Boundary revision of a beam model for a thin-walled waveguide at bending vibration

Abstract

The paper discusses the problem of choosing a model type for a straight thin-walled waveguide with a rectangular cross-section during its vibrations. To do this, calculations were made of the first natural frequency of vibration for waveguides of different geometric sizes. The restraints of the waveguide were accepted by a cantilever, hinged, and fixed supports. The difference between the values of the first natural frequency of vibration for the beam and shell waveguide models was estimated. Calculations were carried out analytically on the theory of beam vibration and by the numerical method of finite elements. The results show that the boundary known in static calculations of the applicability of the beam model Rmax/L = 0.1 requires clarification at bending vibrations for the small thickness of the section wall. With small wall thicknesses, the error of calculating the first natural frequency of vibrations will increase sharply due to the effect of a beam section warping.