Comments on the historical bases of the Rayleigh and Ritz methods

Journal of Sound and Vibration

Volumn 319, Issue 1-2, 2009, Pages 731-733

  Ilanko, Sinniah ^a  

^a UNIVERSITY OF WAIKATO   (New Zealand)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 56749146021     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2008.06.001     Document Type: Note

References (10)

1. A.W. Leissa, The historical bases of the Rayleigh and Ritz methods, Journal of Sound and Vibration 287 (2005) 961-978.
2. Lord Rayleigh, The Theory of Sound, Vol. 1, The Macmillan Company, New York, 1877 (Reprinted 1945 by Dover Publications, New York).
3. Lord Rayleigh, The Theory of Sound, Vol. 2, The Macmillan Company, New York, 1878 (Reprinted 1945 by Dover Publications, New York).
4. Lord Rayleigh, On the calculation of the frequency of vibration in its gravest mode, with an example from hydrodynamics, Philosophical Magazine (1899) 566-572.
5. Lord Rayleigh, On the nodal lines of a square plate, Philosophical Magazine Series 4 (46) (1873) 166-171.
6. W. Ritz, On a new method for solving certain types of variational problems in mathematical physics (in German "Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik"), Journal für Reine und Angewandte Mathematik 135 (1908) 1-61.
7. W. Ritz, Theory of transverse vibrations of a quadratic plate with free edges (in German "Theorie der Transversalschwingungen einer quadratischen Platte mit freien Rändern"), Annalen der Physik 28 (1909) 737-786.
8. R. Courant, Variational methods for the solution of problems of equilibrium and vibrations, Bulletin of the American Mathematics Society 49 (1943) 1-23.
9. R. Courant, D. Hilbert, Methods of Mathematical Physics, Vol. I, Interscience Publishers Inc., New York, 1953, p. 175.
10. Lord Rayleigh, On the calculation of Chladni's figures for a square plate, Philosophical Magazine Sixth Series 22 (1911) 225-229.