﻿ 爆炸冲击波载荷特征对冲击响应谱影响规律研究
 舰船科学技术  2019, Vol. 41 Issue (6): 48-52 PDF

1. 中国人民解放军91439部队，辽宁 大连 116041;
2. 哈尔滨工程大学，机电工程学院，黑龙江 哈尔滨 150001;
3. 哈尔滨工程大学，船舶工程学院，黑龙江 哈尔滨 150001

Research on the influence of the wave spectrum characteristics on the shock response of explosion shock load
ZHANG Yu-tao1, TIAN Xuan-xin2, SUN Bei-sheng3, WANG Zhi-kai3
1. No.91439 Unit of PLA, Dalian 116041, China;
2. Harbin Engineering University, College of Mechanical and Electrical Engineering, Harbin 150001, China;
3. Harbin Engineering University, Marine Engineering College, Harbin 150001, China
Abstract: In this paper, the theory and physical model of explosive shock wave are introduced. The corresponding shock spectrum is calculated and analyzed from different shock wave load conditions, such as shock wave waveform, shock wave pulse width and shock wave peak value. Some laws of the impact of shock wave load characteristics on shock response spectrum are obtained, which provide technical support for the Research of anti-shock protection of warships from the angle of weapon attack.
Key words: shock wave     physical model     shock response spectrum
0 引　言

1 冲击谱理论与物理模型 1.1 冲击谱理论

 图 1 冲击谱形成原理 Fig. 1 Principle of shock spectrum formation

 $m\ddot x(t) + k\left[ {x(t) - {x_0}(t)} \right] = 0\text{。}$ (1)

 $y(t) = x(t) - {x_0}(t)\text{。}$ (2)

 $\ddot y(t) + {\omega ^2}y(t) = - {\ddot x_0}(t)\text{。}$ (3)

 $y(t) = - \frac{1}{\omega }\int_0^t {{{\ddot x}_0}(\tau )\sin \omega \left( {t - \tau } \right){\rm d}\tau }\text{，}$ (4)

 $\ddot x(t) = - {\omega ^2}y\left( t \right)\text{，}$ (5)

 $\ddot x(t) = \omega \int_0^t {{{\ddot x}_0}(\tau )\sin \omega \left( {t - \tau } \right){\rm d}\tau } \text{。}$ (6)

 $\dot y(t) = - \int_0^t {{{\ddot x}_0}(\tau )\cos \omega \left( {t - \tau } \right){\rm d}\tau } \text{，}$ (7)

 ${\dot y_p}(t) = \int_0^t {{{\ddot x}_0}(\tau )\sin \omega \left( {t - \tau } \right){\rm d}\tau } \text{，}$ (8)

 ${\dot y_p}(t) = - \omega y\left( t \right) = \frac{1}{\omega }\ddot x\left( t \right)\text{。}$ (9)

 $\begin{split} &\left| {\int_0^t {{{\ddot x}_0}(\tau )cos\omega \left( {t - \tau } \right)d\tau } - \int_0^t {{{\ddot x}_0}(\tau )sin\omega \left( {t - \tau } \right){\rm d}\tau } } \right|=\\ & \;\;\;\;\left| \left. {\frac{1}{\omega }[{{\ddot x}_0}(\tau )\cos (\omega \tau - \omega t + \frac{{\text{π}} }{4})} \right|_0^t\right. - \\ &\;\;\;\;\left.\int_0^t {{{\dddot x}_0}(\tau )\cos (\omega \tau - \omega t + \frac{{\text{π}} }{4}){\rm d}\tau ]} \right| \leqslant \\ &\;\;\;\;\frac{1}{\omega }\left[ {\frac{{\sqrt 2 }}{2}\left| {{{\ddot x}_0}(t)} \right| + \left| {{{\ddot x}_0}(0)} \right| + \int_0^t {\left| {{{\dddot x}_0}(\tau )} \right|{\rm d}\tau } } \right] \text{。} \end{split}$ (10)

 $\frac{1}{\omega }\left[ {\frac{{\sqrt 2 }}{2}\left| {{{\ddot x}_0}(t)} \right| + \left| {{{\ddot x}_0}(0)} \right| + \int_0^t {\left| {{{\dddot x}_0}(\tau )} \right|{\rm d}\tau } } \right]\xrightarrow[{\omega \to \infty }]{}0\text{，}$ (11)

 $\int_0^t {{{\ddot x}_0}(\tau )cos\omega \left( {t - \tau } \right){\rm d}\tau } \underset {\omega \to \infty } \leftrightarrows \int_0^t {{{\ddot x}_0}(\tau )\sin\omega \left( {t - \tau } \right){\rm d}\tau } \text{。}$ (12)

 $\log V\left( \omega \right) = \log \omega + \log D\left( \omega \right)\text{，}$ (13)
 $\log V\left( \omega \right) = - \log \omega + \log A\left( \omega \right)\text{。}$ (14)

 图 2 四参数冲击谱 Fig. 2 Four parametric shock spectrum

2 计算结构与分析 2.1 输入载荷特征对典型加筋板冲击响应的影响 2.1.1 工况设置

2.1.2 冲击波波形对冲击响应影响研究

 图 3 各脉宽3种波形冲击谱对比图 Fig. 3 Comparisons of shock spectra of three kinds of waveforms with different pulse widths

2.1.3 冲击波脉宽对冲击响应影响研究

 图 4 各波形5种脉宽冲击谱对比图 Fig. 4 Comparisons of five pulse width impulse spectra for each waveform

2.1.4 冲击波峰值对冲击响应影响研究

 图 5 矩形波各脉宽不同峰值冲击谱对比图 Fig. 5 Comparisons of different peak impulse spectra of rectangular wave with different pulse widths

3 结　语

1）外载荷不会影响冲击谱峰值频率，只能影响冲击谱峰值高度。冲击谱峰值频率对应着加筋板的某阶模态，即主振型，结构主振型与外载荷形式无关。

2）波形对冲击谱特性的影响与脉宽有关，当外载荷脉宽与结构峰值对应固有周期之比很小（约小于0.25）时，可认为波形对冲击谱峰值高度无影响。随着脉宽增大，波形的影响越来越大。

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