IMPROVED APPROXIMATIONS VIA RAYLEIGH'S QUOTIENT

1997 ◽  
Vol 199 (1) ◽  
pp. 155-164 ◽  
Author(s):  
D.H. Hodges
Keyword(s):  
Rayleigh’S Quotient

Comments on Rayleigh’s Quotient and Perturbation Theory for the Eigenvalue Problem

1988 ◽  
Vol 55 (4) ◽  
pp. 986-988 ◽  
Author(s):  
Christophe Pierre
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Rayleigh’S Quotient

The connection between Rayleigh’s quotient and perturbation theory for the eigenvalue problem is studied. Equivalence of these techniques is proven under certain conditions.

scholarly journals Rayleigh's quotient for multiple cracked beam and application

2011 ◽  
Vol 33 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Tran Thanh Hai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Shape Function ◽  
Detection Problem ◽  
Cracked Beam ◽  
Rayleigh’S Quotient ◽  
Good Agreement

Rayleigh's quotient for Euler-Bernoulli multiple cracked beam with different boundary conditions has been derived from the governed equation of free vibration. An appropriate choosing of approximate shape function in terms of mode shape of uncracked beam and specific functions satisfying conditions at cracks and boundaries leads to an explicit expression of natural frequencies through crack parameters that can simplify not only the analysis of natural frequencies of cracked beam but also the crack detection problem. Numerical analysis of natural frequencies of the cracked beam by using the obtained expression in comparison with the well-known methods such as the characteristic equation and finite element method shows their good agreement. The analytical expression of natural frequencies applied to the crack detection problem allows the result of detection to be improved.

scholarly journals Modeling Accuracy in FEA of Vibrations of a Drumhead

1993 ◽  
Vol 1 (1) ◽  
pp. 15-20
Author(s):  
Robert J. Melosh
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Analysis Data ◽  
Grid Size ◽  
Element Analysis ◽  
Grid Sampling ◽  
Monotonic Convergence ◽  
Size Accuracy ◽  
Curve Fitting Analysis ◽  
Rayleigh’S Quotient

The study of the problem of predicting values of Rayleigh’s quotient for a square drumhead provides a basis for assessing the relation between grid size, accuracy of analysis results, and efficiency of data processing in finite element analysis. The analysis data indicate that unacceptable grid sampling can occur even for the fine grids, that strictly monotonic convergence is attainable for vibration analysis, and that more efficient computer analysis associates with use of curve fitting analysis of conventional finite element analysis results.

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