High frequency vibrations of crystal plates
Author:
R. D. Mindlin
Journal:
Quart. Appl. Math. 19 (1961), 51-61
DOI:
https://doi.org/10.1090/qam/99967
MathSciNet review:
QAM99967
Full-text PDF Free Access
References |
Additional Information
A. L. Cauchy, Sur l’équilibre et le mouvement d’une plaque élastique dont l’élasticité n’est pas la même dans tous les sens, Exercices de Mathématique 4, 1–14 (1829)
- Raymond D. Mindlin, Thickness-shear and flexural vibrations of crystal plates, J. Appl. Phys. 22 (1951), 316–323. MR 40949
S. D. Poisson, Mémoire sur l’équilibre et le mouvement des corps élastiques, Mém. Acad. Sci., Paris, Ser. 2, 8 357–570 (1829)
G. Kirchhoff, Über das Gleichgewicht und die Bewegung einer elastichen Scheibe, Crelles J. 40, 51–88 (1850)
- H. Ekstein, High frequency vibrations of thin crystal plates, Phys. Rev. (2) 68 (1945), 11–23. MR 13366
A. E. H. Love, A treatise on the mathematical theory of elasticity, Cambridge University Press, London, 1927, p. 106
R. D. Mindlin, An introduction to the mathematical theory of vibrations of elastic plates, U. S. Army Signal Corps, Fort Monmouth, N. J., Contract DA-36-039 SC-56772, pp. 6.02–6.04 (1955)
W. Voigt, Lehrbuch der Krystallphysik, B. G. Teubner, Leipzig, 2nd ed., 1928, p. 698
R. D. Mindlin, Influence of rotatory inertia and shear on flexural vibrations of isotropic, elastic plates, J. Appl. Mech. 18, 31–38 (1951)
S. Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Phil. Mag., Ser. 6, 41, 744–746 (1921)
- Eric Reissner, On bending of elastic plates, Quart. Appl. Math. 5 (1947), 55–68. MR 20440, DOI https://doi.org/10.1090/S0033-569X-1947-20440-X
I. Koga, Thickness vibrations of piezoelectric oscillating crystals, Physics 3, 70–80 (1932)
- R. D. Mindlin, Waves and vibrations in isotropic, elastic plates, Structural mechanics, Pergamon Press, New York, 1960, pp. 199–232. MR 0115387
W. P. Mason, Piezoelectric crystals and their application to ultrasonics, D. Van Nostrand Co., New York, 1950, Chap. VI
R. Bechmann, Elastic and piezoelectric constants of aplha-quartz, Phys. Rev. 110, 1060–1061 (1958)
- E. G. Newman and R. D. Mindlin, Vibrations of a monoclinic crystal plate, J. Acoust. Soc. Amer. 29 (1957), 1206–1218. MR 90261, DOI https://doi.org/10.1121/1.1908747
R. K. Kaul and R. D. Mindlin, Vibrations of a monoclinic crystal plate, II, (forthcoming)
- D. C. Gazis and R. D. Mindlin, Extensional vibrations and waves in a circular disk and a semi-infinite plate, J. Appl. Mech. 27 (1960), 541–547. MR 0119578
- R. D. Mindlin, Simple modes of vibration of crystals, J. Appl. Phys. 27 (1956), 1462–1466. MR 83288
A. L. Cauchy, Sur l’équilibre et le mouvement d’une plaque élastique dont l’élasticité n’est pas la même dans tous les sens, Exercices de Mathématique 4, 1–14 (1829)
R. D. Mindlin, Thickness-shear and flexural vibrations of crystal plates, J. Appl. Phys. 22, 316–323 (1951)
S. D. Poisson, Mémoire sur l’équilibre et le mouvement des corps élastiques, Mém. Acad. Sci., Paris, Ser. 2, 8 357–570 (1829)
G. Kirchhoff, Über das Gleichgewicht und die Bewegung einer elastichen Scheibe, Crelles J. 40, 51–88 (1850)
H. Ekstein, High frequency vibrations of thin crystal plates, Phys. Rev. 68, 11-23 (1945)
A. E. H. Love, A treatise on the mathematical theory of elasticity, Cambridge University Press, London, 1927, p. 106
R. D. Mindlin, An introduction to the mathematical theory of vibrations of elastic plates, U. S. Army Signal Corps, Fort Monmouth, N. J., Contract DA-36-039 SC-56772, pp. 6.02–6.04 (1955)
W. Voigt, Lehrbuch der Krystallphysik, B. G. Teubner, Leipzig, 2nd ed., 1928, p. 698
R. D. Mindlin, Influence of rotatory inertia and shear on flexural vibrations of isotropic, elastic plates, J. Appl. Mech. 18, 31–38 (1951)
S. Timoshenko, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Phil. Mag., Ser. 6, 41, 744–746 (1921)
E. Reissner, On bending of elastic plates, Quart Appl. Math. 5, 55–68 (1947)
I. Koga, Thickness vibrations of piezoelectric oscillating crystals, Physics 3, 70–80 (1932)
R. D. Mindlin, Waves and vibrations in isotropic, elastic plates, Proc. 1st Symp. Naval Structural Mechanics, Pergamon Press, New York, 1960, pp. 199–232
W. P. Mason, Piezoelectric crystals and their application to ultrasonics, D. Van Nostrand Co., New York, 1950, Chap. VI
R. Bechmann, Elastic and piezoelectric constants of aplha-quartz, Phys. Rev. 110, 1060–1061 (1958)
E. G. Newman and R. D. Mindlin, Vibrations of a monoclinic crystal plate, J. Acoust. Soc. Am. 29 1206–1218 (1957)
R. K. Kaul and R. D. Mindlin, Vibrations of a monoclinic crystal plate, II, (forthcoming)
D. C. Gazis and R. D. Mindlin, Extensional vibrations and waves in a circular disk and a semi-infinite plate, J. Appl. Mech. 27, (1960)
R. D. Mindlin, Simple modes of vibration of crystals, J. Appl. Phys. 27, 1462–1466 (1956)
Additional Information
Article copyright:
© Copyright 1961
American Mathematical Society
