PSI - Issue 47

Yaroslav Dubyk et al. / Procedia Structural Integrity 47 (2023) 863–872 Yaroslav Dubyk et al./ Structural Integrity Procedia 00 (2023) 000 – 000

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2.3. Model testing In fact, our solution for dynamic characteristics analysis can be interpreted as an interpolation problem of complex functions on small areas with simpler dependencies - linear or quadratic. Then the question arises to what polynomial degree it is possible to limit our solution. Figure 3 shows the division number influence on the frequency parameter   2 1 / R E        when using second- and third-degree polynomials in the solution. It can be seen from the graphs that third-degree polynomial converges with a smaller partition section number. Analyzing both graphs, we conclude that even when dividing the shell into 100 equal parts, we get a convergent solution.

Fig. 3. C- C conical shell: α=14,20, x2/x1=2,23, h/R=0,00166, R=154.2 mm, E=205 GPa, ρ=7800 kg/m3, µ=0.3, n=1 (a), n=2 (b) 2 degree polynomial 3 degree polynomial 3. Results Experimental data in Hu et al. (1966), where cones had varying angles, has been employed to test the effectiveness of two proposed methods of representing a cone - as a set of cylindrical shells with decreasing radii and as a cone itself. In Table 1 geometry and mechanical characteristics for these shells are presented. Results are shown in Table 2 frequency parameter   2 ' 1000 1 / R E          , for axial wave m=1 and free boundary conditions. Table 1. Geometry of cones with various angle: E=205GPa, ρ=7800 kg/m 3 , µ=0.3 Shell model  x 2 /x 1 h/R R, m model 1 14.2 0 2.23 0.00166 0.154 model 2 30.2 0 2.27 0.00127 0.202 model 3 45.1 0 2.25 0.00112 0.228 model 4 60.5 0 2.25 0.00101 0.254 Based on the results, it can be concluded that the inclination angle increases of the side surface, the better results is shown for a cone solution. But both solutions have better convergence for lower frequencies.