PSI - Issue 36

O.L. Derkach et al. / Procedia Structural Integrity 36 (2022) 71–78 O.L. Derkach et al. / Structural Integrity Procedia 00 (2021) 000 – 000

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Secondly, the relation between the stiffness and inertia parameters of the beam depending on the damage location over its length affects the frequency variation Δ p d . As it is closer to clamped end, decrease in the beam stiffness causes the frequency reduction of the principal mode of flexural vibrations. The data in Fig. 5 are in agreement with those presented in Krawczuk and Ostachowicz (1995), Song et al . (2003), and Kisa (2004) which are obtained without considering the beam mass reduction due to the damage presence. However, with the damage shift to the beam free end, the influence of its inertia properties on the natural frequency arises. At the certain value of T x , the following equality holds: p d = p 0 , i.e. Δ p d = 0. This means that there is an equal influence of the stiffness and inertia properties of the beam on its natural vibration frequency. As a result, it does not vary due to the damage, and it equals the natural frequency of vibrations of the intact beam. Such damage location in Zinkovskii et al . (2015, 2018) is denoted as the transition point, which is corroborated by the calculation-experimental results. With the subsequent displacement of the damage to the beam free end, its natural vibration frequency becomes larger than that one for the intact beam (Δ p d > 0) since it is more susceptible to the variation of the inertia properties of the beam. To determine the influence of the damage parameters of the composite beam and anisotropy of its elastic properties on the mechanisms of occurrence of the transition point, the dependencies of its relative position T x on the reinforcement angle were obtained (Fig. 6).

a

b

Fig. 6. Dependencies of the relative position of the transition point T x on the angle of the fibers θ ( а ) at a = 0.2 (1); 0.4 (2) and 0.6 (3) and relative notch depth а ( b ) at θ = 0 deg (1); 45 deg (2) and 90 deg (3).

As can be seen from the presented results, the position of the transition point at 45 deg is closer to the beam clamped end, whereas at θ = 0 deg it is closer to its free end. With the increase of the relative depth, the distance between the transition point and beam clamped end increases, which correlates with the experimental data presented in Zinkovskii et al . (2015, 2018).

4. Conclusions 1. In this paper has been developed the three-dimensional beam model made of the unidirectional carbon-fiber reinforced plastic with local surface damage using the effective module concept to determine the elastic properties of the composite material. The model adequacy was verified by comparing the results of the frequency determination for the intact beam in the variation of anisotropy of the elastic properties of the composite material with the known experimental data.