Vibrations and Waves in Continuous Mechanical Systems

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 variational formulation

1.3 Free vibration problem: Bernoulli's solution

1.4 Modal analysis

1.5 The initial value problem: solution using Laplace transform

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's solution

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 uniform beam

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 in vibrations

6.1 Self-adjoint operators and eigenvalue problems for undamped free vibrations

6.2 Forced vibrations

6.3 Some discretization methods for free and forced vibrations

References

7 Waves in fluids

7.1 Acoustic waves in fluids

7.2 Surface waves in incompressible

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 DasGupta 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,