Bond Space Expression of Bending Vibration in Timoshenko Beam and Its Application in Muzzle Disturbance Analysis

doi:10.12382/bgxb.2022.0175

Abstract

Abstract:

In order to accurately simulate the dynamic behavior of complex beam system, a dynamic model for the Timoshenko beam is established based on the bond space theory, and the method to analyze the natural frequency is presented. The space vectors of effort, flow, momentum, and displacement for the beam unit are defined, and the state equations expressed in momentum space vectors, displacement space vectors, and their first derivatives are derived. Then, the natural frequencies and corresponding mode shapes of the bending beam are obtained by directly solving the eigenvalue problem. The natural frequencies of the free beam, calculated using the proposed bond space approach, match well with the analytical method. On this basis, the proposed model for the bending beam is used to extend the traditional launching system of the automatic gun. The calculated muzzle disturbance aligns well with the firing experiment, indicating that the proposed method is valid. This study provides a new method for the dynamic analysis of projectile-barrel coupling systems.

Key words: Timoshenko beam, bending vibration, natural frequency, muzzle disturbance, bond space method

LIN Shengye, WANG Maosen, XIE Yangyang, LI Yong, DAI Jinsong. Bond Space Expression of Bending Vibration in Timoshenko Beam and Its Application in Muzzle Disturbance Analysis[J]. Acta Armamentarii, 2023, 44(6): 1775-1783.

Figures/Tables 20

Fig.1 Bond space model for the beam unit

Table 1 First six natural frequencies of the free beam

序号	固有频率/Hz		相对误差/%	MAC
序号	键合空间法	解析法	相对误差/%	MAC
1	184.31	184.34	0.0163	1.0000
2	510.61	508.15	0.4841	1.0000
3	1001.93	996.19	0.5762	0.9999
4	1657.51	1646.76	0.6528	0.9995
5	2478.01	2459.97	0.7333	0.9987
6	3463.18	3435.83	0.7960	0.9972

Fig.2 First-order natural mode of vibration

Fig.3 Second-order natural mode of vibration

Fig.4 Third-order natural mode of vibration

Fig.5 Fourth-order natural mode of vibration

Fig.6 Fifth-order natural mode of vibration

Fig.7 Sixth-order natural mode of vibration

Fig.8 Physical model of the automatic gun

Fig.9 Bond space model of the automatic gun

Table 2 Description of the subscripts

下标	含义
1	炮箱
2~N	炮管
N+1	弹丸
i	身管上与缓冲装置联结点
j	身管上与弹带接触点
k	身管上与弹丸定心部接触点
1r	炮箱后导轨接触点
1f	炮箱前导轨接触点
jr	弹带接触点
kf	前定心部接触点

Fig.10 Test principle for measuring the muzzle disturbance

Fig.11 Setup for measuring muzzle disturbance

Table 3 Parameters of the automatic gun

参数	数值
口径/m	0.03
炮箱质量/kg	45
炮管长度/m	1.2
炮管材料密度/(kg·m^-3)	7800
炮管材料弹性模量/GPa	204
炮管材料泊松比	0.28
射速/(发·min^-1)	600
弹丸不平衡量/(g·mm)	50
连发数	10

Fig.12 Breech pressure

Fig.13 Displacement of the projectile with time

Fig.14 Velocity of the projectile with time

Fig.15 Contact force between the band and the barrel

Fig.16 Contact force between the front bourrelet of the projectile and the barrel

Fig.17 Comparison between simulated and experimental results

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