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Nonzero time periodic solutions to an equation of Petrovsky type with nonlinear boundary conditions: Slow oscillations of beams on elastic bearings. (English) Zbl 0794.73029
At the beginning, the author formulates the transversal displacement equation along with boundary conditions and finds non-zero time periodic solutions to this problem. Then a variational formulation of the problem is discussed. The problem takes the form of a theorem which the author proves following an approximate method of Rayleigh-Ritz. Among other things, the spectral analysis of a linear operator is used in proving the theorem.
The author has submitted a good list of references showing that he has a good knowledge of the literature. The paper, nicely presented from all points of view, pertains to the field of applied mathematics and can be useful for those working on elastic vibrations.
Reviewer: B.B.Sharma (Simla)

MSC:
74H45 Vibrations in dynamical problems in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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References:
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