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E-raamat: Flexible Multibody Dynamics: Efficient Formulations and Applications

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  • Ilmumisaeg: 23-Mar-2016
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119015611
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Flexible Multibody Dynamics: Efficient Formulations and ApplicationsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 23-Mar-2016
  • Kirjastus: John Wiley & Sons Inc
  • Keel: eng
  • ISBN-13: 9781119015611
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"This book describes how to build mathematical models of multibody systems with elastic components. Examples of such systems are the human body itself, construction cranes, cars with trailers, helicopters, spacecraft deploying antennas, tethered satellites, and underwater maneuvering vehicles looking for mines while being connected by a cable to a ship"--


Arun K. Banerjee is one of the foremost experts in the world on the subject of flexible multibody dynamics. This book describes how to build mathermatical models of multibody systems with elastic components. Examples of such systems include the human body itself, construction cranes, cares with trailers, helicopers, spacecraft deploying antennas, tethered satellites, and underwater maneuvering vehicles.

This book provides methods of analysis of complex mechanical
systems that can be simulated in less computer time than other methods. It
equips the reader with knowledge of algorithms that provide accurate results in
reduced simulation time.



Arvustused

"The book is intended for readers with backgrounds in rigid body dynamics and structural dynamics. It is well written and may be useful for structural engineers and researchers in applied mechanics." (Zentralblatt MATH, 2016)

Preface ix
1 Derivation of Equations of Motion
1(28)
1.1 Available Analytical Methods and the Reason for Choosing Kane's Method
1(1)
1.2 Kane's Method of Deriving Equations of Motion
2(9)
1.2.1 Kane's Equations
4(1)
7.2.2 Simple Example: Equations for a Double Pendulum
4(2)
7.2.3 Equations for a Spinning Spacecraft with Three Rotors, Fuel Slosh, and Nutation Damper
6(5)
1.3 Comparison to Derivation of Equations of Motion by Lagrange's Method
11(5)
1.3.1 Lagrange's Equations in Quasi-Coordinates
14(1)
Reader's Exercise
15(1)
1.4 Kane's Method of Direct Derivation of Linearized Dynamical Equation
16(3)
1.5 Prematurely Linearized Equations and a Posteriori Correction by ad hoc Addition of Geometric Stiffness due to Inertia Loads
19(2)
1.6 Kane's Equations with Undetermined Multipliers for Constrained Motion
21(1)
1.7 Summary of the Equations of Motion with Undetermined Multipliers for Constraints
22(1)
1.8 A Simple Application
23(6)
Appendix 1.A Guidelines for Choosing Efficient Motion Variables in Kane's Method
25(2)
Problem Set 1
27(1)
References
28(1)
2 Deployment, Station-Keeping, and Retrieval of a Flexible Tether Connecting a Satellite to the Shuttle
29(34)
2.1 Equations of Motion of a Tethered Satellite Deployment from the Space Shuttle
30(7)
2.7.1 Kinematical Equations
31(1)
2.1.2 Dynamical Equations
32(3)
2.7.5 Simulation Results
35(2)
2.2 Thruster-Augmented Retrieval of a Tethered Satellite to the Orbiting Shuttle
37(10)
2.2.1 Dynamical Equations
37(10)
2.2.2 Simulation Results
47(1)
2.2.3 Conclusion
47(1)
2.3 Dynamics and Control of Station-Keeping of the Shuttle-Tethered Satellite
47(16)
Appendix 2.A Sliding Impact of a Nose Cap with a Package of Parachute Used for Recovery of a Booster Launching Satellites
47(6)
Appendix 2.B Formation Flying with Multiple Tethered Satellites
53(2)
Appendix 2.C Orbit Boosting of Tethered Satellite Systems by Electrodynamic Forces
55(5)
Problem Set 2
60(1)
References
60(3)
3 Kane's Method of Linearization Applied to the Dynamics of a Beam in Large Overall Motion
63(20)
3.1 Nonlinear Beam Kinematics with Neutral Axis Stretch, Shear, and Torsion
63(6)
3.2 Nonlinear Partial Velocities and Partial Angular Velocities for Correct Linearization
69(1)
3.3 Use of Kane's Method for Direct Derivation of Linearized Dynamical Equations
70(6)
3.4 Simulation Results for a Space-Based Robotic Manipulator
76(2)
3.5 Erroneous Results Obtained Using Vibration Modes in Conventional Analysis
78(5)
Problem Set 3
79(3)
References
82(1)
4 Dynamics of a Plate in Large Overall Motion
83(14)
4.1 Motivating Results of a Simulation
83(2)
4.2 Application of Kane's Methodology for Proper Linearization
85(5)
4.3 Simulation Algorithm
90(2)
4.4 Conclusion
92(5)
Appendix 4.A Specialized Modal Integrals
93(1)
Problem Set 4
94(2)
References
96(1)
5 Dynamics of an Arbitrary Flexible Body in Large Overall Motion
97(18)
5.1 Dynamical Equations with the Use of Vibration Modes
98(2)
5.2 Compensating for Premature Linearization by Geometric Stiffness due to Inertia Loads
100(5)
5.2.1 Rigid Body Kinematical Equations
104(1)
5.3 Summary of the Algorithm
105(1)
5.4 Crucial Test and Validation of the Theory in Application
106(9)
Appendix 5.A Modal Integrals for an Arbitrary Flexible Body
112(2)
Problem Set 5
114(1)
References
114(1)
6 Flexible Multibody Dynamics: Dense Matrix Formulation
115(18)
6.1 Flexible Body System in a Tree Topology
115(1)
6.2 Kinematics of a Joint in a Flexible Multibody Body System
115(1)
6.3 Kinematics and Generalized Inertia Forces for a Flexible Multibody System
116(4)
6.4 Kinematical Recurrence Relations Pertaining to a Body and Its Inboard Body
120(1)
6.5 Generalized Active Forces due to Nominal and Motion-Induced Stiffness
121(5)
6.6 Treatment of Prescribed Motion and Internal Forces
126(1)
6.7 "Ruthless Linearization" for Very Slowly Moving Articulating Flexible Structures
126(1)
6.8 Simulation Results
127(6)
Problem Set 6
129(2)
References
131(2)
7 Component Mode Selection and Model Reduction: A Review
133(28)
7.1 Craig-Bampton Component Modes for Constrained Flexible Bodies
133(3)
7.2 Component Modes by Guyan Reduction
136(1)
7.3 Modal Effective Mass
137(1)
7.4 Component Model Reduction by Frequency Filtering
138(1)
7.5 Compensation for Errors due to Model Reduction by Modal Truncation Vectors
138(3)
7.6 Role of Modal Truncation Vectors in Response Analysis
141(2)
7.7 Component Mode Synthesis to Form System Modes
143(2)
7.8 Flexible Body Model Reduction by Singular Value Decomposition of Projected System Modes
145(2)
7.9 Deriving Damping Coefficient of Components from Desired System Damping
147(12)
Problem Set 7
148(1)
Appendix 7.A Matlab Codes for Structural Dynamics
149(10)
7.10 Conclusion
159(2)
References
159(2)
8 Block-Diagonal Formulation for a Flexible Multibody System
161(30)
8.1 Example: Role of Geometric Stiffness due to Interbody Load on a Component
161(3)
8.2 Multibody System with Rigid and Flexible Components
164(1)
8.3 Recurrence Relations for Kinematics
165(3)
8.4 Construction of the Dynamical Equations in a Block-Diagonal Form
168(6)
8.5 Summary of the Block-Diagonal Algorithm for a Tree Configuration
174(1)
8.5.7 First Forward Pass
174(1)
8.5.2 Backward Pass
174(1)
8.5.3 Second Forward Pass
175(1)
8.6 Numerical Results Demonstrating Computational Efficiency
175(1)
8.7 Modification of the Block-Diagonal Formulation to Handle Motion Constraints
176(6)
8.8 Validation of Formulation with Ground Test Results
182(4)
8.9 Conclusion
186(5)
Appendix 8.A An Alternative Derivation of Geometric Stiffness due to Inertia Loads
187(1)
Problem Set 8
188(1)
References
189(2)
9 Efficient Variables, Recursive Formulation, and Multi-Point Constraints in Flexible Multibody Dynamics
191(32)
9.1 Single Flexible Body Equations in Efficient Variables
191(5)
9.2 Multibody Hinge Kinematics for Efficient Generalized Speeds
196(5)
9.3 Recursive Algorithm for Flexible Multibody Dynamics with Multiple Structural Loops
201(8)
9.3.1 Backward Pass
201(6)
9.3.2 Forward Pass
207(2)
9.4 Explicit Solution of Dynamical Equations Using Motion Constraints
209(1)
9.5 Computational Results and Simulation Efficiency for Moving Multi-Loop Structures
210(13)
9.5.1 Simulation Results
210(5)
Acknowledgment
215(1)
Appendix 9.A Pseudo-Code for Constrained nb-Body m-Loop Recursive Algorithm in Efficient Variables
216(4)
Problem Set 9
220(1)
References
220(3)
10 Efficient Modeling of Beams with Large Deflection and Large Base Motion
223(16)
10.1 Discrete Modeling for Large Deflection of Beams
223(3)
10.2 Motion and Loads Analysis by the Order-n Formulation
226(4)
10.3 Numerical Integration by the Newmark Method
230(1)
10.4 Nonlinear Elastodynamics via the Finite Element Method
231(2)
10.5 Comparison of the Order-n Formulation with the Finite Element Method
233(4)
10.6 Conclusion
237(2)
Acknowledgment
238(1)
Problem Set 10
238(1)
References
238(1)
11 Variable-n Order-n Formulation for Deployment and Retraction of Beams and Cables with Large Deflection
239(30)
11.1 Beam Discretization
239(1)
11.2 Deployment/Retraction from a Rotating Base
240(6)
11.2.1 Initialization Step
240(1)
77.2.2 Forward Pass
240(3)
77.2.3 Backward Pass
243(1)
77.2.4 Forward Pass
244(1)
77.2.5 Deployment/Retraction Step
244(2)
11.3 Numerical Simulation of Deployment and Retraction
246(1)
11.4 Deployment of a Cable from a Ship to a Maneuvering Underwater Search Vehicle
247(10)
11.4.1 Cable Discretization and Variable-n Order-n Algorithm for Constrained Systems with Controlled End Body
248(6)
11.4.2 Hydrodynamic Forces on the Underwater Cable
254(1)
11.4.3 Nonlinear Holonomic Constraint, Control-Constraint Coupling, Constraint Stabilization, and Cable Tension
255(2)
11.5 Simulation Results
257(12)
Problem Set 11
261(6)
References
267(2)
12 Order-n Equations of Flexible Rocket Dynamics
269(18)
12.1 Introduction
269(1)
12.2 Kane's Equation for a Variable Mass Flexible Body
269(5)
12.3 Matrix Form of the Equations for Variable Mass Flexible Body Dynamics
274(1)
12.4 Order-n Algorithm for a Flexible Rocket with Commanded Gimbaled Nozzle Motion
275(3)
12.5 Numerical Simulation of Planar Motion of a Flexible Rocket
278(7)
12.6 Conclusion
285(2)
Acknowledgment
285(1)
Appendix 12.A Summary Algorithm for Finding Two Gimbal Angle Torques for the Nozzle
285(1)
Problem Set 12
286(1)
References
286(1)
Appendix A Efficient Generalized Speeds for a Single Free-Flying Flexible Body 287(4)
Appendix B A FORTRAN Code of the Order-n Algorithm: Application to an Example 291(10)
Index 301
Arun Kanti Banerjee, 28 year career at Lockheed Martin Advanced Technology Center (1982 thru 2010), Palo Alto, California, US. Last position Principal Research Scientist. Main Contribution: Developer of DYNACON, Lockheed's simulation tool for Multi-flexible-body dynamics and Control that has been used for many projects. Dr. Banerjee is one of the foremost experts in the world on the subject of flexible multibody dynamics.
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