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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Wiley-ASME Press Series
- Sprache: Englisch
One of the first books to provide in-depth and systematic application of finite element methods to the field of stochastic structural dynamics
The parallel developments of the Finite Element Methods in the 1950’s and the engineering applications of stochastic processes in the 1940’s provided a combined numerical analysis tool for the studies of dynamics of structures and structural systems under random loadings. In the open literature, there are books on statistical dynamics of structures and books on structural dynamics with chapters dealing with random response analysis. However, a systematic treatment of stochastic structural dynamics applying the finite element methods seems to be lacking. Aimed at advanced and specialist levels, the author presents and illustrates analytical and direct integration methods for analyzing the statistics of the response of structures to stochastic loads. The analysis methods are based on structural models represented via the Finite Element Method. In addition to linear problems the text also addresses nonlinear problems and non-stationary random excitation with systems having large spatially stochastic property variations.
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Table of Contents
Cover
Title Page
Series Preface
Preface
Acknowledgments
1 Introduction
1.1 Important Difference between Static and Dynamic Responses
1.2 Classification of Dynamic Systems
1.3 Applications of Control Theory
1.4 Organization of Presentation
References
2 Review of Laplace Transforms
2.1 Definition
2.2 First and Second Shifting Theorems
2.3 Dirac Delta Function (Unit Impulse Function)
2.4 Laplace Transforms of Derivatives and Integrals
2.5 Convolution Theorem
2.6 Initial and Final Value Theorems
2.7 Laplace Transforms of Periodic Functions
2.8 Partial Fraction Method
2.9 Questions and Solutions
2.10 Applications of MATLAB
Exercise Questions
References
3 Dynamic Behaviors of Hydraulic and Pneumatic Systems
3.1 Basic Elements of Liquid and Gas Systems
3.2 Hydraulic Tank Systems
3.3 Nonlinear Hydraulic Tank and Linear Transfer Function
3.4 Pneumatically Actuated Valves
3.5 Questions and Solutions
Appendix 3A: Transfer Function of Two Interacting Hydraulic Tanks
Exercise Questions
4 Dynamic Behaviors of Oscillatory Systems
4.1 Elements of Oscillatory Systems
4.2 Free Vibration of Single Degree-of-Freedom Systems
4.3 Single Degree-of-Freedom Systems under Harmonic Forces
4.4 Single Degree-of-Freedom Systems under Non-Harmonic Forces
4.5 Vibration Analysis of Multi-Degrees-of-Freedom Systems
4.6 Vibration of Continuous Systems
4.7 Questions and Solutions
Appendix 4A: Proof of Equation (4.19b)
Exercise Questions
References
5 Formulation and Dynamic Behavior of Thermal Systems
5.1 Elements of Thermal Systems
5.2 Thermal Systems
5.3 Questions and Solutions
Exercise Questions
6 Formulation and Dynamic Behavior of Electrical Systems
6.1 Basic Electrical Elements
6.2 Fundamentals of Electrical Circuits
6.3 Simple Electrical Circuits and Networks
6.4 Electromechanical Systems
6.5 Questions and Solutions
Exercise Questions
References
7 Dynamic Characteristics of Transducers
7.1 Basic Theory of the Tachometer
7.2 Principles and Applications of Oscillatory Motion Transducers
7.3 Principles and Applications of Microphones
7.4 Principles and Applications of the Piezoelectric Hydrophone
7.5 Questions and Solutions
Appendix 7A: Proof of Approximated Current Solution
Exercise Questions
References
8 Fundamentals of Control Systems
8.1 Classification of Control Systems
8.2 Representation of Control Systems
8.3 Transfer Functions
8.4 Closed-Loop Control Systems
8.5 Block Diagram Reduction
8.6 Questions and Solutions
Exercise Questions
References
9 Analysis and Performance of Control Systems
9.1 Response in the Time Domain
9.2 Transient Responses as Functions of Closed-Loop Poles
9.3 Control System Design Based on Transient Responses
9.4 Control Types
9.5 Steady-State Errors
9.6 Performance Indices and Sensitivity Functions
9.7 Questions and Solutions
Exercise Questions
10 Stability Analysis of Control Systems
10.1 Concept of Stability in Linear Control Systems
10.2 Routh–Hurwitz Stability Criterion
10.3 Applications of Routh–Hurwitz Stability Criterion
10.4 Questions and Solutions
Exercise Questions
References
11 Graphical Methods for Control Systems
11.1 Root Locus Method and Root Locus Plots
11.2 Polar and Bode Plots
11.3 Nyquist Plots and Stability Criterion
11.4 Gain Margin and Phase Margin
11.5 Lines of Constant Magnitude:
M
Circles
11.6 Lines of Constant Phase:
N
Circles
11.7 Nichols Charts
11.8 Applications of MATLAB for Graphical Constructions
Exercise Questions
References
12 Modern Control System Analysis
12.1 State Space Method
12.2 State Transition Matrix
12.3 Relationship between Laplace Transformed State Equation and Transfer Function
12.4 Stability Based on Eigenvalues of the Coefficient Matrix
12.5 Controllability and Observability
12.6 Stabilizability and Detectability
12.7 Applications of MATLAB
Appendix 12A: Solution of System of First-Order Differential Equations
Appendix 12B: Maclaurin’s Series
Appendix 12C: Rank of A Matrix
Exercise Questions
References
Index
End User License Agreement
List of Tables
Chapter 02
Table 2.1 Functions and their Laplace transforms
Table 2.2 Properties of Laplace transforms
List of Illustrations
Chapter 01
Figure 1.1 Dynamic response of a single dof system under unity input
Figure 1.2 Cantilever beam with a point load
Figure 1.3 A lumped-parameter model of a massless cantilever beam
Chapter 02
Figure 2.1 Time history of a second-order system under a unit step input
Figure 2.2 Time histories of two second-order systems
Figure 2.3 Time history of a second-order system under an impulse input
Chapter 03
Figure 3.1 Basic elements of fluid systems: (a) resistance
R
; (b) inertia
I
; and (c) compressibility
C
Figure 3.2 Non-interacting hydraulic tank system
Figure 3.3 Interacting hydraulic tank system
Figure 3.4 Nonlinear hydraulic tank system
Figure 3.5 (a) Pneumatically actuated valve, and (b) free-body diagram of (a)
Figure 3E1 Two water tanks with one inflow and three outflows
Figure 3E2 A two-tank system
Figure 3E3 A hydraulic tank with a non-uniform cross-sectional area
Figure 3E4 (a) Pneumatically actuated valve and (b) free-body diagram of (a)
Figure 3Q1 Three identical non-interacting water tanks
Figure 3Q2 Three interacting water tanks
Figure 3Q3 Three interacting and non-interacting water tanks
Figure 3Q4 A hydraulic system consisting of two cylinders
Figure 3Q5 Section view of a hydraulic valve actuator
Chapter 04
Figure 4.1 (a) Basic translational elements of oscillatory systems; (b) basic rotational elements of oscillatory systems; (c) lever mechanism (rigid bar with pinned joints) and simple gear mechanism
Figure 4.2 Elementary spring constants
Figure 4.3 Two systems in the physical world
Figure 4.4 Single dof models of the systems in Figure 4.3
Figure 4.5 Single dof system and free body diagram
Figure 4.6 Harmonically forced single dof system
Figure 4.7 Vector diagram of a forced single dof system
Figure 4.8 Response and phase relationships of single dof system
Figure 4.9 Dropping of a spring-mass system
Figure 4.10 Two 2-dof systems in the physical world: (a) the coal sizing machine; (b) electronic equipment in a rocket
Figure 4.11 Lumped-parameter models of systems in Figure 4.10
Figure 4.12 (a) Coal sizing machine model and (b) FBD of (a)
Figure 4.13 An elementary length of a vibrating string
Figure 4E1 (a) A simple pendulum, and (b) FBD of (a)
Figure 4E2 (a) An airfoil section with spring support and (b) its FBD
Figure 4E4 (a) The inverted pendulum and (b) FBD at G of (a)
Figure 4E5 (a) Unbalanced centrifugal pump; (b) conceptual model; (c) kinematics of unbalance mass; and (d) FBD of system
Figure 4E6 (a) A flexible cable fixed at the upper end and (b) FBD of elementary length
dy
of the cable
Figure 4E7 (a) A cord fixed at one end and attached to a mass-spring device at the other end, and (b) FBD of the mass-spring device
Figure 4E8 (a) A satellite model rotating with an angular velocity; (b) kinematics of the satellite model
Figure 4Q1 Sphere rolls without slipping on a spherical surface
Figure 4Q2 Slender rod and springs arranged as an “H” plane frame
Figure 4Q3 Periodic square wave force
Figure 4Q4 A simplified landing helicopter model
Figure 4Q5 A hinged rigid bar with a dynamic absorber
Figure 4Q6 A system having two hinged rods and connected to springs
Figure 4Q7 A double pendulum
Figure 4Q8 A single cylinder reciprocating engine mounted on a fixed-fixed beam
Figure 4Q9 A cable being given a triangular initial input
Figure 4Q10 A simple model of a rocket
Chapter 05
Figure 5.1 Elements of thermal systems: (a) resistance, (b) capacitance, and (c) radiation
Figure 5.2 Process control of a compartment
Figure 5.3 Space heating
Figure 5.4 Three-capacitance oven
Figure 5E1 Thermal resistances of a two-layered wall
Figure 5E2 Thermal resistances of two walls in parallel
Figure 5E3 Two identical rooms with an electric heater
Figure 5E4 Heat conduction through the cylindrical wall of a pipe
Figure 5Q2 A heated concert chamber
Figure 5Q3 Heat exchanger in a nuclear power plant
Figure 5Q4 An automobile brake block with rotor in plane view
Figure 5Q5 Heat flow through a three-layer composite wall
Figure 5Q6 Cross-section of the composite pipe
Chapter 06
Figure 6.1 Representations of basic electrical elements: (a) resistance, (b) capacitance, and (c) inductance
Figure 6.2 Resistors connected in (a) series and (b) parallel
Figure 6.3 Simple electrical circuits: (a) simple lag, (b) transient lead, (c) phase lag, and (d) phase lead
Figure 6.4 Classes of DC machines having electromagnetic excitation current: (a) series, (b) shunt, (c) separately excited, and (d) compound
Figure 6.5 An armature-controlled DC motor
Figure 6.6 Field-controlled DC motor
Figure 6.7 DC generator
Figure 6Q1 (a) Amplifier and speaker system and (b) circuit representation
Figure 6Q2 Switch in an electrical circuit
Figure 6Q3 A DC motor system
Figure 6Q4 Separately-excited DC motor
Chapter 07
Figure 7.1 A tachometer as a DC generator with fixed field
Figure 7.2 A typical transducer
Figure 7.3 Transducer model and its FBD
Figure 7.4 Magnitude and phase characteristics of a transducer
Figure 7.5 (a) Sketch of a moving-coil microphone; (b) oscillatory model with FBD; and (c) electrical circuit analog
Figure 7.6 (a) A typical condenser microphone, (b) sketch of a simple condenser microphone, and (c) equivalent electrical circuit
Figure 7.7 (a) General circuit and (b) low-frequency circuit of a piezoelectric hydrophone
Figure 7Q2 Low frequency equivalent circuit of accelerometer with preamplifier
Figure 7Q5 Low-frequency equivalent circuit of condenser microphone with charge preamplifier
Chapter 08
Figure 8.1 Control system forms: (a) open-loop system and (b) closed-loop system
Figure 8.2 Transfer function of an element
Figure 8.3 (a) Elements in series and (b) representation of elements in series
Figure 8.4 (a) Elements in parallel connection and (b) representation of elements in parallel connection
Figure 8.5 A feedback control system
Figure 8.6 A feedback control system with two inputs
Figure 8.7 Equivalent block diagrams of moving a signal
Figure 8.8 Equivalent block diagrams of moving a summing point
Figure 8.9 Control system showing (a) first block diagram reduction, (b) second block diagram reduction, and (c) final feedback control system
Figure 8E1 (a) A two-input feedback control system. (b) Two-input feedback control system with error signals. (c) Block diagram of the control system with two inputs
Figure 8E2 Simplified block diagram of a large antenna
Figure 8E3 (a) A water-level control system. (b) Perturbed lever from equilibrium position. (c) Block diagram of water-level control system. (d) Steps in construction of block diagram in (c)
Figure 8Q1 Block diagram representation of a hydrogovernor-turbine model
Figure 8Q2 Block diagram of a jet aircraft pitch-rate control mechanism
Figure 8Q3 Block diagram of a displacement servo
Figure 8Q4 Block diagram of turntable position control system
Chapter 09
Figure 9.1 Block diagram of a unity feedback system
Figure 9.2 Transient responses as functions of closed-loop poles
Figure 9.3 Response of dynamic system to unit step input (the settling time is not included in this figure because it is beyond the range plotted)
Figure 9.4 Relationship between overshoot and damping ratio
Figure 9.5 System with an added controller
Figure 9.6 System including proportional control
Figure 9.7 System including integral control
Figure 9.8 System including derivative control
Figure 9E1 Speed control system
Figure 9E2 (a) Block diagram representation of oil-level control system; (b) simplified oil-level control system
Figure 9Q1 A system for reducing or eliminating signal loss in mast antennae
Figure 9Q2 Block diagram of a simplified robot
Figure 9Q3 Block diagram of the heart pump and pacemaker
Figure 9Q4 A ship stabilization system: (a) oscillation of ship and (b) block diagram of the stabilization system
Chapter 10
Figure 10.1 Unity feedback control system
Figure 10E1 Block diagram representation of a phase detector
Figure 10E2 Velocity control system for a motorized wheelchair
Figure 10E3 A pure fluid speed control for a 500 kW steam turbine
Figure 10Q2 Direction control system
Figure 10Q4 Block diagram of a vision device used in arc welding
Figure 10Q5 Block diagram of a roll stabilizer for a ship
Chapter 11
Figure 11.1 Root locus diagram of
G
o
(
s
)
Figure 11.2 Polar plot of a simple lag system
Figure 11.3 Bode plot of a simple lag system. (a) Magnitude plot; (b) phase plot
Figure 11.4 Asymptotic Bode plot of a system with
. (a) Magnitude plot; (b) phase plot
Figure 11.5 Nyquist plot of a system
Figure 11.6 Enclosure and encirclement: (a) enclosure and (b) encirclement
Figure 11.7 Use of Cauchy’s theorem: (a) singularities and
Γ
s
; (b) encirclement and
Γ
p
of (a); (c) singularities and
Γ
s
, and (d) encirclement and
Γ
p
of (c)
Figure 11.8 Nyquist plot and mapping for
P
(
s
): (a) Nyquist plot in the
s
-plane; (b) mapping for
P
(
s
)
Figure 11.9 Gain margin and phase margin
Figure 11.10 Gain margin and phase margin on a Bode plot of
G
(
iω
)
H
(
iω
)
Figure 11.11 Open- and closed-loop polar plots of
.
Figure 11.12 Constant
M
-circles on a polar diagram: (a) constant
M
contours; and (b) relationship between
M
contours and response of system
Figure 11.13 Relationship between phase margin and resonance peak of a second-order system
Figure 11.14 Constant
N
-circles on a polar diagram
Figure 11.15 Nichols chart
Figure 11E1 Root locus of a fourth-order system
Figure 11E2 Root locus of a third-order system
Figure 11E3 (a) Root locus of a fourth-order system; (b) root locus of a fourth-order system with controlled axes for plotting
Figure 11E4 (a) Root locus of a fourth-order system; (b) root locus of a fourth-order system with controlled axes for plotting
Figure 11E5 Root locus of a third-order system
Figure 11E6 Bode plot of a first-order system
Figure 11E7 Bode plot of a third-order system
Figure 11E8 Bode plot of a third-order system
Figure 11E9 Bode plot of a fourth-order system
Figure 11E10 Bode plot of a fourth order system
Figure 11E11 Bode plot of a third-order system
Figure 11E12 (a) Nyquist plot of a third-order system. (b) Nyquist plot of a third-order system with imaginary and real axes controlled for plotting
Figure 11E13 (a) Bode plot of a third order system
. (b) Nyquist plot of the same third-order system
Figure 11E14 (a) Bode plot of a third-order system
. (b) Nyquist plot of the same third-order system
Figure 11E15 Nyquist plot of a third-order system
.
Figure 11E16 Nyquist plot of a fourth-order system
.
Figure 11E17 (a) Nyquist plot of a second-order system
. (b) Bode plot of the same second-order system
Chapter 12
Figure 12.1 The single dof oscillator and its free body diagram
Figure 12E1 Responses of a system to step inputs from MATLAB
Figure 12E2 Responses of a system to step inputs from MATLAB
Figure 12E3 Responses of a system to impulse inputs from MATLAB
Figure 12E4 Free response of non-zero initial conditions
Figure 12E5 Responses of a system to sinusoidal inputs from MATLAB
Figure 12E6 Responses of forced rotating rotor to unit step input
Guide
Cover
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Wiley-ASME Press Series List
Introduction to Dynamics and Control in Mechanical Engineering Systems
To
March 2016
Fundamentals of Mechanical Vibrations
Cai
May 2016
Nonlinear Regression Modeling for Engineering Applications: Modeling, Model Validation, and Enabling Design of Experiments
Rhinehart
August 2016
INTRODUCTION TO DYNAMICS AND CONTROL IN MECHANICAL ENGINEERING SYSTEMS
Cho W. S. To
Professor of Mechanical and Materials EngineeringUniversity of Nebraska-Lincoln,Lincoln, NE, USA
This Work is a co-publication between ASME Press and John Wiley & Sons, Ltd.
This edition first published 2016© 2016 by John Wiley & Sons, Ltd
Registered OfficeJohn Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.
The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.
Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
Library of Congress Cataloging-in-Publication data applied for.
ISBN: 9781118934920
A catalogue record for this book is available from the British Library.
To my uncle
Mei Chang Cai (a.k.a. Muljanto Tjokro)
Series Preface
The Wiley-ASME Press Series in Mechanical Engineering brings together two established leaders in mechanical engineering publishing to deliver high-quality, peer-reviewed books covering topics of current interest to engineers and researchers worldwide.
The series publishes across the breadth of mechanical engineering, comprising research, design and development, and manufacturing. It includes monographs, references and course texts.
Prospective topics include emerging and advanced technologies in Engineering Design; Computer-Aided Design; Energy Conversion & Resources; Heat Transfer; Manufacturing & Processing; Systems & Devices; Renewable Energy; Robotics; and Biotechnology.
Preface
It is understood that there are many excellent books on system dynamics, control theory, and control engineering. However, the lengths of the majority of these books are of the order of six or seven hundred pages or more. There are, however, very few books that cover sufficient material and are limited to around 300 pages. The present book is aimed at addressing the balance. While it is more concise than those longer books, it does include many detailed steps in the example solutions. The author does believe that the detailed steps in the example solutions are essential in a first course textbook.
This book is based on lecture notes that have been developed and used by the author since 1986. These lecture notes have been employed in courses such as Mechanical Control and Process Control, as well as Dynamics and Control. The first two courses were taught by the author at the University of Western Ontario, London, Ontario, Canada while the third course has been given by the author at the University of Nebraska, Lincoln, Nebraska, USA, since 1996. All three courses have primarily been taken by junior undergraduates with majors in mechanical engineering and chemical engineering. Therefore, the subject matter dealt with in this book covers material for a first course of three credit hours per semester in system dynamics or control engineering. For a course in Mechanical Control or Process Control the material in the entire book, except the second half of Chapter 4, has been used. For a course in Dynamics and Control the material in the entire book except Chapter 11 has been covered. For a four credit hour course, the component of laboratory experiments has been omitted from the present book for two main reasons. First, the inclusion of the laboratory experiments is not feasible in the sense that its inclusion would increase drastically the length of the book. Second, nowadays many laboratory experiments are computer-aided in the sense that major software is required. Exclusion of laboratory experiments in the present book provides freedom for the instructors to select a particular software and allows them to tailor the design of their experiments to the availability of laboratory instrumentation in a particular department or engineering environment.
Under normal conditions, it is expected that the students using the present book have already taken courses in their sophomore year. These courses include linear algebra and matrix theory, a second course in mathematics with Laplace transformation, and engineering dynamics. In addition, students are expected to be able to use MATLAB, which is introduced during their first year or first semester of their sophomore year.
Acknowledgments
Many figures in Chapters 3–10 were drawn by Professor Jing Sun of Dalian University of Technology, Dalian, China. Professor Sun was a senior visiting scholar at the University of Nebraska, Lincoln, during the academic year 2012 to 2013. The author is grateful for Professor Sun’s kindness in preparing these figures. Specifically, the latter are: Figures 3.2–3.4; Figures 4.4–4.7, 4.9, 4.11–4.13; Figures 5.1–5.4; Figures 6.1–6.3; Figures 7.2 and 7.3; Figures 8.1–8.9; Figures 9.1, 9.2, 9.4–9.8; and Figure 10.1.
Finally, the author would like to express his sincere thanks to Paul Petralia, Senior Editor, Clive Lawson, Project Editor, Anne Hunt, Associate Commissioning Editor, and their team members for their assistance and effort in the production of this book.
1Introduction
This book is concerned with the introduction to the dynamics and controls of engineering systems in general. The emphasis, however, is on mechanical engineering system modeling and analysis.
Dynamics
is a branch of mechanics and is concerned with the studies of particles and bodies in motion.
The term
control
refers to the process of
modifying
the
dynamic behavior
of a system in order to achieve some
desired outputs
.
A
system
is a combination of components or elements so constructed to achieve an objective or multiple objectives.
1.1 Important Difference between Static and Dynamic Responses
The question of why one studies engineering dynamics as well as control, and not statics, is best answered by the fact that in control engineering it is the dynamic behavior of a system that is modified instead of the static one. Furthermore, the most important difference between statics and dynamics from the point of view of a mechanical engineering designer is in the responses of a system to an applied force.
Consider a lightly damped, simple, single degree-of-freedom (dof) system that is subjected to a unit step load. The dynamic response is shown in Figure 1.1. Note that the largest peak or overshoot is about 1.75 units, while the magnitude of the input is 1.0 unit. Owing to the positive damping in the system, the dynamic response approaches asymptotically to its steady-state (s.s.) value of unity. If one looks at the largest for the dynamic response, it is about 3.06 units squared. On the other hand, the mean square value for the s.s. or static response is 1.0 unit squared. Thus, the largest mean square value, which is the main design parameter, for the dynamic case is about 306% that of the static case, indicating the importance of dynamic response compared with that of the static case.
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