UID:
almafu_9959327370302883
Format:
1 online resource
ISBN:
9781118984444
,
1118984447
,
9781118984437
,
1118984439
Series Statement:
Mechanical engineering and solid mechanics series
Content:
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 method, the authors also give simple explanations and analogies to make it easier to understand. Examples include calculation of natural frequencies and critical loads of structures and structural components, such as beams, plates, shells and solids. MATLAB codes for some common problems are also sup.
Note:
Includes index.
,
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.
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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.
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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.
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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.
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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.
Additional Edition:
Print version: Ilanko, Sinniah. Rayleigh-Ritz method for structural analysis ISBN 9781848216389
Language:
English
Keywords:
Electronic books.
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Electronic books.
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Electronic books.
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118984444
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118984444
URL:
https://onlinelibrary.wiley.com/doi/book/10.1002/9781118984444
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