Includes index.

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Title page; Copyright; Preface; Introduction and Historical Notes; 1 Principle of Conservation of Energy and Rayleigh's Principle; 1.1. A simple pendulum; 1.2. A spring-mass system; 1.3. A two degree of freedom system; 2 Rayleigh's Principle and its Implications; 2.1. Rayleigh's principle; 2.2. Proof; 2.3. Example: a simply supported beam; 2.4. Admissible functions: examples; 3 The Rayleigh-Ritz Method and Simple Applications; 3.1. The Rayleigh-Ritz method; 3.2. Application of the Rayleigh-Ritz method; 4 Lagrangian Multiplier Method; 4.1. Handling constraints

4.2. Application to vibration of a constrained cantilever5 Courant's Penalty Method Including Negative Stiffness and Mass Terms; 5.1. Background; 5.2. Penalty method for vibration analysis; 5.3. Penalty method with negative stiffness; 5.4. Inertial penalty and eigenpenalty methods; 5.5. The bipenalty method; 6 Some Useful Mathematical Derivations and Applications; 6.1. Derivation of stiffness and mass matrix terms; 6.2. Frequently used potential and kinetic energy terms; 6.3. Rigid body connected to a beam; 6.4. Finding the critical loads of a beam

7 The Theorem of Separation and Asymptotic Modeling Theorems7.1. Rayleigh's theorem of separation and the basis of the Ritz method; 7.2. Proof of convergence in asymptotic modeling; 7.3. Applicability of theorems (1) and (2) for continuous systems; 8 Admissible Functions; 8.1. Choosing the best functions; 8.2. Strategy for choosing the functions; 8.3. Admissible functions for an Euler-Bernoulli beam; 8.4. Proof of convergence; 9 Natural Frequencies and Modes of Beams; 9.1. Introduction; 9.2. Theoretical derivations of the eigenvalue problems

9.3. Derivation of the eigenvalue problem for beams9.4. Building the stiffness, mass matrices and penalty matrices; 9.5. Modes of vibration; 9.6. Results; 9.7. Modes of vibration; 10 Natural Frequencies and Modes of Plates of Rectangular Planform; 10.1. Introduction; 10.2. Theoretical derivations of the eigenvalue problems; 10.3. Derivation of the eigenvalue problem for plates containing classical constraints along its edges; 10.4. Modes of vibration; 10.5. Results; 11 Natural Frequencies and Modes of Shallow Shells of Rectangular Planform

11.1. Theoretical derivations of the eigenvalue problems11.2. Frequency parameters of constrained shallow shells; 11.3. Results and discussion; 12 Natural Frequencies and Modes of Three-Dimensional Bodies; 12.1. Theoretical derivations of the eigenvalue problems; 12.2. Results; 13 Vibration of Axially Loaded Beams and Geometric Stiffness; 13.1. Introduction; 13.2. The potential energy due to a static axial force in a vibrating beam; 13.3. Determination of natural frequencies; 13.4. Natural frequencies and critical loads of an Euler-Bernoulli beam