复合材料圆柱壳随机动力学解析建模及分析

doi:10.12382/bgxb.2024.0761

摘要/Abstract

摘要：

随着复合材料圆柱壳在导弹发射、潜艇船舶等工程领域中的广泛应用,随机载荷引起的随机振动逐渐成为其动力学设计优化的重要考虑要素。使用1阶剪切壳理论和Hamilton原理构建壳体的运动控制方程,并通过人工虚拟弹簧施加边界条件,结合虚拟激励法与回传射线矩阵法,分离出广义解向量中的非齐次激励方程,推导出基底加速度和随机载荷激励下的统一矩阵列式,以完成对复合材料圆柱壳的随机动力学解析建模及求解。将计算的平稳/非平稳随机响应结果与有限元仿真进行比较,证明新解析模型的有效性。在此基础上,开展了一系列针对功率谱的工程算例,揭示了壳体厚径比、正交各项异性比以及铺层数量对圆柱壳随机振动响应的影响。

关键词: 复合材料圆柱壳, 随机载荷, 平稳/非平稳随机响应, 虚拟激励法, 回传射线矩阵法

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

中图分类号:

TJ301

吴洪瑞, 高国华, 邵东, 梁伟阁, 李池, 孙宁泽. 复合材料圆柱壳随机动力学解析建模及分析[J]. 兵工学报, 2025, 46(5): 240761-.

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-.

图/表 11

图1 复合材料圆柱壳示意图

Fig.1 Schematic diagram of composite cylindrical shell

图2 对偶坐标系

Fig.2 Dual coordinate systems

表1 不同边界条件及刚度矩阵

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)

表2 不同边界条件固有频率对比

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

图3 复合材料圆柱壳的频率与振型比较

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

图4 平稳随机响应结果验证

Fig.4 Verified results of stationary stochastic responses

表3 非平稳随机响应的3种调制函数

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/>

图5 非平稳随机响应结果验证

Fig.5 Verified results of nonstationary stochastic vibration responses

图6 不同厚径比对随机响应的影响

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

图7 不同各向异性比E1/E2对位移PSD的影响

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

图8 不同铺层层数对加速度随机响应的影响

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

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