轴向飞行梁动态特性研究
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摘要
本文主要对轴向飞行梁的振动特性进行了研究,按飞行速度划分为低速和高速两种情况。首先分析了轴向飞行梁在低速时的动态特性,在理论上分别采用牛顿第二定律和Hamilton原理推导了轴向飞行梁的横向振动微分方程,采用Galerkin法将其离散而得到常微分方程,对梁的动态特性进行分析计算,结果表明梁的固有频率随着飞行速度的增加不断降低,并求出梁的临界失稳速度。
试验方面以箭为研究对象对其进行模态参数识别。采用了两种试验方法,一是采用动态分析仪Agilent 35670测得箭的频响函数,然后用I-DEAS软件识别出箭的前三阶模态。二是采用高速摄像机记录箭的飞行过程,对箭的的飞行进行定性和定量分析并根据拍摄结果算出箭的第一阶固有频率。采用有限元模拟求解箭的前三阶模态,与试验结果基本一致。
其次分析了轴向飞行梁在高速时的动态特性,主要研究了轴向飞行梁在高速飞行情况下,由于气动加热引起的高温效应对结构振动特性的影响。介绍了温度场和热应力场的有限元方法,并将温度场等效为热载荷,用弹性力学的处理方法求解温度场对应的热应力场。其次,将热应力作为结构的一种预应力,推导由预应力引起的刚度矩阵修正。结合金属材料热物理参数随温度变化的一般规律,构造结构的热刚度,应用有限元模拟方法得到结构的固有频率。
研究结果表明,升温导致的热应力以及材料属性的改变都会改变结构的固有频率,其中,后者的效果更显著;两者的综合作用下,结构的固有频率有下降趋势,且高阶固有频率比低阶固有频率下降得快。
In this paper, vibration characteristics of the transverse oscillation of the axially flying beam is investigated, according to the flying speed,we divide the question into low and high speed conditions.
Firstly, dynamic characteristics of the axially flying beam at low speed is investigated.The differential equation of transverse motion of the beam is derived by Newton’s second law and Hamilton’s principle Newton’s second law.Then we apply the Galerkin method to truncate the partial differential equation into a set of ordinary differential equations, and the effect of the axially flying speed on the first order natural frequency of the beam is researched. It is found that the first order natural frequency decrease as the axial velocity increase, so there is a critical velocity of the axially flying beam.
Then we take the arrow as the research object to make experiment to analyze the modal parameter of it.There are two methods in our experiment.In the first method,we measure the frequency response function by means of the dynamic signal analyzer 35670, then identyfy the first three order modes by means of I-DEAS software.In the second method, we record the flying process of the arrow with the help of high-speed camera, and make qualitative analysisand and quantitative analysis to it. According to the record,we can get the first order natural frequency.With the help of MSC.Patran/Nastran software,we make simulation of the arrow and get the first three modes,and the results keep consistent with the experiment
Secondly, dynamic characteristics of the axially flying beam at high speed is investigated. The vibration characteristics,especially thermal vibration characteristic of the beam under aerodynamic heating is analyzed. the finite element method is used to analyze the temperature field and thermal stress. The temperature effect which has been taken as 'thermal load' forced on the body, then, such thermal stress is settled as general elasticity mechanics question. Secondly, the thermal stress is taken as‘pre-stress’, then, deduce extra stiffness matrix caused by pre-stress.Considered the mechanical property of the material changed with thermal, get the new system thermal stiffness and the nature frequency of the structure.
By means of FEM method, we get the conclusions as followed: thermal stress and the mechanical property of the material variety can send the nature frequency down; the latter effect stronger; the nature frequency is decreased by the two factors, the higher the nature frequency is, the more it decrease.
试验方面以箭为研究对象对其进行模态参数识别。采用了两种试验方法,一是采用动态分析仪Agilent 35670测得箭的频响函数,然后用I-DEAS软件识别出箭的前三阶模态。二是采用高速摄像机记录箭的飞行过程,对箭的的飞行进行定性和定量分析并根据拍摄结果算出箭的第一阶固有频率。采用有限元模拟求解箭的前三阶模态,与试验结果基本一致。
其次分析了轴向飞行梁在高速时的动态特性,主要研究了轴向飞行梁在高速飞行情况下,由于气动加热引起的高温效应对结构振动特性的影响。介绍了温度场和热应力场的有限元方法,并将温度场等效为热载荷,用弹性力学的处理方法求解温度场对应的热应力场。其次,将热应力作为结构的一种预应力,推导由预应力引起的刚度矩阵修正。结合金属材料热物理参数随温度变化的一般规律,构造结构的热刚度,应用有限元模拟方法得到结构的固有频率。
研究结果表明,升温导致的热应力以及材料属性的改变都会改变结构的固有频率,其中,后者的效果更显著;两者的综合作用下,结构的固有频率有下降趋势,且高阶固有频率比低阶固有频率下降得快。
In this paper, vibration characteristics of the transverse oscillation of the axially flying beam is investigated, according to the flying speed,we divide the question into low and high speed conditions.
Firstly, dynamic characteristics of the axially flying beam at low speed is investigated.The differential equation of transverse motion of the beam is derived by Newton’s second law and Hamilton’s principle Newton’s second law.Then we apply the Galerkin method to truncate the partial differential equation into a set of ordinary differential equations, and the effect of the axially flying speed on the first order natural frequency of the beam is researched. It is found that the first order natural frequency decrease as the axial velocity increase, so there is a critical velocity of the axially flying beam.
Then we take the arrow as the research object to make experiment to analyze the modal parameter of it.There are two methods in our experiment.In the first method,we measure the frequency response function by means of the dynamic signal analyzer 35670, then identyfy the first three order modes by means of I-DEAS software.In the second method, we record the flying process of the arrow with the help of high-speed camera, and make qualitative analysisand and quantitative analysis to it. According to the record,we can get the first order natural frequency.With the help of MSC.Patran/Nastran software,we make simulation of the arrow and get the first three modes,and the results keep consistent with the experiment
Secondly, dynamic characteristics of the axially flying beam at high speed is investigated. The vibration characteristics,especially thermal vibration characteristic of the beam under aerodynamic heating is analyzed. the finite element method is used to analyze the temperature field and thermal stress. The temperature effect which has been taken as 'thermal load' forced on the body, then, such thermal stress is settled as general elasticity mechanics question. Secondly, the thermal stress is taken as‘pre-stress’, then, deduce extra stiffness matrix caused by pre-stress.Considered the mechanical property of the material changed with thermal, get the new system thermal stiffness and the nature frequency of the structure.
By means of FEM method, we get the conclusions as followed: thermal stress and the mechanical property of the material variety can send the nature frequency down; the latter effect stronger; the nature frequency is decreased by the two factors, the higher the nature frequency is, the more it decrease.
引文
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[12]杨自春.受热复合材料层合板的非线性热振动一理论及数值分析[J].复合材料学报,2006,Vo117(1):24~30.
[13]陈文俊.气动加热对飞行器气动弹性特性的影响[J].现代防御技术,2004(3):21~28.
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