Talk:Rayleigh-Ritz method
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A search on Google for the terms in quotes gave the following results: "Rayleigh Ritz" (156,000 hits), "Rayleigh quotient" (90,000 hits), "Ritz method" (104,000 hits). Thus it is clear that the method is widely known by the name "Rayleigh Ritz", or "Rayleigh quotient" in preference to any other name.
Not only does a change in indexing lead to a less accessible article because "Ritz method" is less widely used, it also denies primary credit to the man who originated the method, William Strutt, known as Lord Rayleigh. Rayleighs contribution to science amounted to some 600 papers over his lifetime of 77 years including several published posthumously.
I have used the method to find the first natural frequency for complex systems. All that is needed is a reasonable estimate of the mode shape for which the static deflection curve is often used. This first estimate is usually accurate within less than 10%. The next step is to calculate the inertia loading by using the acceleration due to the first estimate of the frequency, and substituting this for the static weights, derive the second frequency estimate. This second estimate is typically accurate within less than 2%. A third estimate using the frequency from the second would be accurate within less than 1%. The method converges extremely rapidly with any reasonable starting point. In all cases the estimate is higher than the actual natural frequency. CHARLIE ENZ 17:44, 4 December 2006 (UTC)
I recommend to read an article by AW Leissa: The historical bases of the Rayleigh and Ritz methods, Journal of Sound and Vibration 2005, Vol. 287, pp. 961-978 (available at www.sciencedirect.com)
147.229.44.147 09:54, 13 June 2007 (UTC)
My engineering teacher tells me this is for solving degrees of freedom by calculating minimum potential energies?
Is a similar method used for calculating frequencies??
In practice you solve for the minimum frequency, then work out the resulting mode shape. It's worth signing your edits in the talk page with four tildes in a row. Best reference I know of is Thomson - Theory of Vibrations
Greglocock 12:01, 13 May 2006 (UTC)
[edit] This is the same principle as Ritz method
Please, read:
E. Butkov, Mathematical Physics, "Variational Methods", section 13.5
G. Arfken, Mathematical Methods for Physicists, "Calculus of Variations", section 17.8
You must understand that Wave Mechanics (Quantum Mechanics), Electromagnetic Waves, and Acustic Waves are the same mathematical formalism, satisfying the Sturm-Liouville problem, and belonging to Hilbert Space solutions.
Rayleigh-Ritz method is exactly the same as Ritz method.
RafaelBarreto 20:12, 30 August 2006 (UTC)
No, Rayleigh-Ritz is a combination of Rayleigh's method and Ritz's method. By all means combine them, but you'll need a redirect from Rayleigh-Ritz (which is the usual title in the engineering literature), and I'd suggest that the two articles would be hard to combine meaningfully.
Greglocock 00:25, 31 August 2006 (UTC)
I didn't understand your point (the difference between the methods), mainly because I found these studying Sturm-Liouville problem to introduce wave equations into my thesis. At first glance, these were the same variational method to find the least frequency (energy, eigenvalue...) of a wave problem (in my case, quantum mechanics). I think that is just a nomenclature problem. But I'm not sure, because I don't know deeply the engineering approach.
Should Rayleigh method be a particular case of Rayleigh-Ritz method using Fourier series?
RafaelBarreto 20:55, 1 September 2006 (UTC)
R-R as used in engineering does not necessarily use Fourier series. In fact none of the actual examples I have seen have used Fourier, although I have proposed it to other people. Usually you use a polynomial Greglocock 12:35, 14 September 2006 (UTC)
