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Hagedorn, Peter, Dasgupta, Anirvan

Vibrations and Waves in Continuous Mechanical Systems

€ 111.95

Providing a first course on vibrations of continuous system, Vibrations and Waves in Continuous Mechanical Systems deals with the underlying theory and analysis techni


Taal / Language : English

Inhoudsopgave:
Preface xi
1 Vibrations of strings and bars 1
1.1 Dynamics of strings and bars: the Newtonian formulation
1
1.1.1 Transverse dynamics of strings
1
1.1.2 Longitudinal dynamics of bars
6
1.1.3 Torsional dynamics of bars
7
1.2 Dynamics of strings and bars: the variational formulation
9
1.2.1 Transverse dynamics of strings
10
1.2.2 Longitudinal dynamics of bars
11
1.2.3 Torsional dynamics of bars
13
1.3 Free vibration problem: Bernoulli`s solution
14
1.4 Modal analysis
18
1.4.1 The eigenvalue problem
18
1.4.2 Orthogonality of eigenfunctions
24
1.4.3 The expansion theorem
25
1.4.4 Systems with discrete elements
27
1.5 The initial value problem: solution using Laplace transform
30
1.6 Forced vibration analysis
31
1.6.1 Harmonic forcing
32
1.6.2 General forcing
36
1.7 Approximate methods for continuous systems
40
1.7.1 Rayleigh method
41
1.7.2 Rayleigh Ritz method
43
1.7.3 Ritz method
44
1.7.4 Galerkin method
47
1.8 Continuous systems with damping
50
1.8.1 Systems with distributed damping
50
1.8.2 Systems with discrete damping
53
1.9 Non-homogeneous boundary conditions
56
1.10 Dynamics of axially translating strings
57
1.10.1 Equation of motion
58
1.10.2 Modal analysis and discretization
58
1.10.3 Interaction with discrete elements
61
Exercises
62
References
67
2 One-dimensional wave equation: d`Alembert`s solution 69
2.1 D`Alembert`s solution of the wave equation
69
2.1.1 The initial value problem
72
2.1.2 The initial value problem: solution using Fourier transform
76
2.2 Harmonic waves and wave impedance
77
2.3 Energetics of wave motion
79
2.4 Scattering of waves
83
2.4.1 Reflection at a boundary
83
2.4.2 Scattering at a finite impedance
87
2.5 Applications of the wave solution
93
2.5.1 Impulsive start of a bar
93
2.5.2 Step-forcing of a bar with boundary damping
95
2.5.3 Axial collision of bars
99
2.5.4 String on a compliant foundation
102
2.5.5 Axially translating string
104
Exercises
107
References
112
3 Vibrations of beams 113
3.1 Equation of motion
113
3.1.1 The Newtonian formulation
113
3.1.2 The variational formulation
116
3.1.3 Various boundary conditions for a beam
118
3.1.4 Taut string and tensioned beam
120
3.2 Free vibration problem
121
3.2.1 Modal analysis
121
3.2.2 The initial value problem
132
3.3 Forced vibration analysis
133
3.3.1 Eigenfunction expansion method
134
3.3.2 Approximate methods
135
3.4 Non-homogeneous boundary conditions
137
3.5 Dispersion relation and flexural waves in a uniform beam
138
3.5.1 Energy transport
140
3.5.2 Scattering of flexural waves
142
3.6 The Timoshenko beam
144
3.6.1 Equations of motion
144
3.6.2 Harmonic waves and dispersion relation
147
3.7 Damped vibration of beams
149
3.8 Special problems in vibrations of beams
151
3.8.1 Influence of axial force on dynamic stability
151
3.8.2 Beam with eccentric mass distribution
155
3.8.3 Problems involving the motion of material points of a vibrating beam
159
3.8.4 Dynamics of rotating shafts
163
3.8.5 Dynamics of axially translating beams
165
3.8.6 Dynamics of fluid-conveying pipes
168
Exercises
171
References
178
4 Vibrations of membranes 179
4.1 Dynamics of a membrane
179
4.1.1 Newtonian formulation
179
4.1.2 Variational formulation
182
4.2 Modal analysis
185
4.2.1 The rectangular membrane
185
4.2.2 The circular membrane
190
4.3 Forced vibration analysis
197
4.4 Applications: kettledrum and condenser microphone
197
4.4.1 Modal analysis
197
4.4.2 Forced vibration analysis
201
4.5 Waves in membranes
202
4.5.1 Waves in Cartesian coordinates
202
4.5.2 Waves in polar coordinates
204
4.5.3 Energetics of membrane waves
207
4.5.4 Initial value problem for infinite membranes
208
4.5.5 Reflection of plane waves
209
Exercises
213
References
214
5 Vibrations of plates 217
5.1 Dynamics of plates
217
5.1.1 Newtonian formulation
217
5.2 Vibrations of rectangular plates
222
5.2.1 Free vibrations
222
5.2.2 Orthogonality of plate eigenfunctions
228
5.2.3 Forced vibrations
229
5.3 Vibrations of circular plates
231
5.3.1 Free vibrations
231
5.3.2 Forced vibrations
234
5.4 Waves in plates
236
5.5 Plates with varying thickness
238
Exercises
239
References
241
6 Boundary value and eigenvalue problems in vibrations 243
6.1 Self-adjoint operators and eigenvalue problems for undamped free vibrations
243
6.1.1 General properties and expansion theorem
243
6.1.2 Green`s functions and integral formulation of eigenvalue problems
252
6.1.3 Bounds for eigenvalues: Rayleigh`s quotient and other methods
255
6.2 Forced vibrations
259
6.2.1 Equations of motion
259
6.2.2 Green`s function for inhomogeneous vibration problems
260
6.3 Some discretization methods for free and forced vibrations
261
6.3.1 Expansion in function series
261
6.3.2 The collocation method
262
6.3.3 The method of subdomains
266
6.3.4 Galerkin`s method
267
6.3.5 The Rayleigh Ritz method
269
6.3.6 The finite-element method
272
References
288
7 Waves in fluids 289
7.1 Acoustic waves in fluids
289
7.1.1 The acoustic wave equation
289
7.1.2 Planar acoustic waves
294
7.1.3 Energetics of planar acoustic waves
295
7.1.4 Reflection and refraction of planar acoustic waves
297
7.1.5 Spherical waves
300
7.1.6 Cylindrical waves
305
7.1.7 Acoustic radiation from membranes and plates
307
7.1.8 Waves in wave guides
314
7.1.9 Acoustic waves in a slightly viscous fluid
318
7.2 Surface waves in incompressible liquids
320
7.2.1 Dynamics of surface waves
320
7.2.2 Sloshing of liquids in tanks
323
7.2.3 Surface waves in a channel
330
Exercises
334
References
337
8 Waves in elastic continua 339
8.1 Equations of motion
339
8.2 Plane elastic waves in unbounded continua
344
8.3 Energetics of elastic waves
346
8.4 Reflection of elastic waves
348
8.4.1 Reflection from a free boundary
349
8.5 Rayleigh surface waves
353
8.6 Reflection and refraction of planar acoustic waves
357
Exercises
359
References
361
A The variational formulation of dynamics 363
References
365
B Harmonic waves and dispersion relation 367
B.1 Fourier representation and harmonic waves
367
B.2 Phase velocity and group velocity
369
References
372
C Variational formulation for dynamics of plates 373
References 378
Index 379
Extra informatie: 
Hardback
396 pagina's
Januari 2007
839 gram
254 x 178 x 25 mm
Wiley-Blackwell us

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