Alan Palazzolo

Vibration Theory and Applications with Finite Elements and Active Vibration Control

• Gebundenes Buch

Produktbeschreibung

A comprehensive and practical guide to vibration theory with particular emphasis on finite element modeling using real world engineering scenarios

Vibration Theory and Applications with Finite Element Analysis provides extensive coverage of vibration-related topics, with particular emphasis on the three basic areas of modeling, analysis and applications. The author recognizes that a thorough understanding of mathematical and modeling techniques is essential before progressing to methods of analysis and there is a complete section covering the relevant math and programming techniques in MATLAB and MAPLE. By using a wide range of practical examples and exercises, the author demonstrates how the math relates to engineering and its applications, connecting theory to engineering practice and problem solving. Based on many years of research and teaching, this book brings together all the important topics in vibration theory, including failure models, kinematics and modeling, unstable vibrating systems, rotor dynamics and finite element methods utilizing truss, beam, plate and solid elements. It also explores in detail active vibration control, instability, bifurcation theory and paths to chaos. The book provides the modeling skills and knowledge required for modern engineering practice, plus the tools needed to identify, formulate and solve engineering problems effectively.
* Presents a thorough description of vibration topics and mathematical techniques from basic through to advanced levels
* Uses practical examples to illustrate the theory, providing an awareness of the concepts and how they apply to real life engineering situations
* Covers in detail topics such as 3D beams and solid elements and trusses, magnetic theory for active control and magnetic bearings and high cycle fatigue, based on the author's extensive research
* Includes techniques for deriving equations of motion via Newton's Laws, Lagrange, and Gibbs/Ansell approach
* Fully illustrated throughout, with a solution manual including MATLAB and MAPLE codes

An invaluable resource for graduate students of civil, mechanical and aerospace engineering; applied mathematics.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 976
• Erscheinungstermin: 21. März 2016
• Englisch
• Abmessung: 260mm x 187mm x 50mm
• Gewicht: 1721g
• ISBN-13: 9781118350805
• ISBN-10: 1118350804
• Artikelnr.: 40783413

Autorenporträt

Alan Palazzolo, Professor of Mechanical Engineering, Texas A&M University. Professor Palazzolo worked in industry prior to returning to academic research and gaining full Professorship in Mechanical Engineering in 1999.?He has written extensively for international journals, books and conference proceedings and has been the recipient of numerous awards throughout his professional career. His research interests include vibrations, nonlinear vibrations, controls, rotordynamics and finite elements. He is presently an Associate Editor of ASME Journal of Vibrations.

Inhaltsangabe

Preface xv Acknowledgments and Dedication xxi About the Companion Website
xxiii List of Acronyms xxv 1 Background, Motivation, and Overview 1 1.1
Introduction 1 1.2 Background 1 1.2.1 Units 5 1.3 Our Vibrating World 6
1.3.1 Small-Scale Vibrations 6 1.3.2 Medium-Scale (Mesoscale) Vibrations 8
1.3.3 Large-Scale Vibrations 8 1.4 Harmful Effects of Vibration 9 1.4.1
Human Exposure Limits 9 1.4.2 High-Cycle Fatigue Failure 11 1.4.3 Rotating
Machinery Vibration 21 1.4.4 Machinery Productivity 27 1.4.5 Fastener
Looseness 28 1.4.6 Optical Instrument Blurring 28 1.4.7 Ethics and
Professional Responsibility 29 1.4.8 Lifelong Learning Opportunities 29 1.5
Stiffness, Inertia, and Damping Forces 29 1.6 Approaches for Obtaining the
Differential Equations of Motion 34 1.7 Finite Element Method 35 1.8 Active
Vibration Control 37 1.9 Chapter 1 Exercises 37 1.9.1 Exercise Location 37
1.9.2 Exercise Goals 37 1.9.3 Sample Exercises: 1.6 and 1.11 38 References
38 2 Preparatory Skills: Mathematics, Modeling, and Kinematics 41 2.1
Introduction 41 2.2 Getting Started with MATLAB and MAPLE 42 2.2.1 MATLAB
42 2.2.2 MAPLE (Symbolic Math) 45 2.3 Vibration and Differential Equations
50 2.3.1 MATLAB and MAPLE Integration 50 2.4 Taylor Series Expansions and
Linearization 56 2.5 Complex Variables (CV) and Phasors 60 2.6 Degrees of
Freedom, Matrices, Vectors, and Subspaces 63 2.6.1 Matrix-Vector Related
Definitions and Identities 69 2.7 Coordinate Transformations 75 2.8
Eigenvalues and Eigenvectors 79 2.9 Fourier Series 80 2.10 Laplace
Transforms, Transfer Functions, and Characteristic Equations 83 2.11
Kinematics and Kinematic Constraints 86 2.11.1 Particle Kinematic
Constraint 86 2.11.2 Rigid Body Kinematic Constraint 90 2.11.3 Assumed
Modes Kinematic Constraint 96 2.11.4 Finite Element Kinematic Constraint 98
2.12 Dirac Delta and Heaviside Functions 100 2.13 Chapter 2 Exercises 101
2.13.1 Exercise Location 101 2.13.2 Exercise Goals 101 2.13.3 Sample
Exercises: 2.9 and 2.17 101 References 102 3 Equations of Motion by
Newton's Laws 103 3.1 Introduction 103 3.2 Particle Motion Approximation
103 3.3 Planar (2D) Rigid Body Motion Approximation 107 3.3.1 Translational
Equations of Motion 107 3.3.2 Rotational Equation of Motion 108 3.4 Impulse
and Momentum 129 3.4.1 Linear Impulse and Momentum 129 3.4.2 Angular
Impulse and Momentum 134 3.5 Variable Mass Systems 138 3.6 Chapter 3
Exercises 140 3.6.1 Exercise Location 140 3.6.2 Exercise Goals 140 3.6.3
Sample Exercises: 3.8 and 3.21 141 References 141 4 Equations of Motion by
Energy Methods 143 4.1 Introduction 143 4.2 Kinetic Energy 143 4.2.1
Particle Motion 143 4.2.2 Two-Dimensional Rigid Body Motion 144 4.2.3
Constrained 2D Rigid Body Motion 146 4.3 External and Internal Work and
Potential Energy 147 4.3.1 External Work and Potential Energy 150 4.4 Power
and Work-Energy Laws 151 4.4.1 Particles 151 4.4.2 Rigid Body with 2D
Motion 153 4.5 Lagrange Equation for Particles and Rigid Bodies 157 4.5.1
Derivation of the Lagrange Equation 158 4.5.2 System of Particles 160 4.5.3
Collection of Rigid Bodies 162 4.5.4 Potential, Circulation, and
Dissipation Functions 168 4.5.5 Summary for Lagrange Equation 182 4.5.6
Nonconservative Generalized Forces and Virtual Work 183 4.5.7 Effects of
Gravity for the Lagrange Approach 195 4.5.8 "Automating" the Derivation of
the LE Approach 201 4.6 LE for Flexible, Distributed Mass Bodies: Assumed
Modes Approach 211 4.6.1 Assumed Modes Kinetic Energy and Mass Matrix
Expressions 212 4.6.2 Rotating Structures 215 4.6.3 Internal Forces and
Strain Energy of an Elastic Object 216 4.6.4 The Assumed Modes
Approximation 219 4.6.5 Generalized Force for External Loads Acting on a
Deformable Body 221 4.6.6 Assumed Modes Model Generalized Forces for
External Load Acting on a Deformable Body 221 4.6.7 LE for a System of
Rigid and Deformable Bodies 223 4.7 LE for Flexible, Distributed Mass
Bodies: Finite Element Approach--General Formulation 267 4.7.1 Element
Kinetic Energy and Mass Matrix 267 4.7.2 Element Stiffness Matrix 269 4.7.3
Summary 272 4.8 LE for Flexible, Distributed Mass Bodies: Finite Element
Approach--Bar/Truss Modes 275 4.8.1 Introduction 275 4.8.2 1D Truss/Bar
Element 276 4.8.3 1D Truss/Bar Element: Element Stiffness Matrix 276 4.8.4
1D Truss/Bar Element: Element Mass Matrix 277 4.8.5 1D Truss/Bar Element:
Element Damping Matrix 277 4.8.6 1D Truss/Bar Element: Generalized Force
Vector 278 4.8.7 1D Truss/Bar Element: Nodal Connectivity Array 279 4.8.8
System of 1D Bar Elements: Matrix Assembly 280 4.8.9 Incorporation of
Displacement Constraint 285 4.8.10 Modeling of 2D Trusses 289 4.8.11 2D
Truss/Bar Element: Element Stiffness Matrix 292 4.8.12 2D Truss/Bar
Element: Element Mass Matrix 293 4.8.13 2D Truss/Bar Element: Element
Damping Matrix 294 4.8.14 2D Truss/Bar Element: Element Force Vector 295
4.8.15 2D Truss/Bar Element: Element Action Vector 296 4.8.16 2D Truss/Bar
Element: Degree of Freedom Connectivity Array and Matrix Assembly 296
4.8.17 2D Truss/Bar Element: Rigid Region Modeling for 2D Trusses 303 4.9
Chapter 4 Exercises 306 4.9.1 Exercise Location 306 4.9.2 Exercise Goals
307 4.9.3 Sample Exercises: 4.43 and 4.52 307 References 308 5 Free
Vibration Response 309 5.1 Introduction 309 5.2 Single Degree of Freedom
Systems 309 5.2.1 SDOF Eigenvalues (Characteristic Roots) 310 5.2.2 SDOF
Initial Condition Response 311 5.2.3 Log Decrement: A Measure of
Damping--Displacement-Based Measurement 313 5.2.4 Log Decrement: A Measure
of Damping--Acceleration-Based Measurement 315 5.3 Two-Degree-of-Freedom
Systems 319 5.3.1 Special Case I (C=G=KC = 0) (Undamped, Nongyroscopic, and
Noncirculatory Case) 322 5.3.2 Special Case IIC=KC = 0 (Undamped,
Gyroscopic, and Noncirculatory Case) 332 5.3.3 Special Case III C=G=0
(Undamped, Nongyroscopic, and Circulatory Case) 342 5.4 N-Degree-of-Freedom
Systems 346 5.4.1 General Identities 346 5.4.2 Undamped, Nongyroscopic, and
Noncirculatory Systems--Description 346 5.4.3 Undamped, Nongyroscopic, and
Noncirculatory Systems--Solution Form 347 5.4.4 Undamped, Nongyroscopic,
and Noncirculatory Systems--Orthogonality 349 5.4.5 Undamped,
Nongyroscopic, and Noncirculatory Systems--IC Response 351 5.4.6 Undamped,
Nongyroscopic, and Noncirculatory Systems--Rigid Body Modes 352 5.4.7
Summary 353 5.4.8 Undamped, Nongyroscopic, and Noncirculatory
Systems--Response to an IC Modal Displacement Distribution 363 5.4.9
Orthogonally Damped, Nongyroscopic, and Noncirculatory Systems--Description
364 5.4.10 Orthogonally Damped, Nongyroscopic, and Noncirculatory
Systems--Eigenvalues and Eigenvectors 365 5.4.11 Orthogonally Damped,
Nongyroscopic, and Noncirculatory Systems--IC Response 366 5.4.12
Orthogonally Damped, Nongyroscopic, and Noncirculatory
Systems--Determination of C0 367 5.4.13 Nonorthogonally Damped System with
Symmetric Mass, Stiffness, and Damping Matrices 377 5.4.14 Undamped,
Gyroscopic, and Noncirculatory Systems--Description 379 5.4.15 Undamped,
Gyroscopic, and Noncirculatory Systems--Eigenvalues and Eigenvectors 380
5.4.16 Undamped, Gyroscopic, and Noncirculatory Systems--Biorthogonality
385 5.4.17 General Linear Systems--Description 388 5.4.18 General Linear
Systems--Biorthogonality 389 5.5 Infinite Dof Continuous Member Systems 390
5.5.1 Introduction 390 5.5.2 Transverse Vibration of Strings and Cables 390
5.5.3 Axial Vibration of a Uniform Bar 394 5.5.4 Torsion of Bars 396 5.5.5
Euler-Bernoulli (Classical) Beam Theory 400 5.5.6 Timoshenko Beam Theory
404 5.6 Unstable Free Vibrations 408 5.6.1 Oil Film Bearing-Induced
Instability 411 5.7 Summary 418 5.8 Chapter 5 Exercises 418 5.8.1 Exercise
Location 418 5.8.2 Exercise Goals 418 5.8.3 Sample Exercises: 5.25 and 5.35
419 References 419 6 Vibration Response Due to Transient Loading 421 6.1
Introduction 421 6.2 Single Degree of Freedom Transient Response 421 6.2.1
Direct Analytical Solution Method 422 6.2.2 Laplace Transform Method 428
6.2.3 Convolution Integral 434 6.2.4 Response to Successive Disturbances
438 6.2.5 Pulsed Excitations 440 6.2.6 Response Spectrum 444 6.3 Modal
Condensation of Ndof: Transient Forced Vibrating Systems 451 6.3.1 Undamped
and Orthogonally Damped Nongyroscopic, Noncirculatory Systems 452 6.3.2
Unconstrained Structures 465 6.3.3 Base Excitation 475 6.3.4 Participation
Factor and Modal Effective Mass 477 6.3.5 General Nonsymmetric,
Nonorthogonal Damping Models 488 6.4 Numerical Integration of Ndof
Transient Vibration Response 493 6.4.1 Second-Order System NI Algorithms
494 6.4.2 First-Order System NI Algorithms 500 6.5 Summary 521 6.6 Chapter
6 Exercises 522 6.6.1 Exercise Location 522 6.6.2 Exercise Goals 522 6.6.3
Sample Exercises: 6.18 and 6.21 522 References 523 7 Steady-State Vibration
Response to Periodic Loading 525 7.1 Introduction 525 7.2 Complex Phasor
Approach 525 7.3 Single Degree of Freedom Models 527 7.3.1 Class I (f(t) 0,
y(t) = 0): No Support Excitation--Only External Forcing 529 7.3.2 Class II
(f(t) = 0, y(t) 0): Only Support Excitation--No External Forcing 535 7.3.3
Half Power Point Damping Identification 538 7.3.4 Phase Slope Damping
Identification 541 7.3.5 Accurate Measurement of omegan 541 7.3.6
Experimental Parameter Identification: Receptances 543 7.3.7 Steady-State
Harmonic Response of a Jeffcott Rotor and Rotor Balancing 545 7.3.8 Single
Plane Influence Coefficient Balancing 549 7.3.9 Related American Petroleum
Institute Standards for Balancing 551 7.3.10 Response of an SDOF Oscillator
to Nonsinusoidal, Periodic Excitation 552 7.3.11 Forced Harmonic Response
with Elastomeric Stiffness and Damping 556 7.4 Two Degree of Freedom
Response 559 7.4.1 Vibration Absorber: Principles 560 7.4.2 Vibration
Absorber: Mass Ratio Effect 563 7.5 N Degree of freedom Steady-State
Harmonic Response 566 7.5.1 Direct Approach 566 7.5.2 Modal Approach 570
7.5.3 Receptances 572 7.5.4 Receptance-Based Synthesis 575 7.5.5 Dominance
of a Single Mode in the Steady-State Harmonic Response 577 7.5.6
Receptance-Based Modal Parameter Identification: Method I 578 7.5.7
Receptance-Based Modal Parameter Identification: Method II 585 7.5.8 Modal
Assurance Criterion for Mode Shape Correlation 590 7.6 Other Phasor Ratio
Measures of Steady-State Harmonic Response 591 7.7 Summary 593 7.8 Chapter
7 Exercises 593 7.8.1 Exercise Location 593 7.8.2 Exercise Goals 594 7.8.3
Sample Exercises: 7.9 and 7.23 594 References 594 8 Approximate Methods for
Large-Order Systems 595 8.1 Introduction 595 8.2 Guyan Reduction: Static
Condensation 596 8.3 Substructures: Superelements 608 8.4 Modal Synthesis
609 8.4.1 Uncoupled System Equations 610 8.4.2 Coupled System Equations:
Displacement Compatibility at Junction 611 8.4.3 Coupled System Equations:
Subspace Condensation 611 8.5 Eigenvalue/Natural Frequency Changes for
Perturbed Systems 620 8.5.1 Undamped, Nongyroscopic, Noncirculatory M and K
Type Systems 620 8.5.2 Orthogonally Damped Systems 624 8.5.3 Rayleigh's
Quotient 631 8.6 Summary 633 8.7 Chapter 8 Exercises 634 8.7.1 Exercise
Location 634 8.7.2 Exercise Goals 634 8.7.3 Sample Exercises 8.4 and 8.13
634 References 635 9 Beam Finite Elements for Vibration Analysis 637 9.1
Introduction 637 9.2 Modeling 2D Frame Structures with Euler-Bernoulli Beam
Elements 637 9.2.1 2D Frame Element Stiffness Matrix and Strain Energy:
Transverse Deflection 639 9.2.2 2D Frame Element Stiffness Matrix and
Strain Energy: Axial Deflection 641 9.2.3 2D Frame Element Stiffness Matrix
and Strain Energy 642 9.2.4 2D Frame Element Mass Matrix 642 9.2.5 2D Frame
Element Force Vector 644 9.2.6 2D Frame Element Stiffness and Mass Matrices
and Force Vector: Transformation to Global Coordinates 646 9.2.7 2D Frame:
Beam Element Assembly Algorithm 654 9.2.8 Imposed Support Excitation
Modeling 666 9.3 Three-Dimensional Timoshenko Beam Elements: Introduction
670 9.4 3D Timoshenko Beam Elements: Nodal Coordinates 672 9.5 3D
Timoshenko Beam Elements: Shape Functions, Element Stiffness, and Mass
Matrices 679 9.5.1 Strain-Displacement Relations and Shear Form Factors 681
9.5.2 x1 .x2 Plane, Translational Differential Equations, Shape Functions,
and Stiffness and Mass Matrices 684 9.5.3 x1 .x3 Plane, Translational
Differential Equations, Shape Functions, and Stiffness and Mass Matrices
691 9.5.4 Axial (Longitudinal) x1 Differential Equation, Shape Functions,
and Stiffness and Mass Matrices 696 9.5.5 Torsional theta1 Differential
Equation, Shape Functions, and Stiffness and Mass Matrices 698 9.5.6
Twelve-Dof Element Stiffness Matrix 700 9.5.7 Twelve-Dof Element Mass
Matrix 703 9.6 3D Timoshenko Beam Element Force Vectors 704 9.6.1 Axial
Loads 706 9.6.2 Torsional Loads 706 9.6.3 x1 .x2 Plane Loads 707 9.6.4 x1
.x3 Plane Loads 709 9.6.5 Element Load Vector 711 9.7 3D Frame: Beam
Element Assembly Algorithm 713 9.8 2D Frame Modeling with Timoshenko Beam
Elements 725 9.9 Summary 748 9.10 Chapter 9 Exercises 749 9.10.1 Exercise
Location 749 9.10.2 Exercise Goals 749 9.10.3 Sample Exercises: 9.4 and
9.15a 749 References 750 10 2D Planar Finite Elements for Vibration
Analysis 751 10.1 Introduction 751 10.2 Plane Strain (Pepsilon) 751 10.3
Plane Stress (Psigma) 753 10.4 Plane Stress and Plane Strain: Element
Stiffness and Mass Matrices and Force Vector 754 10.4.1 External Forces 760
10.4.2 Concentrated Forces 760 10.4.3 General Volumetric Loading 761 10.4.4
Edge Loads 762 10.5 Assembly Procedure for 2D, 4-Node, Quadrilateral
Elements 763 10.6 Computation of Stresses in 2D Solid Elements 768 10.6.1
Interior Stress Determination 768 10.6.2 Surface Stresses 770 10.7 Extra
Shape Functions to Improve Accuracy 774 10.8 Illustrative Example 776 10.9
2D Axisymmetric Model 786 10.9.1 Axisymmetric Model Stresses and Strains
786 10.9.2 4-Node, Bilinear Axisymmetric Element 788 10.10 Automated Mesh
Generation: Constant Strain Triangle Elements 801 10.10.1 Element Stiffness
Matrix 803 10.10.2 Element Mass Matrix 803 10.10.3 System Matrix Assembly
804 10.11 Membranes 810 10.11.1 Kinetic Energy and Element Mass Matrix 810
10.11.2 Strain Potential Energy and Element Stiffness Matrix 811 10.11.3
Matrix Assembly 812 10.12 Banded Storage 815 10.13 Chapter 10 Exercises 820
10.13.1 Exercise Location 820 10.13.2 Exercise Goals 821 10.13.3 Sample
Exercises: 10.5 and 10.8 821 References 822 11 3D Solid Elements for
Vibration Analysis 823 11.1 Introduction 823 11.2 Element Stiffness Matrix
825 11.2.1 Shape Functions 825 11.2.2 Element Stiffness Matrix Integral and
Summation Forms 828 11.3 The Element Mass Matrix and Force Vector 835
11.3.1 Element Mass Matrix 836 11.3.2 Element External Force Vector 836
11.3.3 Force Vector: Concentrated Nodal Forces 837 11.3.4 Force Vector:
Volumetric Loads 838 11.3.5 Force Vector: Face Loading 839 11.4 Assembly
Procedure for the 3D, 8-Node, Hexahedral Element Model 842 11.5 Computation
of Stresses for a 3D Hexahedral Solid Element 846 11.5.1 Computation of
Interior Stress 846 11.5.2 Computation of Surface Stresses 848 11.5.3
Coordinate Transformation 849 11.5.4 Geometry Mapping in Surface Tangent
Coordinates 850 11.5.5 Displacements in the Surface Tangent Coordinate
System 851 11.5.6 Strains in the Surface Tangent Coordinate System 851
11.5.7 Surface Stresses Obtained from Cauchy's Boundary Formula 852 11.5.8
Surface Stresses Obtained from the Constitutive Law and Surface Strains 853
11.5.9 Summary of Surface Stress Computation 854 11.6 3D Solid Element
Model Example 856 11.7 3D Solid Element Summary 864 11.8 Chapter 11
Exercises 865 11.8.1 Exercise Location 865 11.8.2 Exercise Goals 865 11.8.3
Sample Exercises: 11.2 and 11.3 865 References 866 12 Active Vibration
Control 867 12.1 Introduction 867 12.2 AVC System Modeling 871 12.3 AVC
Actuator Modeling 874 12.4 System Model with an Infinite Bandwidth Feedback
Approximation 878 12.4.1 Closed-Loop Feedback Controlled System Model 882
12.5 System Model with Finite Bandwidth Feedback 886 12.6 System Model with
Finite Bandwidth Feedback and Lead Compensation 893 12.6.1 Transfer
Function Approach 893 12.6.2 State Space Approach 897 12.7 Sensor/Actuator
Noncollocation Effect on Vibration Stability 901 12.8 Piezoelectric
Actuators 907 12.8.1 Piezoelectric Stack Actuator 908 12.8.2 Piezoelectric
Layer (Patch) Actuator 915 12.9 Summary 923 12.10 Chapter 12 Exercises 923
12.10.1 Exercise Location 923 12.10.2 Exercise Goals 923 12.10.3 Sample
Exercise: 12.1 923 References 924 Appendix A Fundamental Equations of
Elasticity 927 Index 941