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 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.