空间飞行器中液固耦合晃动的非线性动力学研究
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摘要
储液箱液固耦合问题广泛存在于工程实际中。在以燃烧高热值液体燃料为主要推动力的空间飞行器中,研究储液箱同液体燃料的耦合晃动问题具有很强的实际意义。本文主要利用运动稳定性理论,摄动法,C-L方法,Melnikov方法,对空间飞行器中的圆柱形液体燃料储液箱同液体燃料的耦合问题进行了研究。具体研究内容与主要研究成果如下。
1.基于弹性力学、流体力学基本理论,建立弹性柱壳弯曲问题的基本微分方程以及液体的运动方程,并通过变分原理证明了等价性。利用模态展开方法,分别建立刚性储液箱同液体耦合模型和弹性储液箱同液体耦合模型。
2.在给定的参数条件下,分析了刚性储液箱同液体燃料耦合晃动的非线性振动微分方程的稳定条件,以及耦合系统在受到周期干扰力时大幅晃动所带来的一些非线性动力学特征,通过耦合系统的相图和分岔图,发现系统在干扰力幅值增大时,会发生混沌现象。研究系统存在内共振的情况,表明:系统进入混沌的途径由非内共振条件下的概周期道路改变为阵发性道路,并在该系统首次发现了“混沌同步性”这一在耦合系统内共振条件下出现的新现象。
3.用多尺度法、C-L方法研究飞行器中弹性充液系统在简谐激励下组合共振情形下的分岔行为,发现了非常复杂的局部分岔现象,得到了这一系统的分岔特性。研究表明:开折参数k1为零时,即为线性系统的情况,并由此可计算出充液转换点;当充液比小于0.43时,系统非线性刚度表现为硬特性;当充液比大于0.43时,表现出软特性。
4.通过对飞行器多频激励模式下燃料晃动方程进行分析,得到了系统的在不同参数下的轨道模式,并确定了系统达到混沌运动的阀值,探明了系统通向混沌的途径通过对系统参数和实际物理参数之间的关系进行了分析,发现了值得注意的充液转换点。
5.非线性动力学系统蕴含着复杂的动力学行为,例如分岔、混沌等现象。通过对多自由度分段光滑非线性自激振动微分方程进行近似解析计算,得到了该多自由度系统的一次近似解析解,提出了一种有效的计算方法解决了分段积分界限的确定问题。同时,利用C-L方法确定了两个自由度汽车悬架系统共振解与系统参数的联系,为实现悬架参数的优化控制提供了理论依据。
It is worthiness to deal with liquid-solid coupled problems, which is widely relyon industrial engineering problems,particularly in space vehicles which filled with high heat value fuel. The liquid-solid coupled sloshing research has practical significance. In this paper, using the dynamic stability theory, perturbation method, C-L method and Melnikov method, the coupled system combined by rigid and elastic cylindrical storage tank and liquid fuel was studied. Specific research contents and key findings are as follows.
1. Based on the basic theory of elastic mechanics and fluid mechanics, the basic equations of the elastic tank and liquid fuel are established respectively, which equivalence is proved by variation principle as well. By using modal expansion method, the nonlinear equations of the rigid coupled system and elastic coupled system are established respectively.
2. Given the system parameter, the stability conditions of rigid tank-liquid coupled system in aircraft are studied. For further analysis, whether or not in case of internal resonance, the bifurcation diagrams of the coupled system are gained respectively. By contrast, under the condition of internal resonance, the chaotic road is changed from almost periodic to paroxysmal, and a new phenomenon called“Chaos Synchronism”is found under the condition of internal resonance.
3. By means of multiple scales and C-L method, the bifurcation behaviors of elastic tank-liquid coupled system with harmonic excitation in the case of combination resonance are studied, so that abundant nonlinear dynamical characteristics of the coupled system are obtained, which can make a further explanation of the relationship between physic parameters and bifurcation solutions. The result shows that: The case of linear systems happened when the unfolding parameter is zero, then the calculation of turning point is possible; furthermore, On one hand,when the fill ratio is less than 0.43, the system elastic performance turns to hard features; On the other hand, when the fill ratio greater than 0.43, the feature of the system become soft.
4. By applying Melnikov method, the global dynamic behaviors of the sloshing equations in aircraft filled with liquid under multi-frequency excitied model are studied. Consequently, threshold values of heteroclinic bifurcation and subhamonic bifurcation are obtained, and mechanism of chaotic motion is determined. Meanwhile, the switch point which is highly noteworthiness is detected.
5. General nonlinear dynamical systems contain the complicated dynamical phenomenon mostly, such as bifurcation, chaos and so on. First of all, the effect of the self-excited vibration of piecewise-smooth nonlinear system caused by dry friction was taken into consideration. Concurrently, a new method which is used to decide the subsection integral limits of the system is highlighted. Second, resonance solution to a suspension system with two degrees of freedom is investigated with the C-L method. Based on the relationship between parameters and the topological bifurcation solutions, motion characteristics with deferent parameters are obtained. The result provides a theoretical basis for the optimal control of vehicle suspension system parameters.
1.基于弹性力学、流体力学基本理论,建立弹性柱壳弯曲问题的基本微分方程以及液体的运动方程,并通过变分原理证明了等价性。利用模态展开方法,分别建立刚性储液箱同液体耦合模型和弹性储液箱同液体耦合模型。
2.在给定的参数条件下,分析了刚性储液箱同液体燃料耦合晃动的非线性振动微分方程的稳定条件,以及耦合系统在受到周期干扰力时大幅晃动所带来的一些非线性动力学特征,通过耦合系统的相图和分岔图,发现系统在干扰力幅值增大时,会发生混沌现象。研究系统存在内共振的情况,表明:系统进入混沌的途径由非内共振条件下的概周期道路改变为阵发性道路,并在该系统首次发现了“混沌同步性”这一在耦合系统内共振条件下出现的新现象。
3.用多尺度法、C-L方法研究飞行器中弹性充液系统在简谐激励下组合共振情形下的分岔行为,发现了非常复杂的局部分岔现象,得到了这一系统的分岔特性。研究表明:开折参数k1为零时,即为线性系统的情况,并由此可计算出充液转换点;当充液比小于0.43时,系统非线性刚度表现为硬特性;当充液比大于0.43时,表现出软特性。
4.通过对飞行器多频激励模式下燃料晃动方程进行分析,得到了系统的在不同参数下的轨道模式,并确定了系统达到混沌运动的阀值,探明了系统通向混沌的途径通过对系统参数和实际物理参数之间的关系进行了分析,发现了值得注意的充液转换点。
5.非线性动力学系统蕴含着复杂的动力学行为,例如分岔、混沌等现象。通过对多自由度分段光滑非线性自激振动微分方程进行近似解析计算,得到了该多自由度系统的一次近似解析解,提出了一种有效的计算方法解决了分段积分界限的确定问题。同时,利用C-L方法确定了两个自由度汽车悬架系统共振解与系统参数的联系,为实现悬架参数的优化控制提供了理论依据。
It is worthiness to deal with liquid-solid coupled problems, which is widely relyon industrial engineering problems,particularly in space vehicles which filled with high heat value fuel. The liquid-solid coupled sloshing research has practical significance. In this paper, using the dynamic stability theory, perturbation method, C-L method and Melnikov method, the coupled system combined by rigid and elastic cylindrical storage tank and liquid fuel was studied. Specific research contents and key findings are as follows.
1. Based on the basic theory of elastic mechanics and fluid mechanics, the basic equations of the elastic tank and liquid fuel are established respectively, which equivalence is proved by variation principle as well. By using modal expansion method, the nonlinear equations of the rigid coupled system and elastic coupled system are established respectively.
2. Given the system parameter, the stability conditions of rigid tank-liquid coupled system in aircraft are studied. For further analysis, whether or not in case of internal resonance, the bifurcation diagrams of the coupled system are gained respectively. By contrast, under the condition of internal resonance, the chaotic road is changed from almost periodic to paroxysmal, and a new phenomenon called“Chaos Synchronism”is found under the condition of internal resonance.
3. By means of multiple scales and C-L method, the bifurcation behaviors of elastic tank-liquid coupled system with harmonic excitation in the case of combination resonance are studied, so that abundant nonlinear dynamical characteristics of the coupled system are obtained, which can make a further explanation of the relationship between physic parameters and bifurcation solutions. The result shows that: The case of linear systems happened when the unfolding parameter is zero, then the calculation of turning point is possible; furthermore, On one hand,when the fill ratio is less than 0.43, the system elastic performance turns to hard features; On the other hand, when the fill ratio greater than 0.43, the feature of the system become soft.
4. By applying Melnikov method, the global dynamic behaviors of the sloshing equations in aircraft filled with liquid under multi-frequency excitied model are studied. Consequently, threshold values of heteroclinic bifurcation and subhamonic bifurcation are obtained, and mechanism of chaotic motion is determined. Meanwhile, the switch point which is highly noteworthiness is detected.
5. General nonlinear dynamical systems contain the complicated dynamical phenomenon mostly, such as bifurcation, chaos and so on. First of all, the effect of the self-excited vibration of piecewise-smooth nonlinear system caused by dry friction was taken into consideration. Concurrently, a new method which is used to decide the subsection integral limits of the system is highlighted. Second, resonance solution to a suspension system with two degrees of freedom is investigated with the C-L method. Based on the relationship between parameters and the topological bifurcation solutions, motion characteristics with deferent parameters are obtained. The result provides a theoretical basis for the optimal control of vehicle suspension system parameters.
引文
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