Tensile-compressive modes and vibration characteristics of penetrating projectile
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摘要: 弹体高速侵彻硬目标时的振动是导致过载信号混杂和装药局部变形放大问题的重要因素，制约了弹体的毁伤能力。为准确表征侵彻弹体的弹性振动特性，基于变截面杆理论推导了弹体的精细化理论模态建模方法，开展了空腔和装药条件下的试验和仿真模态分析，并从特征频率和振型两方面获取了弹体的低阶拉压模态特性，进一步利用模态特性推演了弹体的振动特性。研究表明，等截面杆的预测结果与仿真和试验的偏差较大，而Mindlin-Herrmann杆模型取得了较好的一致性，后者更适合于描述弹体的模态和振动特性。弱载环境中，装药增大了结构阻尼，且弹体模态阶数越高，弹-药的耦合关系越弱，但该结论在强载环境下的适用性还需探究。低阶拉压模态主导了正侵彻弹体的振动特性，弹体的变形和过载分布受一阶拉压模态振型的影响较大，高阶模态对弹体振动起补充作用。受益于变截面效应，内腔短粗且集中的弹体在正侵彻时具有更好的抗振特性。通过拉压模态分析得到的弹体振动特性可为弹体-引信-装药系统的设计提供更可靠的参考。Abstract: Projectile’s structural vibration during high-speed penetration of hard targets is an important factor causing mixed overload signals and charge’s localized-deformation magnification issues, which restricts the destructive capability of projectiles. To accurately characterize the elastic vibration characteristics of the penetrating projectile, a refined theoretical modal modeling method for the projectile was derived based on the theories of variable cross-section rods. Furthermore, two 30-kg mass projectiles with the same mass and outline but different internal cavity structures were manufactured, together with an even hollow cylindrical bar with the same mass and outer diameter. Using these three structures as examples, theory test and simulation mode analyses were conducted to explore the modal features of the projectile from the perspectives of characteristic frequencies and their corresponding low-order tensile-compressive modes. The structural similarities and differences between projectile and even bar were compared, and the influence of charges on projectile modes was explored. Eventually, the vibration characteristics of the projectile penetrating semi-infinite and multi-layer concrete targets were deduced with the introduction of projectile’s modal characteristics measured separately. Research has shown that the Mindlin-Herrmann rod models have derived similar modal characteristic compared with simulation and test results, while the even bar model shows larger discrepancies. In weak load environments, the charge increases the structural damping, and the higher the modal order of the projectile, the weaker the coupling relationship between the projectile and the charge. However, the applicability of this conclusion in harsh load environments still needs to be explored. The low-order tensile-compressive modes dominate the vibration characteristics of the penetrating projectile, and the deformation and overload distribution are mostly affected by the first-order tensile-compressive mode, while the high-order modes supplement the vibration of the projectile. Benefiting from the variable cross-section effect, projectiles with short and concentrated inner cavities have better anti-vibration characteristics during ideal penetration. Projectile’s vibration characteristics obtained through modal analysis provides more reliable guidance for the design of the projectile-fuse-charge system.
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图 4 传感器安装方式不同的工况下弹体的测试状态
Figure 4. Test status of the projectile under different installation conditions of the sensor
图 5 仿真中校准件和弹体的网格状态
Figure 5. Mesh statuses of a calibrator and a projectile in simulation
图 7 仿真得到的校准件前三阶拉压模态振型
Figure 7. The first three order tensile-compressive mode vibration characteristics of the calibrator obtained by simulation
图 9 试验中弹体的FRF幅值曲线（不装药）
Figure 9. FRF amplitude curves obtained from projectiles in test (charge-hollow)
图 10 理论、仿真与试验获取的特征频率的偏差（不装药）
Figure 10. Deviation of characteristic frequencies obtained from theory, simulation and test (charge-hollow)
图 11 弹体前三阶拉压振型理论预测（不装药）
Figure 11. Theoretical prediction of the first three order tensile-compressive mode vibration characteristics of the projectile (charge-hollow)
图 12 仿真预测的弹体前三阶拉压模态振型（剖视图，不装药）
Figure 12. Simulation prediction of the first three order tensile-compressive mode vibration characteristics of the projectiles (cross-section, charge-hollow)
图 13 理论、仿真和试验获得的弹体前三阶拉压振型（不装药）
Figure 13. The first three order tensile-compressive vibration characteristics of the projectiles obtained from theory, simulation and test (charge-hollow)
图 14 试验获得的弹体FRF幅值曲线（装药）
Figure 14. FRF amplitude curves of projectiles obtained from test (charge-loaded)
图 15 试验获得的弹体各阶拉压模态阻尼比
Figure 15. Damping ratio of each order tensile-compressive mode of the projectiles obtained from test
图 16 理论、仿真与试验获取的特征频率的偏差（装药）
Figure 16. Deviation of characteristic frequencies obtained from theory simulation and test (charge-loaded)
图 17 仿真预测的弹体前三阶拉压模态振型（装药，剖视图）
Figure 17. Simulation prediction of the first three order tensile-compressive mode vibration characteristics of the projectiles (cross-section, charge-loaded)
图 18 仿真中的各类型模态阶数与频率的关系（菱形代表前三阶拉压模态）
Figure 18. Relationship between the different types of modal orders and frequencies in the simulation (diamond scatter stands for first three order tensile-compressive modes)
图 19 理论、仿真和试验给出的装药弹体前三阶拉压振型
Figure 19. The first three order tensile-compressive vibration characteristics of the projectile obtained from theory, simulation and test (charge-loaded).
图 20 弹体以不同初速度侵彻靶板时的刚体减速度时程和对应FFT频谱
Figure 20. Rigid body deceleration time histories and FFT spectra of the projectiles penetrating targets at different initial velocities
图 21 弹体Ⅰ以800 m/s初速度侵彻靶板后典型时刻的各截面轴向和径向应变
Figure 21. Axial and radial strains at typical moments after a projectile Ⅰ penetrating the targets at an initial velocity of 800 m/s
图 22 弹体以800 m/s初速度侵彻不同靶板后各截面的过载极值和震荡指数
Figure 22. Overload peak and vibration index of each section after the projectiles penetrating different targets at an initial velocity of 800 m/s
表 1 弹体几何特征
Table 1. Geometric characteristics of the projectiles
弹体 直径/mm 长度/mm 壁厚/mm 头部曲径比 内腔长度/mm 内腔曲径比 Ⅰ 118.13 590.63 27.79 3 442.95 3.78 Ⅱ 118.13 590.63 23.63 3 342.38 1 
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表 2 侵彻弹体的物理特征
Table 2. Physical characteristics of the penetrating projectiles
结构 材料 密度/(kg·m−3) 杨氏模量/GPa 泊松比 质量/kg 壳体 45钢 7816.7 209.5 0.269 33.27 尾盖 铝合金 2700 70 0.33 0.54 模拟装药 细沙&石蜡 1900 1 0.3 2.10
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表 3 不同方法得到的校准件前三阶拉压特征频率
Table 3. The first three order tensile-compressive characteristic frequencies of the calibrator obtained by different methods
模态阶数 特征频率/kHz 仿真-试验相对误差/% 理论-试验相对误差/% 试验 仿真 理论 一 4.371 4.371 4.383 0 0.3 二 8.652 8.649 8.765 0.03 1.3 三 12.528 12.574 13.148 0.4 5.0
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表 4 不同方法得到的弹体前三阶拉压特征频率（不装药）
Table 4. The first three order tensile-compressive characteristic frequencies of the projectiles obtained by different methods (charge-hollow)
弹体 模态阶数 特征频率/kHz 等截面杆理论 经典变截面杆理论 MH理论 仿真 试验（轴向） 试验（径向） Ⅰ 一 4.383 4.846 4.838 4.808 4.930 4.924 二 8.765 9.980 9.905 9.712 9.827 9.864 三 13.148 14.737 14.501 13.903 14.042 13.996 Ⅱ 一 4.383 4.827 4.818 4.752 4.751 4.779 二 8.765 10.248 10.166 9.963 10.127 10.181 三 13.148 14.245 14.041 13.379 13.522 13.540
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表 5 不同方法得到的弹体前三阶拉压特征频率（装药）
Table 5. The first three order tensile-compressive characteristic frequencies of the projectiles with different methods (charge-loaded)
弹体 模态阶数 特征频率/kHz 等截面杆理论 经典变截面杆理论 MH理论 仿真 试验（轴向） 试验（径向） Ⅰ 一 4.383 4.744 4.736 4.635 4.725 二 8.765 9.703 9.635 9.709 9.820 9.903 三 13.148 14.350 14.135 13.567 13.980 14.047 Ⅱ 一 4.383 4.689 4.682 4.499 4.555 二 8.765 9.893 9.820 9.862 10.141 10.212 三 13.148 13.885 13.697 13.342 13.511 13.581
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