The subject of vibrations is of fundamental importance in
engineering and technology. Discrete modelling is sufficient to
understand the dynamics of many vibrating systems; however a large
number of vibration phenomena are far more easily understood when
modelled as continuous systems. The theory of vibrations in
continuous systems is crucial to the understanding of engineering
problems in areas as diverse as automotive brakes, overhead
transmission lines, liquid filled tanks, ultrasonic testing or room
acoustics.
Starting from an elementary level, Vibrations and Waves in
Continuous Mechanical Systems helps develop a comprehensive
understanding of the theory of these systems and the tools with
which to analyse them, before progressing to more advanced
topics.
* Presents dynamics and analysis techniques for a wide range of
continuous systems including strings, bars, beams, membranes,
plates, fluids and elastic bodies in one, two and three
dimensions.
* Covers special topics such as the interaction of discrete and
continuous systems, vibrations in translating media, and sound
emission from vibrating surfaces, among others.
* Develops the reader’s understanding by progressing from
very simple results to more complex analysis without skipping the
key steps in the derivations.
* Offers a number of new topics and exercises that form essential
steppingstones to the present level of research in the field.
* Includes exercises at the end of the chapters based on both the
academic and practical experience of the authors.
Vibrations and Waves in Continuous Mechanical Systems
provides a first course on the vibrations of continuous systems
that will be suitable for students of continuous system dynamics,
at senior undergraduate and graduate levels, in mechanical, civil
and aerospace engineering. It will also appeal to researchers
developing theory and analysis within the field.
Table of Content
Preface.
1 Vibrations of strings and bars.
1.1 Dynamics of strings and bars: the Newtonian formulation.
1.2 Dynamics of strings and bars: the variationalformulation.
1.3 Free vibration problem: Bernoulli’s solution.
1.4 Modal analysis.
1.5 The initial value problem: solution using Laplacetransform.
1.6 Forced vibration analysis.
1.7 Approximate methods for continuous systems.
1.8 Continuous systems with damping.
1.9 Non-homogeneous boundary conditions.
1.10 Dynamics of axially translating strings.
Exercises.
References.
2 One-dimensional wave equation: d’Alembert’ssolution.
2.1 D’Alembert’s solution of the wave equation.
2.2 Harmonic waves and wave impedance.
2.3 Energetics of wave motion.
2.4 Scattering of waves.
2.5 Applications of the wave solution.
Exercises.
References.
3 Vibrations of beams.
3.1 Equation of motion.
3.2 Free vibration problem.
3.3 Forced vibration analysis.
3.4 Non-homogeneous boundary conditions.
3.5 Dispersion relation and flexural waves in a uniformbeam.
3.6 The Timoshenko beam.
3.7 Damped vibration of beams.
3.8 Special problems in vibrations of beams.
Exercises.
References.
4 Vibrations of membranes.
4.1 Dynamics of a membrane.
4.2 Modal analysis.
4.3 Forced vibration analysis.
4.4 Applications: kettledrum and condenser microphone.
4.5 Waves in membranes.
Exercises.
References.
5 Vibrations of plates.
5.1 Dynamics of plates.
5.2 Vibrations of rectangular plates.
5.2.1 Free vibrations.
5.3 Vibrations of circular plates.
5.4 Waves in plates.
5.5 Plates with varying thickness.
Exercises.
References.
6 Boundary value and eigenvalue problems invibrations.
6.1 Self-adjoint operators and eigenvalue problems for undampedfree vibrations.
6.2 Forced vibrations.
6.3 Some discretization methods for free and forcedvibrations.
References.
7 Waves in fluids.
7.1 Acoustic waves in fluids.
7.2 Surface waves in incompressible liquids.
Exercises.
References.
8 Waves in elastic continua.
8.1 Equations of motion.
8.2 Plane elastic waves in unbounded continua.
8.3 Energetics of elastic waves.
8.4 Reflection of elastic waves.
8.5 Rayleigh surface waves.
8.6 Reflection and refraction of planar acoustic waves.
Exercises.
References.
A The variational formulation of dynamics.
References.
B Harmonic waves and dispersion relation.
B.1 Fourier representation and harmonic waves.
B.2 Phase velocity and group velocity.
References.
C Variational formulation for dynamics of plates.
References.
Index.
About the author
Dr. Peter Hagedorn Dynamics and Vibrations Group,
Department of Mechanical Engineering Technische Universität
Darmstadt has over 200 publications which includes papers in
international journals (such as ASME Journal of Applied Mechanics,
International Journal of Non-linear Mechanics, Journal of Sound and
Vibration, Journal of Fluids and Structures, Journal of Vibration
and Control Nonlinear Dynamics, Journal of Vibrations and
Acoustics, Archive for Rational Mechanics and Analysis, AIAA
Journal, Journal of Optimization Theory and Applications, Wind and
Structures, ZAMM, ZAMP), refereed conferences, book chapters,
lecture notes and books. The books are: Nonlinear
oscillations. Since 1974, he is a Professor at TU Darmstadt
(Germany). He has 7 patents to his credit. He has taught various
courses such as Vibrations of continuous systems, Machine dynamics,
Multi-body dynamics, Statics, Theory of elasticity, and
Dynamics. He has been Visiting Professor at COPPE, Rio de
Janeiro (Brasil), Lecturer at University of Karlsruhe (Germany),
Research Fellow at Stanford University (US), Visiting Professor at
UC Berkeley (US), Universities in Paris (France), Irbid (Jordan),
and Christchurch (New Zealand). He has also served as the Director
of the Institute of Mechanics, Dean, and Vice-President, all at TU
Darmstadt.
Dr. Anirvan Das Gupta Indian Institute of Technology
Kharagpur, Kharagpur – 721302, INDIA obtained his Doctoral degree
in Mechanical Engineering from IIT Kanpur (India) in 1999. He has
about 35 publications which includes papers in International
journals and refereed conferences. He joined the Mechanical
Engineering department at IIT Kharagpur (India) in 1999 as an
Assistant Professor, and is presently an Associate Professor. He
has taught courses such as Mechanics, Dynamics, Kinematics of
Machines, Dynamics of Machines, and Machine Vibration Analysis. He
has supervised two Doctoral students. He has been at the University
of Tokyo (Japan) as a research fellow, and at TU Darmstadt
(Germany) as an Alexander von Humboldt research fellow.
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