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Problem on Periodic Vibrations of an I-beam with Clamped Endpoint in the Resonance Case

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Abstract We consider the problem about periodic solutions to a quasilinear equation of forced vibrations of an I-beam with one endpoint clamped and the other hinged. We derive conditions for… Click to show full abstract

Abstract We consider the problem about periodic solutions to a quasilinear equation of forced vibrations of an I-beam with one endpoint clamped and the other hinged. We derive conditions for the existence, smoothness, and uniqueness of a periodic solution for the cases in which either the nonlinear term satisfies the nonresonance condition at infinity or the difference between this term and a linear function whose coefficient coincides with some eigenvalue of the differential operator is a bounded function.

Keywords: endpoint; periodic vibrations; problem periodic; beam clamped; vibrations beam

Journal Title: Differential Equations
Year Published: 2020

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