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The Rayleigh-Ritz Method for Structural Analysis.
A presentation of the theory behind the Rayleigh-Ritz (R-R) method, as well as a discussion of the choice of admissible functions and the use of penalty methods, including recent developments such as using negative inertia and bi-penalty terms. While presenting the mathematical basis of the R-R meth...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken :
Wiley,
2014.
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| Colección: | Mechanical engineering and solid mechanics series.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title Page; Copyright; Contents; 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; 3.2.1.1. Short cut to setting up the stiffness and mass matrices.
- 4: Lagrangian Multiplier Method4.1. Handling constraints; 4.2. Application to vibration of a constrained cantilever; 5: 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 beam7: The Theorem of Separation and Asymptotic Modeling Theorems; 7.1. Rayleigh's theorem of separation and the basis of the Ritz method; 7.2. Proof of convergence in asymptotic modeling; 7.2.1. The natural frequencies of an n DOF system with one additional positive or negative restraint; 7.2.2. The natural frequencies of an n DOF system with h additional positive or negative restraints; 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 beam8.4. 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 beams; 9.4. Building the stiffness, mass matrices and penalty matrices; 9.4.1. Terms Kij of the non-dimensional stiffness matrix K; 9.4.2. Terms Mij of the non-dimensional mass matrix M; 9.4.3. Terms Pij of the non-dimensional penalty matrix P; 9.5. Modes of vibration; 9.6. Results; 9.6.1. Free-free beam; 9.6.2. Clamped-clamped beam using 250 terms.
- 9.6.3. Beam with classical and sliding boundary conditions using inertial restraints to model constraints at the edges of the beam9.7. 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 problems.