The historical bases of the Rayleigh and Ritz methods

Journal of Sound and Vibration

Volumn 287, Issue 4-5, 2005, Pages 961-978

  Leissa, A W ^a  

^a Engineering Research Center and Hydraulics Laboratory   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACOUSTIC WAVES; KINETIC ENERGY; NATURAL FREQUENCIES; PROBLEM SOLVING; VIBRATIONS (MECHANICAL);

CONTINUUM SYSTEMS; DISPLACEMENT FUNCTIONS; MODE SHAPES; RITZ METHODS;

RAYLEIGH FADING;

EID: 24344449634     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2004.12.021     Document Type: Article

References (23)

1. Lord Rayleigh, The Theory of Sound, vol. 1, The Macmillan Company 1877 (reprinted 1945 by Dover Publications, New York).
2. Lord Rayleigh, The Theory of Sound, vol. 2, The Macmillan Company 1878 (reprinted 1945 by Dover Publications, New York).
3. W. Ritz Über eine neue Methode zur Lösung gewisser Variationsprobleme der mathematischen Physik Journal für Reine und Angewandte Mathematik 135 1908 1 61
4. W. Ritz Theorie der Transversalschwingungen einer quadratische Platte mit freien Rändern Annalen der Physik 28 1909 737 786
5. R. Courant Variational methods for the solution of problems of equilibrium and vibrations Bulletin of the American Mathematics Society 49 1943 1 23
6. W. Ritz Oeuvres Complètes 1911 Gauthier-Villars Paris
7. A.W. Leissa, Vibration of Plates (NASA SP-160), Government Printing Office 1969, Washington, US (reprinted 1993 by The Acoustical Society of America).
8. Lord Rayleigh On the calculation of Chladni's figures for a square plate Philosophical Magazine Sixth Series 22 1911 225 229
9. G.B. Warburton The vibration of rectangular plates Proceedings of the Institution of Mechanical Engineers Series A 168 1954 371 384
10. A.W. Leissa The free vibration of rectangular plates Journal of Sound and Vibration 31 1973 257 293
11. G. Temple, and W.G. Bickley Rayleigh's Principle and its Applications to Engineering 1933 Oxford University Press Oxford (reprinted 1956 by Dover Publications, New York)
12. E.F.F. Chladni Entdeckung über die Theorie des Klanges 1787 Leipzig
13. E.F.F. Chladni Die Akustik 1802 Leipzig
14. E.F.F. Chladni Neue Beitrage zur Akustik 1817 Leipzig
15. E.F.F. Chladni Annalen der Physik 5 1825 345
16. C. Wheatstone On the figures obtained by strewing sand on vibrating surfaces, commonly called acoustic figures Philosophical Transactions of the Royal Society 1833 593 633
17. Lord Rayleigh On the nodal lines of a square plate Philosophical Magazine Series 4 46 1873 166 171
18. Lord Rayleigh On the calculation of the frequency of vibration in its gravest mode, with an example from hydrodynamics Philosophical Magazine 1899 566 572
19. B.G. Galerkin Rods and Plates. Series occurring in various questions concerning the elastic equilibrium of rods and plates Engineers Bulletin (Vestnik Inzhenerov) 19 1915 897 908 (in Russian)
20. L.V. Kantorovich, V.I. Krylov, Approximate Methods of Higher Analysis (English translation of fourth edition by C.D. Benster). P. Noordhoff Ltd., Gronigen, 1964 (first Russian edition in 1936).
21. I.G. Bubnov, Report on the works of Professor Timoshenko which were awarded the Zhuranski Prize, Symposium of the Institute of Communication Engineers, No. 81, All Union Special Planning Office (SPB), 1913 (in Russian).
22. S.G. Mikhlin, Variational Methods in Mathematical Physics (English translation by T. Boddington), Pergamon Press, Oxford, 1964 (first published in Russian in 1957).
23. S. Timoshenko, and S. Woinowsky-Krieger Theory of Plates and Shells second ed. 1959 McGraw-Hill New York