REFINED MODEL OF DYNAMIC DEFORMATION OF A FLAT ROD WITH A FINITE-LENGTH FIXED REGION ON AN OUTER SURFACE

Abstract

This paper presents a solution to the problem of forced bending vibrations of a flat rod with two cantilevers and a finite-length fixed region on one of the outer surfaces. The cantilever deformation processes are described using the Timoshenko model with no account for transverse compression and the fixed region: the same deformation model with allowance for transverse compression, modified by considering the presence of an unmoving fixed region. Conditions for the kinematic coupling of the cantilevers and the fixed region are formulated. The Hamilton–Ostrogradsky variational principle serves as a basis for equations of motion, boundary conditions, and force conditions for the coupling of the rod regions. Exact analytical solutions to the equations of motion under the influence of a harmonic transverse force at the end of one of the cantilevers are obtained. The passage of resonant vibrations through a finite-length fixed region in duralumin and fiber composite rods with and without account for the transverse compression of the fixed region is studied in numerical experiments. There is a significant increase in the vibration amplitude of the end of the unloaded cantilever of a duralumin rod due to transverse compression of the fixed region. The vibration amplitude for the composite rod increases slightly.