Notch-type damage influence on the frequency of the principal mode of the composite cantilever beam flexural vibrations

Abstract

The results of calculation investigations aimed at the determination of the influence mechanisms of the surface damage in the form of a rectangular notch and fibers’ orientation on the frequency of the principal mode of the composite cantilever beam flexural vibrations are presented. The three-dimensional finite element model of the beam made of the unidirectional carbon-fiber-reinforced plastic with the local surface rectangular notch-type damage has been developed using the effective modulus concept to determine the composite material elastic properties. Its adequacy is corroborated via the comparison of the determination results of the principal frequency of flexural vibrations of the intact beam as a function of the degree of anisotropy in composite material with the known experimental data. In this paper has been found the mechanisms of influence of the damage parameters (notch depth and its location along the beam length) and the degree of anisotropy of the elastic properties in composite material, which is defined by the angle of the fibers, on the variation of the frequency of the principal mode of flexural vibrations. It is established that there is such a notch location along the beam length for its specified depth and width, the so-called transition point, where the natural frequency of vibrations of the damaged and intact beams are equal independent of the angle of the fibers. This fact indicates that there is a simultaneous damage effect on both the variation of flexural stiffness of the beam and its inertia properties. The location of the transition point depends on the notch depth and fibers’ orientation. With the larger distance of the notch from the transition point to the free end, the principal frequency of vibrations of the damaged beam becomes larger as compared with that one for the intact beam.