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E-raamat: Theory of Vibration Protection

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  • Ilmumisaeg: 09-May-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319280202
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Theory of Vibration ProtectionSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 09-May-2016
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319280202
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This text is an advancement of the theory of vibration protection of mechanical systems with lumped and distributed parameters. The book offers various concepts and methods of solving vibration protection problems, discusses the advantages and disadvantages of different methods, and the fields of their effective applications.Fundamental approaches of vibration protection, which are considered in this book, are the passive, parametric and optimal active vibration protection. The passive vibration protection is based on vibration isolation, vibration damping and dynamic absorbers. Parametric vibration protection theory is based on the Shchipanov-Luzin invariance principle. Optimal active vibration protection theory is based on the Pontryagin principle and the Krein moment method.The book also contains special topics such as suppression of vibrations at the source of their occurrence and the harmful influence of vibrations on humans. About the Authors.Igor A Karnovsky, Ph.D., D

r. Sci., is a specialist in structural analysis, theory of vibration and optimal control of vibration. He has 40 years of experience in research, teaching and consulting in this field, and is the author of more than 70 published scientific papers, including two books in Structural Analysis (published with Springer in 2010-2012) and three handbooks in Structural Dynamics (published with McGraw Hill in 2001-2004). He also holds a number of vibration-control-related patents.Evgeniy Lebed, Ph.D., is a specialist in applied mathematics and engineering. He has 10 years of experience in research, teaching and consulting in this field. The main sphere of his research interests are qualitative theory of differential equations, integral transforms and frequency-domain analysis with application to image and signal processing. He is the author of 15 published scientific papers and a US patent (2015).

Mechanical Exposure and Vibration Protection Methods.- Part I Passive Vibration Protection.- Vibration Isolation of Systems with One Degree of Freedom.- Mechanical Two-Port Network for System with Lumped Parameters.- Mechanical Two and Multi-Portal Networks of Mixed Systems.- Arbitrary Excitation.- Vibration Damping.- Vibration Suppression of the Structures with Lumped Parameters.- Vibration Suppression of the Structures with Distributed Parameters.- Invariant (Parametric) Vibration Protection of Linear Systems.- Nonlinear Theory of Vibration Protection Systems.- Part II Active Vibration Protection.- Pontryagin"s Maximal Principle.- Krein"s Moment Method.- Structural Theory of Vibration Protection Systems.- Part III Shock and Transient Vibration.- Transient Vibration.- Shock and Spectral Theory.- Stability of Vibration Protection Systems.- Vibration Protection of Human-Operator.
Introduction xxiii
Part I Passive Vibration Protection
1 Vibration Isolation of a System with One or More Degrees of Freedom
3(34)
1.1 Design Diagrams of Vibration Protection Systems
3(2)
1.2 Linear Viscously Damped System. Harmonic Excitation and Vibration Protection Criteria
5(10)
1.2.1 Simplest Mechanical Model of a Vibration Protection System
6(1)
1.2.2 Force Excitation. Dynamic and Transmissibility Coefficients
6(4)
1.2.3 Kinematic Excitation. Overload Vibration Coefficient and Estimation of Relative Displacement
10(5)
1.3 Complex Amplitude Method
15(6)
1.3.1 Vector Representation of Harmonic Quantities
15(2)
1.3.2 Single-Axis Vibration Isolator
17(2)
1.3.3 Argand Diagram
19(1)
1.3.4 System with Two Degrees of Freedom
20(1)
1.4 Linear Single-Axis Vibration Protection Systems
21(7)
1.4.1 Damper with Elastic Suspension. Transmissibility Coefficient
22(2)
1.4.2 Simplification of Vibration Isolators
24(2)
1.4.3 Vibration Isolators Which Cannot Be Simplified
26(1)
1.4.4 Special Types of Vibration Isolators
26(2)
1.5 Vibration Protection System of Quasi-Zero Stiffness
28(9)
Problems
32(3)
References
35(2)
2 Mechanical Two-Terminal Networks for a System with Lumped Parameters
37(38)
2.1 Electro-Mechanical Analogies and Dual Circuits
37(5)
2.2 Principal Concepts of Mechanical Networks
42(6)
2.2.1 Vector Representation of Harmonic Force
42(1)
2.2.2 Kinematic Characteristics of Motion
42(1)
2.2.3 Impedance and Mobility of Passive Elements
43(5)
2.3 Construction of Two-Terminal Networks
48(7)
2.3.1 Two-Terminal Network for a Simple Vibration Isolator
49(3)
2.3.2 Two-Cascade Vibration Protection System
52(1)
2.3.3 Complex Dynamical System and Its Coplanar Network
53(2)
2.4 Mechanical Network Theorems
55(5)
2.4.1 Combination of Mechanical Elements
56(2)
2.4.2 Kirchhoff's Laws
58(1)
2.4.3 Reciprocity Theorem
59(1)
2.4.4 Superposition Principle
59(1)
2.5 Simplest One-Side m--k--b Vibration Isolator
60(6)
2.5.1 Force Excitation
60(4)
2.5.2 Kinematic Excitation
64(2)
2.6 Complex One-Sided m--k--b Vibration Isolators
66(9)
2.6.1 Vibration Isolator with Elastic Suspension
66(1)
2.6.2 Two-Cascade Vibration Protection System
67(4)
Problems
71(2)
References
73(2)
3 Mechanical Two-Terminal and Multi-Terminal Networks of Mixed Systems
75(66)
3.1 Fundamental Characteristics of a Deformable System with a Vibration Protection Device
75(9)
3.1.1 Input and Transfer Impedance and Mobility
76(6)
3.1.2 Impedance and Mobility Relating to an Arbitrary Point
82(2)
3.2 Deformable Support of a Vibration Protection System
84(9)
3.2.1 Free Vibrations of Systems with a Finite Number of Degrees of Freedom
84(5)
3.2.2 Generalized Model of Support and Its Impedance
89(2)
3.2.3 Support Models and Effectiveness Coefficient of Vibration Protection
91(2)
3.3 Optimal Synthesis of the Fundamental Characteristics
93(17)
3.3.1 Problem Statement of Optimal Synthesis. Brune's Function
94(1)
3.3.2 Foster's Canonical Schemes
95(5)
3.3.3 Cauer's Canonical Schemes
100(4)
3.3.4 Support as a Deformable System with Distributed Mass
104(6)
3.4 Vibration Protection Device as a Mechanical Four-Terminal Network
110(17)
3.4.1 Mechanical Four-Terminal Network for Passive Elements with Lumped Parameters
111(4)
3.4.2 Connection of an M4TN with Support of Impedance Zf
115(1)
3.4.3 Connections of Mechanical Four-Terminal Networks
116(11)
3.5 Mechanical Multi-Terminal Networks for Passive Elements with Distributed Parameters
127(8)
3.5.1 M4TN for Longitudinal Vibration of Rod
128(2)
3.5.2 Mechanical Eight-Terminal Network for Transversal Vibration of a Uniform Beam
130(5)
3.6 Effectiveness of Vibration Protection
135(6)
Problems
138(1)
References
139(2)
4 Arbitrary Excitation of Dynamical Systems
141(26)
4.1 Transfer Function
141(10)
4.1.1 Analysis in the Time Domain
141(7)
4.1.2 Logarithmic Plot of Frequency Response. Bode Diagram
148(3)
4.2 Green's Function and Duhamel's Integral
151(8)
4.2.1 System with Lumped Parameters
152(4)
4.2.2 System with Distributed Parameters
156(3)
4.3 Standardizing Function
159(8)
Problems
163(2)
References
165(2)
5 Vibration Damping
167(40)
5.1 Phenomenological Aspects
168(8)
5.1.1 Models of Material
168(2)
5.1.2 Complex Modulus of Elasticity
170(1)
5.1.3 Dissipative Forces
171(1)
5.1.4 Dimensionless Parameters of Energy Dissipation
172(4)
5.2 Hysteretic Damping
176(6)
5.2.1 Hysteresis Loop
176(2)
5.2.2 Hysteretic Damping Concept
178(1)
5.2.3 Forced Vibration of a System with One Degree of Freedom
179(3)
5.2.4 Comparison of Viscous and Hysteretic Damping
182(1)
5.3 Structural Damping
182(7)
5.3.1 General
183(2)
5.3.2 Energy Dissipation in Systems with Lumped Friction
185(1)
5.3.3 Energy Dissipation in Systems with Distributed Friction
186(3)
5.4 Equivalent Viscous Damping
189(2)
5.4.1 Absorption Coefficient
189(1)
5.4.2 Equivalent Viscoelastic Model
189(2)
5.5 Vibration of a Beam with Internal Hysteretic Friction
191(3)
5.6 Vibration of a Beam with External Damping Coating
194(6)
5.6.1 Vibration-Absorbing Layered Structures
195(1)
5.6.2 Transverse Vibration of a Two-Layer Beam
196(4)
5.7 Aerodynamic Damping
200(7)
5.7.1 The Interaction of a Structure with a Flow
201(1)
5.7.2 Aerodynamic Reduction of Vibration
202(1)
Problems
203(1)
References
204(3)
6 Vibration Suppression of Systems with Lumped Parameters
207(38)
6.1 Dynamic Absorber
207(6)
6.2 Dynamic Absorbers with Damping
213(6)
6.2.1 Absorber with Viscous Damping
214(2)
6.2.2 Viscous Shock Absorber
216(1)
6.2.3 Absorber with Coulomb Damping
217(2)
6.3 Roller Inertia Absorbers
219(3)
6.4 Absorbers of Torsional Vibration
222(6)
6.4.1 Centrifugal Pendulum Vibration Absorber
222(4)
6.4.2 Pringle's Vibration Absorber
226(2)
6.5 Gyroscopic Vibration Absorber
228(6)
6.5.1 Elementary Theory of Gyroscopes
229(3)
6.5.2 Schlick's Gyroscopic Vibration Absorber
232(2)
6.6 Impact Absorbers
234(4)
6.6.1 Pendulum Impact Absorber
235(2)
6.6.2 Floating Impact Absorber
237(1)
6.6.3 Spring Impact Absorber
238(1)
6.7 Autoparametric Vibration Absorber
238(7)
Problems
240(2)
References
242(3)
7 Vibration Suppression of Structures with Distributed Parameters
245(20)
7.1 Krylov--Duncan Method
245(5)
7.2 Lumped Vibration Absorber of the Beam
250(4)
7.3 Distributed Vibration Absorber
254(3)
7.4 Extension Rod as Absorber
257(8)
Problems
262(1)
References
263(2)
8 Parametric Vibration Protection of Linear Systems
265(24)
8.1 General
265(1)
8.2 Invariance Principle
266(5)
8.2.1 Shchipanov--Luzin Absolute Invariance
266(2)
8.2.2 Invariance up to ε
268(3)
8.3 Parametric Vibration Protection of the Spinning Rotor
271(4)
8.4 Physical Feasibility of the Invariance Conditions
275(5)
8.4.1 Uncontrollability of "Perturbation-Coordinate" Channel
275(2)
8.4.2 Petrov's Two-Channel Principle
277(1)
8.4.3 Dynamic Vibration Absorber
278(2)
8.5 Parametric Vibration Protection of the Plate Under a Moving Load
280(9)
8.5.1 Mathematical Model of a System
280(4)
8.5.2 Petrov's Principle
284(1)
Problems
285(2)
References
287(2)
9 Nonlinear Theory of Vibration Protection Systems
289(44)
9.1 General
289(6)
9.1.1 Types of Nonlinearities and Theirs Characteristics
290(4)
9.1.2 Features of Nonlinear Vibration
294(1)
9.2 Harmonic Linearization Method
295(8)
9.2.1 Method Foundation
295(5)
9.2.2 Coefficients of Harmonic Linearization
300(3)
9.3 Harmonic Excitation
303(16)
9.3.1 Duffing's Restoring Force
303(4)
9.3.2 Nonlinear Restoring Force and Viscous Damping
307(4)
9.3.3 Linear Restoring Force and Coulomb's Friction
311(5)
9.3.4 Internal Friction
316(3)
9.4 Nonlinear Vibration Absorber
319(3)
9.5 Harmonic Linearization and Mechanical Impedance Method
322(2)
9.6 Linearization of a System with an Arbitrary Number of Degrees of Freedom
324(9)
Problems
328(1)
References
329(4)
Part II Active Vibration Protection
10 Pontryagin's Principle
333(52)
10.1 Active Vibration Protection of Mechanical Systems as a Control Problem
333(8)
10.1.1 Mathematical Model of Vibration Protection Problem
333(7)
10.1.2 Classification of Optimal Vibration Protection Problems
340(1)
10.2 Representation of an Equation of State in Cauchy's Matrix Form
341(6)
10.3 Qualitative Properties of Vibration Protection Systems
347(8)
10.3.1 Accessibility, Controllability, Normality
347(3)
10.3.2 Stability
350(5)
10.4 Pontryagin's Principle
355(2)
10.5 Vibration Suppression of a System with Lumped Parameters
357(12)
10.5.1 Vibration Suppression Problems Without Constraints
358(9)
10.5.2 Vibration Suppression Problem with Constrained Exposure. Quadratic Functional, Fixed Time and Fixed End
367(2)
10.6 Bushaw's Minimum-Time Problem
369(8)
10.7 Minimum Isochrones
377(8)
Problems
380(3)
References
383(2)
11 Krein Moments Method
385(42)
11.1 The Optimal Active Vibration Protection Problem as the l-moments Problem
386(7)
11.1.1 Formulation of the Problem of Vibration Suppression as a Moment Problem
386(5)
11.1.2 The l-moments Problem and Numerical Procedures
391(2)
11.2 Time-Optimal Problem for a Linear Oscillator
393(5)
11.2.1 Constraint of Energy
393(2)
11.2.2 Control with Magnitude Constraint
395(3)
11.3 Optimal Active Vibration Protection of Continuous Systems
398(17)
11.3.1 Truncated Moments Problem
398(1)
11.3.2 Vibration Suppression of String. Standardizing Function
398(6)
11.3.3 Vibration Suppression of a Beam
404(9)
11.3.4 Nonlinear Moment Problem
413(2)
11.4 Modified Moments Procedure
415(5)
11.5 Optimal Vibration Suppression of a Plate as a Mathematical Programming Problem
420(7)
Problems
424(1)
References
425(2)
12 Structural Theory of Vibration Protection Systems
427(58)
12.1 Operator Characteristics of a Dynamical System
428(22)
12.1.1 Types of Operator Characteristics
428(4)
12.1.2 Transfer Function
432(2)
12.1.3 Elementary Blocks
434(7)
12.1.4 Combination of Blocks. Bode Diagram
441(7)
12.1.5 Block Diagram Transformations
448(2)
12.2 Block Diagrams of Vibration Protection Systems
450(15)
12.2.1 Representation of b--k and b--m Systems as Block Diagram
450(7)
12.2.2 Vibration Protection Closed Control System
457(6)
12.2.3 Dynamic Vibration Absorber
463(2)
12.3 Vibration Protection Systems with Additional Passive Linkages
465(2)
12.3.1 Linkage with Negative Stiffness
465(1)
12.3.2 Linkage by the Acceleration
466(1)
12.4 Vibration Protection Systems with Additional Active Linkages
467(18)
12.4.1 Functional Schemes of Active Vibration Protection Systems
468(1)
12.4.2 Vibration Protection on the Basis of Excitation. Invariant System
469(2)
12.4.3 Vibration Protection on the Basis of Object State. Effectiveness Criteria
471(6)
12.4.4 Block Diagram of Optimal Feedback Vibration Protection
477(2)
Problems
479(2)
References
481(4)
Part III Shock and Transient Vibration
13 Active and Parametric Vibration Protection of Transient Vibrations
485(34)
13.1 Laplace Transform
485(6)
13.2 Heaviside Method
491(10)
13.3 Active Suppression of Transient Vibration
501(7)
13.3.1 Step Excitation
501(4)
13.3.2 Impulse Excitation
505(3)
13.4 Parametric Vibration Suppression
508(11)
13.4.1 Recurrent Instantaneous Pulses
508(2)
13.4.2 Recurrent Impulses of Finite Duration
510(3)
Problems
513(4)
References
517(2)
14 Shock and Spectral Theory
519(42)
14.1 Concepts of Shock Excitation
519(18)
14.1.1 Types of Shock Exposures
519(2)
14.1.2 Different Approaches to the Shock Problem
521(6)
14.1.3 Fourier Transform
527(9)
14.1.4 Time and Frequency Domain Concepts
536(1)
14.2 Forced Shock Excitation of Vibration
537(7)
14.2.1 Heaviside Step Excitation
538(2)
14.2.2 Step Excitation of Finite Duration
540(3)
14.2.3 Impulse Excitation
543(1)
14.3 Kinematic Shock Excitation of Vibration
544(4)
14.3.1 Forms of the Vibration Equation
545(1)
14.3.2 Response of a Linear Oscillator to Acceleration Impulse
546(2)
14.4 Spectral Shock Theory
548(6)
14.4.1 Biot's Dynamic Model of a Structure: Primary and Residual Shock Spectrum
549(2)
14.4.2 Response Spectra for the Simplest Vibration Protection System
551(1)
14.4.3 Spectral Method for Determination of Response
552(2)
14.5 Brief Comments on the Various Methods of Analysis
554(7)
Problems
557(2)
References
559(2)
15 Statistical Theory of the Vibration Protection Systems
561(44)
15.1 Random Processes and Their Characteristics
562(8)
15.1.1 Probability Distribution and Probability Density
563(2)
15.1.2 Mathematical Expectation and Dispersion
565(3)
15.1.3 Correlational Function
568(2)
15.2 Stationary Random Processes
570(12)
15.2.1 Properties of Stationary Random Processes
570(3)
15.2.2 Ergodic Processes
573(1)
15.2.3 Spectral Density
574(3)
15.2.4 Transformations of Random Exposures by a Linear System
577(5)
15.3 Dynamic Random Excitation of a Linear Oscillator
582(9)
15.3.1 Transient Vibration Caused by Impulse Shock
583(4)
15.3.2 Force Random Excitation
587(4)
15.4 Kinematic Random Excitation of Linear Oscillator
591(14)
15.4.1 Harmonic and Polyharmonic Excitations
591(6)
15.4.2 Shock Vibration Excitation by a Set of Damped Harmonics
597(3)
Problems
600(1)
References
601(4)
Part IV Special Topics
16 Rotating and Planar Machinery as a Source of Dynamic Exposures on a Structure
605(18)
16.1 Dynamic Pressure on the Axis of a Rotating Body
605(4)
16.2 Types of Unbalancing Rotor
609(3)
16.2.1 Static Unbalance
609(1)
16.2.2 Couple Unbalance
610(1)
16.2.3 Dynamic Unbalance
610(1)
16.2.4 Quasi-Static Unbalance
611(1)
16.3 Shaking Forces of a Slider Crank Mechanism
612(11)
16.3.1 Dynamic Reactions
614(3)
16.3.2 Elimination of Dynamic Reactions
617(1)
Problems
618(4)
References
622(1)
17 Human Operator Under Vibration and Shock
623(34)
17.1 Introduction
623(5)
17.1.1 Vibration Exposures and Methods of Their Transfer on the Person
624(4)
17.1.2 International and National Standards
628(1)
17.2 Influence of Vibration Exposure on the Human Subject
628(7)
17.2.1 Classification of the Adverse Effects of Vibration on the Person
629(2)
17.2.2 Effect of Vibration on the Human Operator
631(4)
17.3 Vibration Dose Value
635(4)
17.4 Mechanical Properties and Frequency Characteristics of the Body
639(6)
17.4.1 Mechanical Properties of the Human Body
640(2)
17.4.2 Frequency Characteristics of the Human Body
642(3)
17.5 Models of the Human Body
645(12)
17.5.1 Basic Dynamic 1D Models
647(4)
17.5.2 Dynamic 2D--3D Models of the Sitting Human Body at the Collision
651(2)
17.5.3 Parameters of the Human Body Model
653(4)
References 657(4)
Appendix A Complex Numbers 661(4)
Appendix B Laplace Transform 665(4)
Index 669
Igor A Karnovsky, Ph.D., Dr. Sci., is a specialist in structural analysis, theory of vibration and optimal control of vibration. He has 40 years  of experience in research, teaching and consulting in this field, and is the author of more than 70 published scientific papers, including two books in Structural Analysis (published with Springer in 2010-2012) and three handbooks in Structural Dynamics (published with McGraw Hill in 2001-2004). He also holds a number of vibration-control-related patents.



Evgeniy Lebed, Ph.D., is a specialist in applied mathematics and engineering. He has 10 years of experience in research, teaching and consulting in this field. The main sphere of his research interests are qualitative theory of differential equations, integral transforms and frequency-domain analysis with application to image and signal processing. He is the author of 15 published scientific papers and a US patent (2015).
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