Stochastic Dynamic Analytical Modeling and Analysis for the Composite Cylindrical Shells

doi:10.12382/bgxb.2024.0761

Abstract

Abstract:

With the widespread application of composite cylindrical shells in engineering fields such as missile launch and submarines, the random vibration caused by random loads has gradually become an important consideration for their dynamic design optimization. The first-order shear shell theory and Hamilton’s principle are used to construct the motion control equations of the shell, and the boundary conditions are applied by artificial virtual springs. The pseudo-excitation method and the reverberation-ray matrix method are used to separate the non-homogeneous excitation equations in the generalized solution vector, and the unified matrix column formula under base acceleration and random load excitation is derived to complete the stochastic dynamic analytical modeling and solution of composite cylindrical shells. The calculated stationary/non-stationary random response results are compared with finite element simulations to prove the effectiveness of the proposed analytical model. On this basis, a series of engineering examples for power spectrum are developed to reveal the influences of shell thickness-to-diameter ratio, orthogonal anisotropy ratio and number of plies on the random vibration response of cylindrical shell.

Key words: composite cylindrical shell, random load, stationary/nonstationary stochastic response, pseudo excitation method, reverberation-ray matrix method

CLC Number:

TJ301

WU Hongrui, GAO Guohua, SHAO Dong, LIANG Weige, LI Chi, SUN Ningze. Stochastic Dynamic Analytical Modeling and Analysis for the Composite Cylindrical Shells[J]. Acta Armamentarii, 2025, 46(5): 240761-.

Figures/Tables 11

Fig.1 Schematic diagram of composite cylindrical shell

Fig.2 Dual coordinate systems

Table 1 Different boundary conditions and stiffness matrices

边界	刚度矩阵
自由(F)	diag(0,0,0,0,0)
简支(S)	diag(0,10¹⁵,10¹⁵,0,10¹⁵)
固支(C)	diag(10¹⁵,10¹⁵,10¹⁵,10¹⁵,10¹⁵)
弹性(E)	diag(K_u,K_v,K_w,K_φx,K_φy)

Table 2 Comparison of natural frequencies under different boundary conditionsHz

边界条件	阶数	本文方法	FEM	误差/%
	[1,1]	86.28	86.53	0.29
	[1,2]	341.04	341.36	0.09
C-F边界	[1,3]	703.33	702.91	0.06
	[2,1]	718.99	717.24	0.24
	[2,2]	791.00	789.25	0.22
	[2,3]	921.35	919.77	0.17
	[1,1]	251.46	251.66	0.08
	[1,2]	577.51	577.58	0.01
C-S边界	[1,3]	917.17	917.04	0.01
	[2,1]	710.88	709.13	0.25
	[2,2]	762.01	760.14	0.25
	[2,3]	873.05	871.30	0.20

Fig.3 Comparisons of mode shapes and frequencies of composite cylindrical shells

Fig.4 Verified results of stationary stochastic responses

Table 3 Three types of modulated functions for the nonstationary stochastic vibration responses

类型	参数	g(t)
类型Ⅰ	B=4 α=0.0995 β=2α	g(t)=B(e^-^αt-e^-^βt)
类型Ⅱ	α=0.2 t_b=1.5s t_c=15s	g(t)=<inline-formula/>
类型Ⅲ	t₀=0.0004s t₁=t₂=12.2s B=0.0744g α=0.413 β=0.552	g(t)=<inline-formula/>

Fig.5 Verified results of nonstationary stochastic vibration responses

Fig.6 Effect of thickness to diameter ratio parameters on the stationary stochastic vibration responses

Fig.7 Effect of different anisotropic ratios E1/E2 on displacement PSD responses

Fig.8 Effect of different lamina numbers on acceleration PSD responses

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