An introduction to the mathematical theory of vibrations of elastic plates

An Introduction to the Mathematical Theory of Vibrations of Elastic Plates

Volumn , Issue , 2006, Pages 1-191

  Mindlin, R D ^a   Yang, Jiashi ^b  

^a University of Nebraska Lincoln ^*

^b UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84967355675     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/6309     Document Type: Book

References (52)

1. Benscoter, S. U., Review of "Timoshenko’s shear coefficient for flexural vibrations of beams," by R. D. Mindlin and H. Deresiewicz, Applied Mechanics Review, Vol. 8, (1995) pp. 510-511.
2. Bresse, M., "Cours de Mécanique Appliquée," Mallet-Bachelier, Paris, (1859) p. 126.
3. Carrier, Q R, "The propagation of waves in orthotropic media," Quarterly of Applied Mathematics, Vol. 4, (1946) pp. 160-165.
4. Cauchy, A. L., "Sur I’ équilibre et le mouvement d’une plaque solide," Exercices de Mathématique, vol. 3, (1828) pp. 328-355. Also, Todhunter and Pearson, Vol. I, p. 336.
5. Cauchy, A. L., "Sur I’ équilibre et le mouvement d’une plaque élastique dont I’ élasticité n’est pis la meme dans tous les sens," Exercies de Mathématique, Vol. 4, (1829) pp. 1-14.
6. Ekstein, H., "High frequency vibrations of thin crystal plates," Physical Review, Vol. 68, (1945) pp. 11-23.
7. Germain, Sophie, "Recherches sur la Théorie des Surfaces Élastiques," Courcier, Paris, (1821).
8. Goodman, L. E., "Circular-crested vibrations of an elastic solid bounded by two parallel planes," Proceedings of the First U. S. National Congress of Applied Mechanics, (1951) pp. 65-73. American Society of Mechanical Engineers, New York, N. Y.
9. Holden, A. N., "Longitudinal modes of elastic waves in isotropic cylinders and slabs," Bell System Technical Jouranl, Vol. 30, № 4, Part 1, (1951) pp. 956-969.
10. Institute of Radio Engineers, "Standards on Piezoelectric Crystals," (1949); Proceedings of the I.R.E., Vol. 37, № 12, December, (1949).
11. Kane, T. R., and Mindlin, R. D., "High-frequency extensional vibrations of plates," Journal of Applied Mechanics, Paper № 55-A-50, (1955).
12. Kellogg, O. D., "Foundations of Potential Theory," Julius Springer, Berlin, (1929).
13. Kirchhoff, G, "Über das Gleichgewicht und die Bewegung einer elastischen Scheibe," Crelles Journal, Vol. 40, (1850) pp. 51-88. (Todhunter and Pearson, Vol. II, Part II, pp. 39-50.)
14. Knott, C. G, "Reflection and refraction of elastic waves," Philosophical Magazine (5) Vol. 48, (1899) pp. 64-97.
15. Koga, Issac, "Thickness vibrations of piezoelectric oscillating crystals," Physics, Vol. 3, (1932) pp. 70-80.
16. Lamb. H., "On waves in an elastic plate," Proceedings of the Royal Society, London, Series A, Vol. 93, (1917) pp. 114-128.
17. Lamé, M. G, "Leçons sur la Theorie Mathématique de I’Élasticity des Corps Solides," Gauthier-Villars, Paris, Second Edition, (1866).
18. Love, A. E. H., "A Treatise on the Mathematical Theory of Elasticity," Cambridge University Press, London, (1927).
19. Mason, W. P., "Quartz Crystal Applications," Charter I, "Quartz Crystals for Electrical Circuits," edited by Raymond A. Heising, D. Van Nostrand Co., New York, N. Y., (1946) pp. 11-56.
20. Mason, W. P., "Piezoelectric Crystals and Their Application to Ultrasonics," D. Van Nostrand Co., New York, N. Y, (1950).
21. Mindlin, R. D., "Influence of rotatory inertia and shear on flexural vibrations of isotropic, elastic plates," Journal of Applied Mechanics, Vol. 18, (Trans. ASME, Vol. 73) (1951) pp. 31-38. (A)
22. Mindlim, R. D., "Thickness-shear and flexural vibrations of crystal plates," Journal of Applied Physics, Vol. 22, (1951) pp. 316-323. (B)
23. Mindlin, R. D., "Forced thickness-shear and flexural vibrations of piezoelectric crystal plates," Journal of Applied Physics, Vol. 23, (1952) pp. 83-88.
24. Poisson, S. D., "Mémoire sur I’ équilibre et le mouvement des corps élastiques," Mém, Acad. Sci., Ser. 2, Vol. 8, Paris, (1829) pp. 357-570.
25. Rayleigh, Lord, "On waves propagated along the plane surface of an elastic solid," Proceedings of the London Mathematical Society, Vol. 17 (1887) pp. 4-11.
26. Rayleigh, Lord, "On the free vibrations of an infinite plate of homogeneous isotropic elastic matter," Proceedings of the London Mathematical Society, Vol. 20, (1889) pp. 225-234.
27. Reissner, E., "The effect of transverse shear deformation on the bending of elastic plates," Journal of Applied Mechanics, Vol. 12, (Trans. ASME, Vol. 67) (1945) pp. 69-77.
28. Reissner, E., "On bending of elastic plates," Quarterly of Applied Mathematics, Vol. 5, (1947) pp. 55-68.
29. Sokolnikoff, I. S., "Mathematical Theory of Elasticity," McGraw Hill Book Co., New York, N.Y., (1946).
30. Sommerfeld, Arnold, "Spezielle Lösungen des Problems der elastischen Eigenschwingungen beim Quader und Würfel," S.-B. Math. -Nat. Abt. Bayer. Akad. Wiss. 1945-46, (1947) pp. 51-88.
31. Sternberg, E., and Eubanks, R. A., "On the concept of concentrated loads and an extension of the uniqueness theorem in the linear theory of elasticity," Journal of Rational Mechanics and Analysis, Vol. 4, (1955) pp. 135-168.
32. Sykes, R. A., "Modes of Motion in Quartz Crystals, the Effects of Coupling and Methods of Design," Chapter VI, "Quartz Crystals for Electrical Circuits," edited by Raymond A. Heising, D. Van Nostrand Co., New York, N. Y., (1946) pp. 205-248.
33. Timoshenko, S., "On the correction for shear of the differential equation for transverse vibrations of prismatic bars," Philosophical Magazine, Series 6, Vol. 41, (1921) pp. 744-746.
34. Timoshenko, S., "Theory of Plates and Shells," McGraw Hill Book Co., New York, N. Y, (1940).
35. Timoshenko, S., "On transverse vibrations of bars of uniform cross-section," Philosophical Magazine, Series 6, Vol. 43, (1922) pp. 125-131.
36. Timoshenko, S., and Goodier, J. N., "Theory of Elasticity," McGraw-Hill Book Co., New York, N. Y, Second Edition, (1951).
37. Todhunter, I., and Pearson, K., "A History of the Theory of Elasticity," Cambridge University Press, London, (1886).
38. Uflyand, Ya. S., "The propagation of waves in the transverse vibrations of bars and plates," Akad. Nauk, SSSR, Prikl. Mat. Mekh., Vol. 12, (1948) pp. 287-300.
39. Voigt, W., "Lehrbuch der Kristallphysik," B. G. Teubner, Leipzing, (1928); Edwards Brothers, Inc., Ann Arbor, Michigan, (1946).
40. Mindlin, R. D., "Influence of rotatory inertia and sher on flexural vibrations of isotropic, elastic plates," Journal of Applied Mechanics, Vol. 18, Trans. ASME, Vol. 73" (1951) pp. 31-38.
41. Mindlin, R. D., "Thickness-shear and flexural vibrations of crystal plates," Journal of Applied Physics, Vol. 22, (1951) pp. 316-323.
42. Mindlin, R. D., "Forced thickness-shear and flexural vibrations of piezoelectric crystal plates," Jouranl of Applied Physics, Vol. 23, (1952) pp. 83-88.
43. Mindlin, R. D., and Forray, M., "Thickness-shear and flexural vibrations of contoured crystal plates," Journal of Applied Physics, Vol. 25, (1954) pp. 12-20.
44. Mindlin, R. D., and Deresiewicz. H., "Thickness-shear vibrations of piezoelectric crystal plates with incomplete electrodes," Journal of Applied Physics, Vol. 25, (1954) pp. 21-24.
45. Mindlin, R. D., and Deresiewicz, H., "Suppression of overtones of thickness-shear and flexural vibrations of crystal plates," Journal of Applied Physics, Vol. 25, (1954) pp. 25-27.
46. Mindlin, R. D., and Deresiewicz, H., "Thickness-shear and flexural vibrations of a circular disk," Journal of Applied Physics, Vol. 25, (1954) pp. 1329-1332.
47. Mindlin, R. D., and Deresiewicz, H., "Timoshenko’s shear coefficient for flexural vibrations of beams," Proceedings of the Second U. S. National Congress of Applied Mechanics, (1954) pp. 175-178. American Society of Mechanical Engineers, New York, N. Y.
48. Deresiewicz, H., and Mindlin, R. D., "Axially symmetric flexural vibrations of a circular disk," Journal of Applied Mechanics, Vol. 22, (Trans. ASM, Vol. 77) (1955) pp. 86-88.
49. Mindlin, R. D., and Deresiewicz, H., "Thickness-shear and flexural vibrations of rectangular crystal plates," Journal of Applied Physics, Vol. 26, (1955) pp. 1435-1442.
50. Kane, T. R., and Mindlin, R. D., "High-frequency extensional vibrations of plates," Journal of Applied Mechanics, Paper № 55-A-50, (1955).
51. Mindlin, R. D., Schacknow, A., and Deresiewicz, H., "Flexural vibrations of rectangular plates," Journal of Applied Mechanics, Paper № 55-A-78, (1955).
52. Deresiewicz, H., "Symmetric flexural vibrations of a clamped circular disk," scheduled for publication in the Journal of Applied Mechanics.