Flexible Multibody Dynamics

Efficient Formulations with Applications

Arun Banerjee

• Publisher: CRC Press
• Year: 2022
• Print ISBN: 9781032139197
• eBook ISBN: 9781000543902
• Edition: 2
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

This book demonstrates how to formulate the equations of mechanical systems. Providing methods of analysis of complex mechanical systems, the book has a clear focus on efficiency, equipping the reader with knowledge of algorithms that provide accurate results in reduced simulation time.

• The book uses Kane's method due to its efficiency, and the simple resulting equations it produces in comparison to other methods and extends it with algorithms such as order-n
• Kane's method compensates for the errors of premature linearization, which are often inherent within vibrations modes found in a great deal of public domain software
• Describing how to build mathematical models of multibody systems with elastic components, the book applies this to systems such as construction cranes, trailers, helicopters, spacecraft, tethered satellites, and underwater vehicles
• It also looks at topics such as vibration, rocket dynamics, simulation of beams, deflection, and matrix formulation

Flexible Multibody Dynamics will be of interest to students in mechanical engineering, aerospace engineering, applied mechanics and dynamics. It will also be of interest to industry professionals in aerospace engineering, mechanical engineering and construction engineering.

1 Derivation of Equations of Motion

DOI: 10.1201/9781003231523-2

1.1 Available Analytical Methods and the Reason for Choosing Kane’s Method

In this book, we formulate equations of motion for a system of rigid and flexible bodies undergoing large overall motion, where large overall motion for a flexible body means a small elastic vibration of the body with respect to a frame moving in large rotation and/or translation. Various choices of analytical methods are available for deriving equations of motion, v, such as Newton–Euler methods and methods based on D’Alembert’s principle together with the principle of virtual work, Lagrange’s equations, Hamilton’s equations, Boltzmann–Hamel equations, Gibbs equations, and Kane’s equations. The most recent among these is Kane’s method, based on a paper published in 1965, by Kane and Wang [1], and the method was given detailed exposition, with extensive applications, by Kane [2], Kane and Levinson [3], and Kane, Likins, and Levinson [4].

In a survey paper, Kane and Levinson [5] took up a fairly complex example, of an 8 degree of freedom (dof) system consisting of a spacecraft containing a four-bar linkage to show the difference between seven analytical methods; an application to a flexible spacecraft was also considered. The conclusion in Ref. [5] was that (i) D’Alembert’s method is less laborious than a method using the conservation of momentum, with both methods requiring the introduction and elimination of constraint forces;...

Table of contents

• Cover
• Half-Title
• Title
• Copyright
• Dedication
• Contents
• Preface
• About the Author
• Introduction Background Material on Dynamics and Vibrations
• Chapter 1 Derivation of Equations of Motion
• Chapter 2 Deployment, Station-Keeping, and Retrieval of a Flexible Tether Connecting a Satellite to the Shuttle
• Chapter 3 Kane’s Method of Linearization Applied to the Dynamics of a Beam in Large Overall Motion
• Chapter 4 Dynamics of a Plate in Large Overall Motion
• Chapter 5 Dynamics of an Arbitrary Flexible Body in Large Overall Motion
• Chapter 6 Flexible Multibody Dynamics: Dense Matrix Formulation
• Chapter 7 Component Mode Selection and Model Reduction: A Review
• Chapter 8 Block-Diagonal Mass Matrix Formulation of Equations of Motion for Flexible Multibody Systems
• Chapter 9 Efficient Variables, Recursive Formulation, and Multi-Loop Constraints in Flexible Multibody Dynamics
• Chapter 10 An Order-n Formulation for Beams with Undergoing Large Deflection and Large Base Motion
• Chapter 11 Deployment/Retraction of Beams and Cables from Moving Vehicles: Small Deflection Analysis, and Variable-N Order-N Formulations for Large Deflection
• Chapter 12 Flexible Rocket Dynamics, Using Geometric Softness and a Block-Diagonal Mass Matrix
• Chapter 13 Large Amplitude Fuel Slosh in Spacecraft in Large Overall Motion
• Appendix A: Modal Integrals for an Arbitrary Flexible Body
• Appendix B: Flexible Multibody Dynamics for Small Overall Motion
• Appendix C: A FORTRAN Code of the Order-n Algorithm: Application to an Example
• Index