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Gregory, R. D.

A note on bi-orthogonality relations for elastic cylinders of general cross section. (English) Zbl 0522.73052

J. Elasticity 13, 351-355 (1983).
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Cited in 8 Documents

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K15 Membranes
74B99 Elastic materials

Keywords:

bi-orthogonality relation; elastodynamic eigenfunctions; elastostatic; cylindrical rod; general cross section; relation depends only upon elastic reciprocal theorem, and elastic symmetry of cylinder in planes perpendicular to its generators
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References:

[1] P.F. Papkovich, Two questions of the theory of bending of thin elastic plates.P.M.M. 5 (1941).
[2] R.T.C. Smith, The bending of a semi-infinite strip.Austral. J. Sci. Res. A 5 (1952) 227-237.
[3] M.W. Johnson and R.W. Little, The semi-infinite strip.Quart. Appl. Math. 22 (1965) 335-344.
[4] R.W. Little and S.B. Childs, Elastostatic boundary region problem in solid cylinders.Quart. Appl. Math. 25 (1967) 261-274. · Zbl 0161.44001
[5] J.L. Klemm and R.W. Little, The semi-infinite elastic cylinder under self-equilibrated end loading,S.I.A.M. J. Appl. Math. 19 (1970) 712-729. · Zbl 0224.73072 · doi:10.1137/0119073
[6] M.E.D. Fama, Radial eigenfunctions for the elastic circular cylinder.Q. J. Mech. Appl. Math. 25 (1972) 479-495. · Zbl 0245.73011 · doi:10.1093/qjmam/25.4.479
[7] W.B. Fraser, Orthogonality relation for the Rayleigh-Lamb modes of vibration of a plate.J. Acoust. Soc. Amer. 59 (1976) 215-216. · Zbl 0324.73022 · doi:10.1121/1.380851
[8] B.G. Prakash, Generalised orthogonality relation for rectangular strips in elastodynamics.Mech. Res. Comm. 5 (1978) 251-255. · Zbl 0397.73023 · doi:10.1016/0093-6413(78)90019-8
[9] W.B. Fraser, An orthogonality relation for the modes of wave propagation in an elastic circular cylinder.J. Sound Vib. 43 (1975) 568-571. · Zbl 0324.73021 · doi:10.1016/0022-460X(75)90011-5
[10] F.E. Byrnes and R.R. Archer, Orthogonality relations for the ?End Problem? for transversely isotropic cylinders.A.I.A.A. Journal 13 (1975) 357-360. · Zbl 0308.73011
[11] F.E. Byrnes and R.R. Archer, Orthogonality relations for ?End Problem? for orthotropic clyinders.J. Appl. Mech. 44 (1977) 784-785. · Zbl 0369.73012 · doi:10.1115/1.3424181
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