Multibody Systems II 36210 Derivation and Computation of Transfer Matrices 37710.1 Introduction 37710.2 Derivation from Dynamics Equations 37810.3 Derivation from an nth-order Differential Equation 38810.4 Derivation from n First-order Differential Equations 39810.5 Derivation from Stiffness Matrices 40110.6 Computational Method of the Transfer Matrix 40210.7 Improved Algorithm for Eigenvalue Problems 40610.8 Properties of the Inverse Matrix of a Transfer Matrix 40810.9 Riccati Transfer Matrix Method for Multibody Systems 41710.10 Stability of the Transfer Matrix Method for Multibody Systems 42811 Theorem to Deduce the Overall Transfer Equation Automatically 43311.1 Introduction 43311.2 Topology Figure of Multibody Systems 43311.3 Automatic Deduction of the Overall Transfer Equation of a Closed-loop System 43511.4 Automatic Deduction of the Overall Transfer Equation of a Tree System 43511.5 Automatic Deduction of the Overall Transfer Equation of a General System 43911.6 Automatic Deduction Theorem of the Overall Transfer Equation 44211.7 Numerical Example of Closed-loop System Dynamics 44311.8 Numerical Example of Tree System Dynamics 45111.9 Numerical Example of Multi-level System Dynamics 47011.10 Numerical Example of General System Dynamics 474Part IV Applications of the Transfer Matrix Method for Multibody Systems 48912 Dynamics of Multiple Launch Rocket Systems 49112.1 Introduction 49112.2 Launch Dynamics Model of the System and its Topology 49212.3 State Vector, Transfer Equation and Transfer Matrix 49612.4 Overall Transfer Equation of the System 50212.5 Vibration Characteristics of the System 50412.6 Dynamics Response of the System 50612.7 Launch Dynamics Equation and Forces Acting on the System 51212.8 Dynamics Simulation of the System and its Test Verifying 51612.9 Low Rocket Consumption Technique for the System Test 53312.10 High Launch Precision Technique for the System 54113 Dynamics of Self-propelled Launch Systems 54513.1 Introduction 54513.2 Dynamics Model of the System and its Topology 54513.3 State Vector, Transfer Equation and Transfer Matrix 54913.4 Overall Transfer Equation of the System 55513.5 Vibration Characteristics of the System 55513.6 Dynamic Response of the System 55713.7 Launch Dynamic Equations and Forces Analysis 56313.8 Dynamics Simulation of the System and its Test Verifying 57014 Dynamics of Shipboard Launch Systems 58114.1 Introduction 58114.2 Dynamics Model of Shipboard Launch Systems 58114.3 State Vector, Transfer Equation and Transfer Matrix 58314.4 Overall Transfer Equation of the System 58714.5 Launch Dynamics Equation and Forces of the System 58914.6 Solution of Shipboard Launch System Motion 59814.7 Dynamics Simulation of the System and its Test Verifying 59915 Transfer Matrix Library for Multibody Systems 60715.1 Introdution 60715.2 Springs 60715.3 Rotary Springs 60915.4 Elastic Hinges 61015.5 Lumped Mass Vibrating in a Longitudinal Direction 61115.6 Vibration of Rigid Bodies 61215.7 Beam with Transverse Vibration 61515.8 Shaft with Torsional Vibration 62015.9 Rod with Longitudinal Vibration 62115.10 Euler-Bernoulli Beam 62215.11 Rectangular Plate 62415.12 Disk 62915.13 Strip Element of a Two-dimensional Thin Plate 63515.14 Thick-walled Cylinder 63815.15 Thin-walled Cylinder 64015.16 Coordinate Transformation Matrix 64215.17 Linearization and State Vectors 64515.18 Spring and Damper Hinges Connected to Rigid Bodies 64615.19 Smooth Hinges Connected to Rigid Bodies 64815.20 Rigid Bodies Moving in a Plane 64915.21 Spatial Rigid Bodies with Large Motion and Various Connections 65115.22 Planar Beam with Large Motion 65415.23 Spatial Beam with Large Motion 65615.24 Fixed Hinges Connected to a Planar Beam with Large Motion 65815.25 Fixed Hinges Connected to a Spatial Beam with Large Motion 66015.26 Smooth Hinges Connected to a Beam with Large Planar Motion 66315.27 Smooth Hinges Connected to a Beam with Large Spatial Motion 66615.28 Elastic Hinges Connected to a Beam with Large Planar Motion 66815.29 Elastic Hinges Connected to a Beam Moving in Space 67215.30 Controlled Elements of a Linear System 67515.31 Controlled Elements of a General Time-variable System 676Appendix I Rotation Formula Around an Axis 681Appendix II Orientation of a Body-fixed Coordinate System 683Appendix III List of Symbols 687Appendix IV International Academic Communion for the Transfer Matrix Method for Multibody Systems 693References 707Index 729

O autorze

Xiaoting Rui, Guoping Wang and Jianshu Zhang - Nanjing University of Science and Technology, P. R. China

Blurb

TRANSFER MATRIX METHOD FOR MULTIBODY SYSTEMS: THEORY AND APPLICATIONS

Xiaoting Rui, Guoping Wang and Jianshu Zhang – Nanjing University of Science and Technology, China 

Featuring a new method of multibody system dynamics, this book introduces the high programming transfer matrix method systematically for the first time. First developed by the lead author and his research team, this method has found numerous engineering and technological applications. Readers are first introduced to fundamental concepts like the body dynamics equation, augmented operator and augmented eigenvector before going in depth into precision analysis and computations of eigenvalue problems as well as dynamic responses. The book also covers a combination of mixed methods and practical applications in multiple rocket launch systems, self–propelled artillery as well as launch dynamics of on–ship weaponry.

Comprehensively introduces a new method of analyzing multibody dynamics for engineers 

Provides a logical development of the transfer matrix method as applied to the dynamics of multibody systems that consist of interconnected bodies

Features varied applications in weaponry, aeronautics, astronautics, vehicles and robotics 

Written by an internationally renowned author and research team with many years′ experience in multibody systems Transfer Matrix Method of Multibody System and Its Applications is an advanced level text for researchers and engineers in mechanical system dynamics. It is a comprehensive reference for advanced students and researchers in the related fields of aerospace, vehicle, robotics and weaponry engineering.