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188 ALEKSANDR KORJAKIN ET AL.
Table 1. Natural frequencies f nm for a sandwich
clamped-clamped conical shell.
n m CLW54
Ramesh and
Ganesan (1993)
Wilkins
(1970)
1 1 — 299.9 —
2 184.7 184.9 177.2
3 127.4 128.3 126.0
4 110.7 111.3 110.7
5 127.0 127.3 126.7
6 164.2 164.7 163.5
7 212.7 213.8 212.3
8 268.9 271.3 269.1
2 1 — 521.0 —
2 349.2 350.1 340.1
3 250.0 252.3 254.3
4 200.1 202.5 209.7
5 188.0 190.2 197.7
6 207.9 210.2 214.8
7 250.4 252.9 254.5
8 307.5 310.7 310.0
The results for natural frequencies of sandwich conical shell obtained by using
the presented finite element CLW54 and the results from the reference of [35,48]
are shown in the Table 1. The values for modes m =1,n = 1 and m =1,n =2havenot
been analyzed at this time due to a prohibitive amount of calculations.
Vibration and Damping Analysis of
Composite Sandwich Cylindrical Panel
The free vibration frequencies and the corresponding loss factors are studied
for a cylindrical panel under clamped conditions on the straight sides. The geometry
of the panel is characterized by the following quantities: the thickness of
the outer layers h t = 0.001 m and the thickness of core h c = 0.002; 0.004; 0.006; ...;
0.018 m. The panel has the sizes 0.5 × 0.5 m in plane. The radius of the cylinder
R = 0.5 m, Figure 7. The layers of the panel are made from materials with the
following properties: for the aluminium outer layers, E t =70GPa;ν t = 0.20;
p t = 2800 kg/m 3 ; and for the aluminium honeycomb core E1
c = 0.529 GPa;
G12 c = 0.2204 GPa;G13= c 0.126 GPa; ν c c
12 = ν 23 = 0.2; ρ c = 280 kg/m 3 . The loss factor
was assumed zero (η t = 0) for outer layers and η c = 0.4 for the core. The results obtained
by the presented method for the first four natural frequencies and the corresponding
loss factors of sandwich cylindrical panel are shown in Figure 8 and Figure
9.