Modeling of Forced Bending Vibrations of a Strip-Bar with a Fixed Finite-Length Section under Prescribed Displacements of an Elastic Support Element
V.N. Paimushin1,2, V.M. Shishkin3
1Kazan National Research Technical University named after A.N. Tupolev, Kazan, Russia
2Kazan (Volga Region) Federal University, Kazan, Russia
3Vyatka State University, Kirov, Russia
Keywords: vibrations, strip-bar, elastic support element, fixed finite-length section, transverse compression
Abstract
The problem of forced bending vibrations of a strip-bar with two cantilevers and a fixed finite-length section on one of the lateral surfaces is addressed. The classical Kirchhoff-Love model is used to describe deformation of the cantilevers, and the fixed section is described by a refined Timoshenko shear model accounting for transverse compression, modified to consider the prescribed displacements of the support element. Kinematic coupling conditions for the fixed section and cantilevers are formulated, and using Hamilton-Ostrogradsky’s principle, equations of motion, boundary conditions, and force coupling conditions for the bar sections are derived. An exact analytical solution is obtained for harmonic forced vibrations under the action of a harmonic transverse force at the end of one cantilever. Numerical experiments were conducted to study forced bending vibrations of a strip-bar made of D16AT duralumin. It was shown that vibrations of the unloaded cantilever are primarily determined by the prescribed displacements of the support element.
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