# Rayleigh-Ritz method

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## Rayleigh-Ritz method

[′rā·lē ′rits ‚meth·əd]
(mathematics)
An approximation method for finding solutions of functional equations in terms of finite systems of equations.
References in periodicals archive ?
Balmes [7, 8] proposed the Parametric Reduced Order Model (PROM) method by expanding the Rayleigh-Ritz method.
Lee and Kwak [1] constructed a dynamic model for the free vibration analysis of a circular cylindrical shell by using the Rayleigh-Ritz method and compared the results based on different theories such as Donnell-Mushtari theory, Sanders theory, FlUgge theory, Vlasov theory, Love-Timoshenko theory, and Reissner theory and the results under different boundary conditions.
Dyakonov's monograph on optimization for elliptic problems [3] and its Chapter 9 on the Rayleigh-Ritz method for spectral problems.
2007) derived the frequency equation in the form of eigen-value problem by employing Rayleigh-Ritz method.
After reviewing the primary methods of analysis for vibration problems in shaped structures, this mechanical engineering graduate textbook develops boundary characteristic orthogonal polynomials and applies the Rayleigh-Ritz method to transverse vibration of elliptic and circular plates, triangular plates, rectangular and skew plates, and annular plates.
Free Vibration and Buckling Response of Width-Tapered Laminated Composite Beam-Columns Using Rayleigh-Ritz Method
In this work, we propose explicit solutions for critical buckling load of the T-section webs based on the torsional restraint model through Rayleigh-Ritz method and finite element (FE) analysis.
Naeem and Sharma, 2000) have employed Rayleigh-Ritz method to predict natural frequencies for thin cylindrical shells using Ritz polynomial for axial model dependence.
Section 6 points out connections of these families with the usual harmonic Rayleigh-Ritz method for the generalized eigenvalue problem, and a new variant of this approach (the left-harmonic Rayleigh-Ritz method).
In Section 2 we review the harmonic Rayleigh-Ritz method for the generalized eigenproblem, after which this method is generalized for the MEP in Section 3.
We investigate several generalizations of the harmonic and refined Rayleigh-Ritz method.
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