Vibration of mechanical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Cambridge Univ. Press
2014
|
| Edition: | 1. paperback ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | 1. publ. 2010 |
| Physical Description: | XV, 308 S. graph. Darst. |
| ISBN: | 9780521518734 1107694175 9781107694170 |
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| 245 | 1 | 0 | |a Vibration of mechanical systems |c Alok Sinha |
| 250 | |a 1. paperback ed. | ||
| 264 | 1 | |a New York, NY |b Cambridge Univ. Press |c 2014 | |
| 300 | |a XV, 308 S. |b graph. Darst. | ||
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| adam_text | CONTENTS/)
Preface page
xiii
1
Equivalent Single-Degree-of-Freedom System and Free
Vibration
...................................................... 1
1.1
Degrees of Freedom
3
1.2
Elements of a Vibratory System
5
/.2./
Aims and/or Mass-Moment of Inertia
5
Pure Translational Motion
5
Pure Rotational Motion
6
Planar Motion (Combined Rotation
and Translation) of a Rigid Body
6
Special Case: Pure Rotation about a Fixed Point
8
1.2.2
Spring
8
Pure Translational Motion
8
Pure Rotational Motion
9
1.2.3
Damper
10
Pure Translational Motion
10
Pure Rotational Motion
11
1.3
Equivalent Mass, Equivalent Stiffness, and Equivalent
Damping Constant for an SDOF System
12
13,1
Λ
Rotor-Shaft System
13
1.3.2
Equivalent Mass of a Spring
14
1.3.3
Springs in Series and Parallel
16
Springs in Series
16
Springs in Parallel
17
1.3.4
An SDOF System with Two Springs and Combined
Rotational and Translational Motion
19
/.3.5
Viscous Dampers in Series and Parallel
22
viii Contents
Dampers in Series
22
Dampers in Parallel
23
1.4
Free Vibration of an Undamped SDOF System
25
1.4.1
Differential Equation of Motion
25
Energy Approach
27
1.4.2
Solution of the Differential Equation of Motion
Governing Free Vibration of an Undamped
Spring-Mass System
34
1.5
Free Vibration of a Viscously Damped SDOF System
40
1.5.1
Differential Equation of Motion
40
1.5.2
Solution of the Differential Equation of Motion
Governing Free Vibration of a Damped
Spring—Mass
Systern
41
Case I: Underdamped
(0 <
ξ
< 1
or
0 <
ce(,
<
cc)
42
Case II: Critically Damped
(ξ
= 1
or
сщ
=
cc)
45
Case III: Overdamped
(ξ
> 1
or ceq
>
cL)
46
1.5.3
Logarithmic Decrement: Identification of Damping
Ratio from Free Response of an Underdamped
System
(0 <
ξ
< 1) 51
Solution
55
1.6
Stability of an SDOF Spring-M ass-Damper System
58
Exercise Problems
63
2
Vibration of a Single-Degree-of-Freedom System Under
Constant and Purely Harmonic Excitation
...................... 72
2.1
Responses of Undamped and Damped SDOF Systems
to a Constant Force
72
Case I: Undamped
(£ = 0)
and Underdamped
(0 <
ξ
< 1) 74
Case II: Critically Damped
(£ = 1
or ceq
— cv) 75
Case III: Overdamped
(ξ
> 1
or ceq
>
сс)
76
2.2
Response of an Undamped SDOF System
to a Harmonic Excitation
82
Case
Ι: ω φ ωη
83
Case II:
ω
=
co,,
(Resonance)
84
Case
Ι: ω φ
co,,
87
Case
II:
ω
=
co,¡
87
2.3
Response of a Damped SDOF System to a Harmonic
Excitation
88
Particular Solution
89
Case I: Underdamped
(0 <
ξ
< 1
or
0 <
ceq
<
cť)
92
Contents ix
Case II:
Critically Damped
(§ = 1
or
ceí¡
=
cc)
92
Case III: Overdamped
(£ > 1
or cecj
>
cr)
94
2.5./
Steady State Response
95
2.3.2
Porce Transmiss
ibiľity
101
2.J.
J
Quality Factor and Bandwidth
106
Quality Factor
106
Bandwidth
107
2.4
Rotating Unbalance
109
2.5
Base Excitation
116
2.6
Vibration Measuring Instruments
121
2.6.
1
Vi
brom eter
123
2.6.2
Acceler
ometer
126
2.7
Equivalent Viscous Damping for Nonviscous Energy
Dissipation
128
Exercise Problems
132
3
Responses of an SDOF Spring-Mass-Damper System
to Periodic and Arbitrary Forces
............................... 138
3.1
Response of an SDOF System to a Periodic Force
138
3.1.1
Periodic Function and its Fourier Series Expansion
139
3.1.2
Even and Odd Periodic Functions
142
Fourier Coefficients for Even Periodic Functions
143
Fourier Coefficients for Odd Periodic Functions
145
3.1.3
Fourier Series Expansion of a Function
with a Finite Duration
147
3.1.4
Particular Integral (Steady-State Response
with Damping) Under Periodic Excitation
151
3.2
Response to an Excitation with Arbitrary Nature
154
3.2.1
Unit Impulse Function S(t
—
a)
155
3.2.2
Unit Impulse Response of an SDOF System
with Zero Initial Conditions
156
Case I: Undamped and Underdamped System
(0 <£ < 1) 158
Case II: Critically Damped
(£ = 1
or ceq
=
c<)
158
Case III: Overdamped
(£ > 1
or
cťq >ct)
159
3.2.3
Convolution Integral: Response to an Arbitrary
Excitation with Zero Initial Conditions
160
3.2.4
Convolution Integral: Response to an Arbitrary
Excitation with Nonzero Initial Conditions
165
Case I: Undamped and Underdamped
(0 <
ξ
< 1
or
0 <
ceq
<
с,.)
166
Contents
Case II: Critically Damped
(ξ
— 1
or ceq
=
cc)
166
Case III: Overdamped (f
> 1
or ceq
>
q)
166
3.3
Lapiace
Transformation
168
3.3.1
Properties of Eaplace Transformation
169
3.3.2
Response of an SDOF System via Laplace
Transformation
170
3.3.3
Transfer Function and Frequency Response
Function
173
Significance of Transfer Function
175
Poles and Zeros of Transfer Function
175
Frequency Response Function
176
Exercise Problems
179
4
Vibration of Two-Degree-of-Freedom-Systems
................. 186
4.1
Mass, Stiffness, and Damping Matrices
187
4.2
Natural Frequencies and Mode Shapes
192
4.2.1
Eigenvalue/Eigenvector Interpretation
197
4.3
Free Response of an Undamped 2DOF System
198
Solution
200
4.4
Forced Response of an Undamped 2DOF System Under
Sinusoidal Excitation
201
4.5
Free Vibration of a Damped 2DOF System
203
4.6
Steady-State Response of a Damped 2DOF System
Under Sinusoidal Excitation
209
4.7
Vibration Absorber
212
4.7.1
Undamped Vibration
Λ
bsorber
212
4.7.2
Damped Vibration Absorber
220
Case I: Tuned Case
(ƒ = 1
or
¿022
=ωιι)
224
Case II: No restriction on
ƒ
(Absorber not tuned
to main system)
224
4.8
Modal Decomposition of Response
227
Case I: Undamped System (C
= 0) 228
Case II: Damped System (C
φ
0) 228
Exercise Problems
231
5
Finite and Infinite (Continuous) Dimensional Systems
.......... 237
5.1
Multi-Degree-of-Freedom Systems
237
5.1.1
Natural Frequencies and Modal Vectors
(Mode Shapes)
239
5.1.2
Orthogonality of Eigenvectors for Symmetric Mass
and Symmetric Stiffness Matrices
242
Contents xi
5.1.3
Modal Decomposition
245
Case I: Undamped System (C
= 0) 246
Case II: Proportional or Rayleigh Damping
249
5.2
Continuous Systems Governed by Wave Equations
250
5.2.1
Transverse Vibration of a String
250
Natural Frequencies and Mode Shapes
251
Computation of Response
255
5.2.2
Longitudinal Vibration of a Bar
258
5.2.3
Torsionai
Vibration of a Circular Shaft
261
5.3
Continuous Systems: Transverse Vibration of a Beam
265
5.3. /
Governing Partial Differential Equation of Motion
265
5.3.2
Natural Frequencies and Mode Shapes
267
Simply Supported Beam
269
Cantilever Beam
271
5.3.3
Computation of Response
213
5.4
Finite Element Analysis
279
5.4.1
Longitudinal Vibration of a Bar
279
Total Kinetic and Potential Energies of the Bar
283
5.4.2
Transverse Vibration of a Beam
286
Total Kinetic and Potential Energies of the Beam
291
Exercise Problems
295
APPENDIX A: EQUIVALENT STIFFNESSES (SPRING
CONSTANTS) OF BEAMS, TORSIONAL SHAFT, AND
LONGITUDINAL BAR
.................................................... 299
APPENDIX B: SOME MATHEMATICAL FORMULAE
................. 302
APPENDIX C: LAPLACE TRANSFORM TABLE
........................ 304
References
305
Index
307
This is a textbook for a first course in mechanical vibrations. There are many books in
this area that try to include everything, thus they have become exhaustive
compendi¬
ums
that are overwhelming for an undergraduate. In this book, all the basic concepts
in mechanical vibrations are clearly identified and presented in a concise and simple
manner with illustrative and practical examples. Vibration concepts include a review
of selected topics in mechanics; a description of single-degree-of-freedom (SDOF)
systems in terms of equivalent mass, equivalent stiffness, and equivalent damping; a
unified treatment of various forced response problems (base excitation and rotating
balance); an introduction to systems thinking, highlighting the fact that SDOF analysis
is a building block for mufti-degree-of-freedom {MDOF) and continuous system analy¬
ses via modal analysis; and a simple introduction to finite element analysis to connect
continuous system and MDOF analyses. There are more than
60
exercise problems
and a complete solutions manual. The use of
MATLAB®
software is emphasized.
ALOK SINHA is a Professor of Mechanical Engineering at The Pennsylvania State
University
(PSU),
University Park. He received his PhD degree in mechanical engineer¬
ing from Carnegie Mellon University. He has been a PSU faculty member since August
1983.
His areas of teaching and research are vibration, control systems, jet engines,
robotics, neural networks, and nanotechnology. He is the author of Linear Systems:
Optimal and Robust Control.
He has served as a Visiting Associate Professor of Aeronautics and Astronautics at MIT,
Cambridge, MA, and as a researcher at Pratt
&
Whitney, East Hartford, CT. He has also
been an associate editor of
ASME
Journal of Dynamic Systems, Measurement and
Control. At present, he serves as an associate editor of
ASME
Journal of Turbomachin-
ery and AIAA Journal.
Alok Sinha is a Fellow of
ASME. He
has received the NASA certificate of recognition for
significant contributions to the Space Shuttle Microgravity Mission.
|
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| discipline | Maschinenbau / Maschinenwesen Physik |
| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV042330180 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T06:43:18Z |
| institution | BVB |
| isbn | 9780521518734 1107694175 9781107694170 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027766948 |
| oclc_num | 912325731 |
| open_access_boolean | |
| owner | DE-703 DE-573 DE-862 DE-BY-FWS DE-1050 |
| owner_facet | DE-703 DE-573 DE-862 DE-BY-FWS DE-1050 |
| physical | XV, 308 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spellingShingle | Sinha, Alok K. Vibration of mechanical systems Mechanische Schwingung (DE-588)4138305-9 gnd Maschinendynamik (DE-588)4130692-2 gnd Mechanisches System (DE-588)4132811-5 gnd Schwingung (DE-588)4053999-4 gnd Maschinenschwingung (DE-588)4130655-7 gnd |
| subject_GND | (DE-588)4138305-9 (DE-588)4130692-2 (DE-588)4132811-5 (DE-588)4053999-4 (DE-588)4130655-7 |
| title | Vibration of mechanical systems |
| title_auth | Vibration of mechanical systems |
| title_exact_search | Vibration of mechanical systems |
| title_full | Vibration of mechanical systems Alok Sinha |
| title_fullStr | Vibration of mechanical systems Alok Sinha |
| title_full_unstemmed | Vibration of mechanical systems Alok Sinha |
| title_short | Vibration of mechanical systems |
| title_sort | vibration of mechanical systems |
| topic | Mechanische Schwingung (DE-588)4138305-9 gnd Maschinendynamik (DE-588)4130692-2 gnd Mechanisches System (DE-588)4132811-5 gnd Schwingung (DE-588)4053999-4 gnd Maschinenschwingung (DE-588)4130655-7 gnd |
| topic_facet | Mechanische Schwingung Maschinendynamik Mechanisches System Schwingung Maschinenschwingung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027766948&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027766948&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT sinhaalokk vibrationofmechanicalsystems |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 ZL 3050 S617 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |