新型飞机起落架阻尼器的数学建模与理论  

Mathematical Modeling and Theory of New Aircraft Dampers

作　　者：谭忠[1,2] TAN Zhong(School of Mathematical Sciences,Xiamen University,Xiamen,Fujian 361005,China;Shenzhen Research Institute,Xiamen University,Shenzhen,Guangdong 518000,China)

机构地区：[1]厦门大学数学科学学院,福建厦门361005 [2]厦门大学深圳研究院,广东深圳518000

出　　处：《数学建模及其应用》2023年第1期1-7,共7页Mathematical Modeling and Its Applications

基　　金：国家自然科学基金重点项目(12231016);国家自然科学基金面上项目(12071391);广东省基础与应用基础研究基金(2022A1515010860)。

摘　　要：20世纪90年代,科学家发现了一种智能材料——磁流变液:在不通磁场时,铁磁颗粒随机悬浮在特定的油液中,呈现低黏度牛顿流体状态;一旦通磁,铁磁颗粒瞬间被磁化成磁偶极子,首尾相连成为柱状结构,其黏度瞬间升高几十倍,呈现非牛顿流体状态,剪切应力大大增强,即可达到吸能减振的效果,磁场撤销后流体恢复原状.利用这一特性可为制造新型飞机起落架的阻尼器提供理论支撑.根据数学建模技能表明,该运动过程能应用守恒律的数学思想和精细的微积分推导建立起偏微分方程组模型.因此,该偏微分方程组的建立及其稳定性问题、自由边界问题和边界层问题等基础理论问题的解决,就构成了新型飞机起落架的阻尼器制造的核心技术,这让我们深刻领会到习近平总书记在中央政治局第三次集体学习时所强调的“切实加强基础研究,夯实科技自立自强根基”的重要意义.In the 1990s,scientists discovered an intelligent material-magnetorheological fluid:when no magnetic field is added,ferromagnetic particles are randomly suspended in a specific fluid,showing a low-viscosity Newtonian fluid state;once magnetized,ferromagnetic particles are instantly magnetized into magnetic dipoles,connected by the head and tail into a columnar structure,and their viscosity instantly rises tens of times,showing a non-Newtonian fluid state.At the same time,its shear stress would be enhanced so greatly that energy absorption and vibration reduction can be achieved.After the magnetic field is withdrawn,the fluid returns to its original state.Thus we can use this property to provide theoretical support for the manufacture of dampers for new aircraft landing gear.According to the mathematical modeling skills,it is shown that the motion process can be modeled as a system of partial differential equations by applying mathematical ideas of conservation laws and careful calculus derivations.Therefore,the establishment of this system of partial differential equations and the solution of the basic theoretical research problems such as stability problem、free boundary problem and boundary layer problem constitute the new engineering problem-the core technology of the manufacture of new aircraft dampers,which makes us deeply appreciate the importance significance of"strengthening basic research so as to consolidate self-reliance and strength in science and technology"emphasized by general secretary Xi Jinping at the third group study session of the Political Bureau of the 20th CPC Central Committee.

关 键 词：飞机起落架阻尼器 磁流变液 非牛顿流体方程组 稳定性问题 自由边界问题 边界层问题 

分 类 号：O29[理学—应用数学]