梯度弹体结构轴向振动仿真研究

doi:10.12382/bgxb.2024.0500

摘要/Abstract

摘要：

弹体侵彻过程中伴随着振动,降低了毁伤能力。将梯度材料应用于弹体设计并开展减振研究,基于梯度梁轴向振动理论,分析梯度弹体轴向振动频率特性。采用数值模拟的方法得到梯度弹体的轴向振动固有频率并与理论结果对比分析,总结偏差原因。研究梯度弹和均质弹在不同位置的主导振动模态,分析两种弹体的屈曲模态。研究结果表明,梯度弹主要呈现1阶振动模态,模态数量少,其1、2阶共振频率均低于均质弹并且梯度弹和均质弹均发生1阶和2阶的屈曲。研究成果可为解决弹体侵彻过程中振动失稳问题提供思路。

关键词: 梯度弹体, 轴向振动, 数值模拟, 振动模态

Abstract:

During the penetration process, a projectile vibrates to reduce its destructive power. The gradient materials are used for the design of projectiles, and the research on vibration reduction is made. Based on the theory of axial vibration in graded beams, the axial vibration frequency characteristics of graded projectiles are analyzed. The axial vibration natural frequencies of graded projectiles are obtained by using the numerical simulation methods, and the simulated results are compared with the theoretical results for analysis. The reasons for the deviation between the simulated and theoretical results are summarized. The dominant vibration modes of graded projectiles and homogeneous projectiles at different locations are studied, and their buckling modes are analyzed. The research results show that the graded projectiles primarily exhibit a first-order vibration mode with a limited number of modes. Both their first- and second-order resonance frequencies are lower than those of homogeneous projectiles, and the graded and homogeneous projectiles undergo the first- and second-order bucklings. The research findings can provide insights into addressing the issue of vibration-induced instability during projectile penetration.

Key words: graded projectile, axial vibration, numerical simulation, vibration mode

中图分类号:

TJ430

王卿硕, 郭磊, 高洪寅, 何源, 王传婷, 陈鹏翔, 何勇. 梯度弹体结构轴向振动仿真研究[J]. 兵工学报, 2024, 45(S1): 191-199.

WANG Qingshuo, GUO Lei, GAO Hongyin, HE Yuan, WANG Chuanting, CHEN Pengxiang, HE Yong. Simulation Study of Axial Vibration of Graded Projectile Structure[J]. Acta Armamentarii, 2024, 45(S1): 191-199.

图/表 19

图1 梯度弹体梯度结构配置

Fig.1 Configuration of gradient structure of graded projectile

表1 弹体的结构参数

Table 1 Structural parameters of projectile

CRH	长径比	长度/mm	直径/mm
3	8	96	12

表2 梯度和均质弹体参数设置

Table 2 Parameter setting of graded and homogeneous projectiles

弹体类型	E₁/GPa	E₂/GPa	E₃/GPa	E₄/GPa
梯度弹	240	230	220	210
均质弹	210	210	210	210

表3 混凝土材料H-J-C本构模型参数[19]

Table 3 Parameters of H-J-C constitutive model for concrete materials[19]

ρ/ (kg·m^-3)	G/GPa	A	B	C	N	f_c/ MPa
2 400	14.86	0.79	1.6	0.007	0.61	60
T/MPa	D₁	D₂	p_crush/GPa	μ_crush	p_lock/GPa	μ_lock
4	0.04	1	0.016	0.001	0.8	0.1

图2 弹靶1/4模型

Fig.2 1/4 model of projectile and target

图3 弹体侵彻方向加速度与时间关系

Fig.3 Acceleration versus time in the direction of projectile penetration

图4 弹体速度时程曲线

Fig.4 Velocity-time curve of projectile

图5 弹体前8阶模态

Fig.5 The first eight order modes of projectile

图6 两种弹体模态模态分析前20阶结果

Fig.6 Analyzed Rresults of the first 20 order modes in the analysis of the two types of projectile modes

图7 两种弹体的变形量

Fig.7 Deformations of two types of projectiles

图8 特征节点位置图

Fig.8 Location map of feature nodes

表4 均质弹理论模型与谐响应分析结果对比

Table 4 Comparison of the theoretical values and analyzed results of harmonic response of graded projectile

阶数	理论值/kHz	谐响应分析/kHz	偏差/%
1	14.1	15.1	7.1
2	42.2	45.1	6.9

表5 梯度弹理论模型与谐响应分析结果对比

Table 5 Comparison between the theoretical model of gradient elasticity and the results of harmonic response analysis

阶数	理论值/kHz	谐响应分析/kHz	偏差/%
1	13.4	14.4	7.4
2	41.4	44.3	7.0

图9 均质弹各位置轴向加速度过载-频率曲线

Fig.9 Overload-frequency curve of axial acceleration at each position of homogeneous projectile

图10 梯度弹各位置轴向加速度过载-频率曲线

Fig.10 Overload-frequency curve of axial acceleration at each position of graded projectile

图11 均质弹前6阶屈曲模态

Fig.11 The first six-order buckling modes of homogeneous projectile

图12 梯度弹前6阶屈曲模态

Fig.12 The first six-order buckling modes of graded projectile

表6 均质弹前15阶屈曲临界载荷

Table 6 The first 15-order buckling critical loads of homogeneous projectile

模态阶数	屈曲临界载荷/kN	模态阶数	屈曲临界载荷/kN	模态阶数	屈曲临界载荷/kN
1	77.64	6	1 710.10	11	5 599.10
2	77.64	7	2 996.90	12	5 599.10
3	668.55	8	2 996.90	13	6 727.20
4	668.55	9	4 338.10	14	6 727.20
5	1 710.10	10	4 338.10	15	7 748.00

表7 梯度弹前15阶屈曲临界载荷

Table 7 The first 15-order buckling critical loads of graded projectile

模态阶数	屈曲临界载荷/kN	模态阶数	屈曲临界载荷/kN	模态阶数	屈曲临界载荷/kN
1	68.28	6	1 557.30	11	5 133.80
2	68.28	7	2 723.60	12	5 133.80
3	607.35	8	2 723.60	13	6 185.50
4	607.35	9	3 963.70	14	6 185.50
5	1 557.30	10	3 963.70	15	7 115.30

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