移动随机载荷下波纹夹芯板的非平稳响应特性分析

doi:10.12382/bgxb.2024.0442

摘要/Abstract

摘要：

为研究波纹夹芯板在移动随机载荷作用下引起的非平稳振动问题,建立了一个通用的动力学解析模型。利用简化一阶剪切变形理论和Hamilton原理推导得到了单个胞元的控制微分方程,基于回传射线矩阵法和虚拟激励法,引入了递推技术有效的模拟了整个结构在移动随机载荷作用下的全域响应。通过将负载的连续移动过程划分为3个阶段,提出了针对于移动随机载荷的统一加载机制,并通过有限元仿真软件验证了计算模型的精度。研究结果表明:通过调节波纹夹芯板的厚度和倾角可以有效拓宽结构的Bragg带隙;低速移动随机载荷在作用时间内会引起更多的振动行为。研究结果为波纹夹芯板在复杂载荷条件下的设计和优化提供了理论支持,并为航空航天和海洋工程等领域中相关装备的研制提供参考。

关键词: 波纹夹芯, 模态阻尼, 回传射线矩阵法, 移动随机载荷, 非平稳响应

Abstract:

A general dynamic analytical model is proposed to study the non-stationary vibration of corrugated sandwich panels under moving random load.The governing differential equation of a single cell unit is derived by using a simplified first-order shear deformation theory and Hamilton principle.Based on the reverberation-ray matrix method and the pseudo excitation method,the recursive technique is introduced to effectively simulate the global response of the whole structure under moving random loads.In addition,a unified loading mechanism for moving random loads is proposed by dividing the continuous load moving process into three stages,and the accuracy of the calculation model is verified by finite element simulation software.Then the calculated results are compared with the simulation data of the finite element software.The findings indicate that the Bragg band gap of the structure can be effectively widened by adjusting the thickness and inclination angle of the corrugated sandwich panel.The low-velocity moving random loads will cause more vibration behaviors within the action time;The study can provide theoretical support for the design and optimization of corrugated sandwich panels under complex load conditions,and offers the valuable insights for the development of related equipment in aerospace and marine engineering.

Key words: corrugated sandwich, modal damping, reverberation-ray matrix method, moving random load, non-stationary response

中图分类号:

TJ03
TJ85

李博, 邵东, 曹渊, 梁伟阁. 移动随机载荷下波纹夹芯板的非平稳响应特性分析[J]. 兵工学报, 2025, 46(7): 240442-.

LI Bo, SHAO Dong, CAO Yuan, LIANG Weige. Analysis of Non-stationary Characteristics of Corrugated Sandwich Panels under Moving Random Load[J]. Acta Armamentarii, 2025, 46(7): 240442-.

图/表 11

图1 三角形波纹夹芯结构

Fig.1 Triangular corrugated sandwich structure

图2 波纹夹芯板的动力学求解过程

Fig.2 The dynamic solving process of corrugated sandwich panels

图3 MRRM的耦合建模和求解过程

Fig.3 The coupling modeling and solving process of MRRM

图4 不同边界条件下波纹夹芯板的第1阶模态云图

Fig.4 The first-order vibration mode of corrugated sandwich panels under different boundary conditions

表1 不同边界条件下波纹夹芯板的前7阶固有频率

Table 1 The first seven natural frequencies of corrugated sandwich panels under different boundary conditions Hz

边界条件	敷层角度	固有频率
边界条件	敷层角度	1	2	3	4	5	6	7
CCFF	[0°/90°]	30.57 (30.60)	32.51 (32.18)	40.90 (40.93)	72.42 (72.27)	75.82 (75.72)	77.38 (77.40)	82.70 (82.92)
	误差/%	0.10	1.01	0.07	0.20	0.13	0.02	0.26
	[0°/90°/0°]	32.05 (32.16)	35.75 (35.82)	41.92 (41.61)	45.39 (45.44)	69.36 (69.43)	75.44 (75.52)	85.83 (87.19)
	误差/%	0.28	0.19	0.07	0.11	0.11	0.10	1.52
CCCC	[0°/90°]	31.66 (32.18)	40.91 (40.92)	77.35 (77.40)	85.05 (84.34)	88.75 (88.83)	97.96 (97.91)	118.57(120.67)
	误差/%	1.64	0.02	0.06	0.83	0.09	0.05	1.74
	[0°/90°/0°]	33.52 (34.13)	39.09 (38.34)	45.38 (45.44)	71.41 (70.91)	75.46 (75.52)	97.28 (97.39)	102.03(101.87)
	误差/%	1.81	1.91	0.13	0.70	0.07	0.11	0.15

图5 移动载荷作用下的确定性动力响应验证

Fig.5 Validation of dynamic response under moving loads

表2 不同网格数量的计算时间及误差

Table 2 Calculation time and errors of different mesh numbers

计算方法	网格数量	计算时间/s	相对误差
有限元方法	120000	728	-
	30000	228	0.059
	19200	155	0.234
	13872	122	0.673
	8112	53	0.921
本文方法	-	7.3	0.351

图6 不同厚度对结构带隙特性的影响

Fig.6 Effects of different thicknesses on the characteristics of band gap

图7 波纹芯倾角对结构带隙特性的影响

Fig.7 Effect of corrugated core inclination angle on the band gap characteristics of structure

图8 移动随机载荷作用下频率范围对时变RMS的影响(v0=100m/s)

Fig.8 Influence of frequency range on time-varying RMS under moving random loads(v0=100m/s)

图9 波纹夹芯板在移动随机载荷作用下演化PSD响应

Fig.9 Evolution of PSD response of corrugated sandwich panels under moving random load

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