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Transfer Matrix Method for Multibody Systems

Author Jianshu Zhang , Guoping Wang , Xiaoting Rui
Release Date: 2018/11/01
ISBN: 9781118724804
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Book Description

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. 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. 

Table of Contents

  1. Cover
  2. Introduction
  3. Foreword One for the Chinese Edition
  4. Foreword Two for the Chinese Edition
  5. Foreword Three for the Chinese Edition
  6. Foreword Four for the Chinese Edition
  7. Preface
  8. 1 Introduction
    1. 1.1 The Status of the Multibody System Dynamics Method
    2. 1.2 The Transfer Matrix Method and the Finite Element Method
    3. 1.3 The Status of the Transfer Matrix Method for a Multibody System
    4. 1.4 Features of the Transfer Matrix Method for Multibody Systems
    5. 1.5 Launch Dynamics
    6. 1.6 Features of this Book
    7. 1.7 Sign Conventions
  9. Part I: Transfer Matrix Method for Linear Multibody Systems
    1. 2 Transfer Matrix Method for Linear Multibody Systems
      1. 2.1 Introduction
      2. 2.2 State Vector, Transfer Equation and Transfer Matrix
      3. 2.3 Overall Transfer Equation, Overall Transfer Matrix and Boundary Conditions
      4. 2.4 Characteristic Equation
      5. 2.5 Computation for State Vector and Vibration Characteristics
      6. 2.6 Vibration Characteristics of Multibody Systems
      7. 2.7 Eigenvalues of Damped Vibration
      8. 2.8 Steady‐state Response to Forced Vibration
      9. 2.9 Steady‐state Response of Forced Damped Vibration
    2. 3 Augmented Eigenvector and System Response
      1. 3.1 Introduction
      2. 3.2 Body Dynamics Equation and Parameter Matrices
      3. 3.3 Basic Theory of the Orthogonality of Eigenvectors
      4. 3.4 Augmented Eigenvectors and their Orthogonality
      5. 3.5 Examples of the Orthogonality of Augmented Eigenvectors
      6. 3.6 Transient Response of a Multibody System
      7. 3.7 Steady‐state Response of a Damped Multibody System
      8. 3.8 Steady‐state Response of a Multibody System
      9. 3.9 Static Response of a Multibody System
    3. 4 Transfer Matrix Method for Nonlinear and Multidimensional Multibody Systems
      1. 4.1 Introduction
      2. 4.2 Incremental Transfer Matrix Method for Nonlinear Systems
      3. 4.3 Finite Element Transfer Matrix Method for Two‐dimensional Systems
      4. 4.4 Finite Element Riccati Transfer Matrix Method for Two‐dimensional Nonlinear Systems
      5. 4.5 Fourier Series Transfer Matrix Method for Two‐dimensional Systems
      6. 4.6 Finite Difference Transfer Matrix Method for Two‐dimensional Systems
      7. 4.7 Transfer Matrix Method for Two‐dimensional Systems
  10. Part II: Transfer Matrix Method for Multibody Systems
    1. 5 Transfer Matrix Method for Multi‐rigid‐body Systems
      1. 5.1 Introduction
      2. 5.2 State Vectors, Transfer Equations and Transfer Matrices
      3. 5.3 Overall Transfer Equation and Overall Transfer Matrix
      4. 5.4 Transfer Matrix of a Planar Rigid Body
      5. 5.5 Transfer Matrix of a Spatial Rigid Body
      6. 5.6 Transfer Matrix of a Planar Hinge
      7. 5.7 Transfer Matrix of a Spatial Hinge
      8. 5.8 Transfer Matrix of an Acceleration Hinge
      9. 5.9 Algorithm of the Transfer Matrix Method for Multibody Systems
      10. 5.10 Numerical Examples of Multibody System Dynamics
    2. 6 Transfer Matrix Method for Multi‐flexible‐body Systems
      1. 6.1 Introduction
      2. 6.2 State Vector, Transfer Equation and Transfer Matrix
      3. 6.3 Overall Transfer Equation and Overall Transfer Matrix
      4. 6.4 Transfer Matrix of a Planar Beam
      5. 6.5 Transfer Matrix of a Spatial Beam
      6. 6.6 Numerical Examples of Multi‐flexible‐body System Dynamics
  11. Part III: Discrete Time Transfer Matrix Method for Multibody Systems
    1. 7 Discrete Time Transfer Matrix Method for Multibody Systems
      1. 7.1 Introduction
      2. 7.2 State Vector, Transfer Equation and Transfer Matrix
      3. 7.3 Step‐by‐step Time Integration Method and Linearization
      4. 7.4 Transfer Matrix of a Planar Rigid Body
      5. 7.5 Transfer Matrices of Spatial Rigid Bodies
      6. 7.6 Transfer Matrices of Planar Hinges
      7. 7.7 Transfer Matrices of Spatial Hinges
      8. 7.8 Algorithm of the Discrete Time Transfer Matrix Method for Multibody Systems
      9. 7.9 Numerical Examples of Multibody System Dynamics
    2. 8 Discrete Time Transfer Matrix Method for Multi‐flexible‐body Systems
      1. 8.1 Introduction
      2. 8.2 Dynamics of a Flexible Body with Large Motion
      3. 8.3 State Vector, Transfer Equation and Transfer Matrix
      4. 8.4 Transfer Matrix of a Beam with Large Planar Motion
      5. 8.5 Transfer Matrices of Smooth Hinges Connected to a Beam with Large Planar Motion
      6. 8.6 Transfer Matrices of Spring Hinges Connected to a Beam with Large Planar Motion
      7. 8.7 Transfer Matrix of a Fixed Hinge Connected to a Beam
      8. 8.8 Dynamics Equation of a Spatial Large Motion Beam
      9. 8.9 Transfer Matrix of a Spatial Large Motion Beam
      10. 8.10 Transfer Matrices of Fixed Hinges Connected to a Beam with Large Spatial Motion
      11. 8.11 Transfer Matrices of Smooth Hinges Connected to a Beam with Large Spatial Motion
      12. 8.12 Transfer Matrices of Spring Hinges Connected to a Beam with Large Spatial Motion
      13. 8.13 Algorithm of the Discrete Time Transfer Matrix Method for Multi‐flexible‐body Systems
      14. 8.14 Planar Multi‐flexible‐body System Dynamics
      15. 8.15 Spatial Multi‐flexible‐body System Dynamics
    3. 9 Transfer Matrix Method for Controlled Multibody Systems
      1. 9.1 Introduction
      2. 9.2 Mixed Transfer Matrix Method for Multibody Systems
      3. 9.3 Finite Element Transfer Matrix Method for Multibody Systems
      4. 9.4 Finite Segment Transfer Matrix Method for Multibody Systems
      5. 9.5 Transfer Matrix Method for Controlled Multibody Systems I
      6. 9.6 Transfer Matrix Method for Controlled Multibody Systems II
    4. 10 Derivation and Computation of Transfer Matrices
      1. 10.1 Introduction
      2. 10.2 Derivation from Dynamics Equations
      3. 10.3 Derivation from an nth‐order Differential Equationth‐order Differential Equation
      4. 10.4 Derivation from n First‐order Differential Equations First‐order Differential Equations
      5. 10.5 Derivation from Stiffness Matrices
      6. 10.6 Computational Method of the Transfer Matrix
      7. 10.7 Improved Algorithm for Eigenvalue Problems
      8. 10.8 Properties of the Inverse Matrix of a Transfer Matrix
      9. 10.9 Riccati Transfer Matrix Method for Multibody Systems
      10. 10.10 Stability of the Transfer Matrix Method for Multibody Systems
    5. 11 Theorem to Deduce the Overall Transfer Equation Automatically
      1. 11.1 Introduction
      2. 11.2 Topology Figure of Multibody Systems
      3. 11.3 Automatic Deduction of the Overall Transfer Equation of a Closed‐loop System
      4. 11.4 Automatic Deduction of the Overall Transfer Equation of a Tree System
      5. 11.5 Automatic Deduction of the Overall Transfer Equation of a General System
      6. 11.6 Automatic Deduction Theorem of the Overall Transfer Equation
      7. 11.7 Numerical Example of Closed‐loop System Dynamics
      8. 11.8 Numerical Example of Tree System Dynamics
      9. 11.9 Numerical Example of Multi‐level System Dynamics
      10. 11.10 Numerical Example of General System Dynamics
  12. Part IV: Applications of the Transfer Matrix Method for Multibody Systems
    1. 12 Dynamics of Multiple Launch Rocket Systems
      1. 12.1 Introduction
      2. 12.2 Launch Dynamics Model of the System and its Topology
      3. 12.3 State Vector, Transfer Equation and Transfer Matrix
      4. 12.4 Overall Transfer Equation of the System
      5. 12.5 Vibration Characteristics of the System
      6. 12.6 Dynamics Response of the System
      7. 12.7 Launch Dynamics Equation and Forces Acting on the System
      8. 12.8 Dynamics Simulation of the System and its Test Verifying
      9. 12.9 Low Rocket Consumption Technique for the System Test
      10. 12.10 High Launch Precision Technique for the System
    2. 13 Dynamics of Self‐propelled Launch Systems
      1. 13.1 Introduction
      2. 13.2 Dynamics Model of the System and its Topology
      3. 13.3 State Vector, Transfer Equation and Transfer Matrix
      4. 13.4 Overall Transfer Equation of the System
      5. 13.5 Vibration Characteristics of the System
      6. 13.6 Dynamic Response of the System
      7. 13.7 Launch Dynamic Equations and Forces Analysis
      8. 13.8 Dynamics Simulation of the System and its Test Verifying
    3. 14 Dynamics of Shipboard Launch Systems
      1. 14.1 Introduction
      2. 14.2 Dynamics Model of Shipboard Launch Systems
      3. 14.3 State Vector, Transfer Equation and Transfer Matrix
      4. 14.4 Overall Transfer Equation of the System
      5. 14.5 Launch Dynamics Equation and Forces of the System
      6. 14.6 Solution of Shipboard Launch System Motion
      7. 14.7 Dynamics Simulation of the System and its Test Verifying
    4. 15 Transfer Matrix Library for Multibody Systems
      1. 15.1 Introdution
      2. 15.2 Springs
      3. 15.3 Rotary Springs
      4. 15.4 Elastic Hinges
      5. 15.5 Lumped Mass Vibrating in a Longitudinal Direction
      6. 15.6 Vibration of Rigid Bodies
      7. 15.7 Beam with Transverse Vibration
      8. 15.8 Shaft with Torsional Vibration
      9. 15.9 Rod with Longitudinal Vibration
      10. 15.10 Euler–Bernoulli Beam
      11. 15.11 Rectangular Plate
      12. 15.12 Disk
      13. 15.13 Strip Element of a Two‐dimensional Thin Plate
      14. 15.14 Thick‐walled Cylinder
      15. 15.15 Thin‐walled Cylinder
      16. 15.16 Coordinate Transformation Matrix
      17. 15.17 Linearization and State Vectors
      18. 15.18 Spring and Damper Hinges Connected to Rigid Bodies
      19. 15.19 Smooth Hinges Connected to Rigid Bodies
      20. 15.20 Rigid Bodies Moving in a Plane
      21. 15.21 Spatial Rigid Bodies with Large Motion and Various Connections
      22. 15.22 Planar Beam with Large Motion
      23. 15.23 Spatial Beam with Large Motion
      24. 15.24 Fixed Hinges Connected to a Planar Beam with Large Motion
      25. 15.25 Fixed Hinges Connected to a Spatial Beam with Large Motion
      26. 15.26 Smooth Hinges Connected to a Beam with Large Planar Motion
      27. 15.27 Smooth Hinges Connected to a Beam with Large Spatial Motion
      28. 15.28 Elastic Hinges Connected to a Beam with Large Planar Motion
      29. 15.29 Elastic Hinges Connected to a Beam Moving in Space
      30. 15.30 Controlled Elements of a Linear System
      31. 15.31 Controlled Elements of a General Time‐variable System
  13. Appendix I: Rotation Formula Around an Axis
  14. Appendix II: Orientation of a Body‐fixed Coordinate System
    1. II.1 First Rotation
    2. II.2 Second Rotation
    3. II.3 Third Rotation
  15. Appendix III: List of Symbols
  16. Appendix IV: International Academic Communion for the Transfer Matrix Method for Multibody Systems
  17. References
  18. Index
  19. End User License Agreement
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