Geometrically nonlinear vibration analysis of eccentrically stiffened porous functionally graded annular spherical shell segments

Figures & data

Figure 1. Configuration of annular spherical shells.

Figure 2. Geometry of the shell with stiffeners.

Table 1. Material properties of FGM constituents.

Properties	Steel	Alumina ($A{l}_2{O}_3$)
E	210 (GPa)	390 (GPa)
Ρ	7800 ($kg/m^3$)	3960 ($kg/m^3$)
Ν	0.3	0.24

Table 2. Validation of vibration frequency of spherical shell for various material gradient exponent (R/r₀=3).

	Duc et al. (2017)	Present
p = 0	0.9118	0.9118
p = 1	1.7794	1.7794
p = 5	2.2130	2.2130

Table 3. Validation of vibration frequency (Hz) of FG spherical shells at curvature radius (p = 1).

	Fadaee et al. (2013)	Present
R/a = 2.5	1578.1	1578.3
R/a = 5	2221.1	2221.2
R/a = 10	3826.7	3826.8
R/a = 20	7313.6	7313.6

Figure 3. Variation of vibration frequency versus normalized deflection of annular spherical shells for various open angles (R = 200 h, r₁=100 h, r₀=0.5r₁, p = 1, ξ = 0.2, K_w=0, K_p=0).

Figure 4. Variation of vibration frequency versus normalized deflection of annular spherical shells for various porosity volume fractions (R = 200 h, r₁=100 h, r₀=0.5r₁, K_w=0, K_p=0). (a) p = 2; (b) p = 5.

Figure 5. Variation of vibration frequency versus normalized deflection of annular spherical shells for various porosity distribution types (R = 200 h, r₁=100 h, r₀=0.5r₁, p = 5, ξ = 0.3, ψ = π).

Figure 6. Variation of vibration frequency versus normalized deflection of annular spherical shells for various porosity distribution types (r₁=100 h, r₀=0.5r₁, p = 5, ξ = 0.3, ψ = π).

Figure 7. Variation of vibration frequency versus normalized deflection of annular spherical shells for various foundation factors (r₁=100 h, r₀=0.5r₁, p = 5, ξ = 0.3, ψ = π).

Figure 8. Variation of vibration frequency versus normalized deflection of annular spherical shells for various number of stiffeners (r₁=100 h, r₀=0.5r₁, p = 5, ξ = 0.3, h₁=0.5 h, b₁=0.5 h, ψ = π).

Duc, N. D., V. D. Quang, and V. T. T. Anh. 2017. The nonlinear dynamic and vibration of the S-FGM shallow spherical shells resting on an elastic foundations including temperature effects. International Journal of Mechanical Sciences 123:54–63. doi:https://doi.org/10.1016/j.ijmecsci.2017.01.043.

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Fadaee, M., S. R. Atashipour, and S. Hosseini-Hashemi. 2013. Free vibration analysis of Lévy-type functionally graded spherical shell panel using a new exact closed-form solution. International Journal of Mechanical Sciences 77:227–38. doi:https://doi.org/10.1016/j.ijmecsci.2013.10.008.

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