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Sinniah Ilanko, Luis E. Monterrubio and Yusuke Mochida, The Rayleigh-Ritz Method for Structural Analysis, Wiley, 2014, 252 pages

In many practical engineering problems, it is neither possible nor convenient to develop exact solutions. A convenient method for solving such problems originated from attempts to calculate natural frequencies and modes of structures. This method is known as the Rayleigh–Ritz Method or simply the Ritz Method. This book is 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 supplied.

Table of Contents:
1. Principle of Conservation of Energy and Rayleigh’s Principle.
2. Rayleigh’s Principle and Its Implications.
3. The Rayleigh–Ritz Method and Simple Applications.
4. Lagrangian Multiplier Method.
5. Courant’s Penalty Method Including Negative Stiffness and Mass Terms.
6. Some Useful Mathematical & Derivations and Applications.
7. The Theorem of Separation and Asymptotic Modeling Theorems.
8. Admissible Functions.
9. Natural Frequencies and Modes of Beams.
10. Natural Frequencies and Modes of Plates of Rectangular Planform.
11. Natural Frequencies and Modes of Shallow Shells of Rectangular Planform.
12. Natural Frequencies and Modes of Three-dimensional Bodies.
13. Vibration of Axially Loaded Beams and Geometric Stiffness.
14.The RRM in Finite Elements Method.

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