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A remark on the equation of a vibrating plate. (English) Zbl 0625.73064

The nonlinear equations for the transversal displacement and the Airy- stress function of a vibrating plate are considered. It is shown that for clamped or completely free boundary there exists a unique solution. As the main tool a set of integral equations is used, which may be deduced from the “variation of constants”.
Reviewer: W.Schnell

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74K20 Plates
74B10 Linear elasticity with initial stresses
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
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References:

[1] Wahl, Bayreuth. Math. Schr. 20 pp 205– (1985)
[2] Wahl, Bayreuth. Math. Schr. 7 pp 1– (1981)
[3] Triebel, Interpolation Theory, Function Spaces, Differential Operators (1978) · Zbl 0387.46033
[4] DOI: 10.1007/BF01258907 · Zbl 0457.35059 · doi:10.1007/BF01258907
[5] Landau, Lehrbuch der theoretischen Physik vii (1975)
[6] DOI: 10.1007/BF00281421 · Zbl 0187.05901 · doi:10.1007/BF00281421
[7] Taylor, Pseudodifferential Operators (1981)
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