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.
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.