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1、南京航空航天大学博士学位论文磁流变液夹层梁的动力学研究姓名：胡白香申请学位级别：博士专业：工程力学指导教师：夏品奇20080301南京航空航天大学博士学位论文 i 摘 要 智能材料结构是为适应现代航空、航天、电子、机械等高技术领域提出的高要求而发展起来的一类新型结构。磁流变液是一种智能材料，利用磁流变效应开发出来的产品具有无级调控、噪音低、响应速度快、结构简单可靠、能耗低，在航空、航天、土木、机械、汽车等领域有着巨大的应用潜力。 磁流变液在外加磁场作用下，其物理性能粘度、剪切模量、阻尼会发生快速、可控、可逆变化，将磁流变液与其他弹性材料进行复合，形成磁流变液夹层梁、板结构，通过改变磁场强度来控
2、制夹层结构的刚度、阻尼等特性从而实现对结构振动特性的控制，这对于控制飞行器、汽车以及机械结构的工作性能有着重要的应用价值。为此，本文对磁流变液夹层梁结构的动力学问题进行了理论与试验研究，主要工作包括： 1. 将夹层梁结构中的磁流变液处理为线性粘弹性材料，应力应变关系用复模量表示，建立了磁流变液夹层梁结构的弯曲振动模型，分析了磁流变液夹层梁结构在简支和悬臂两种边界条件下的振动特性。 2. 提出了磁流变液非连续分布的夹层梁的结构形式和设计方法，得到了该种梁结构的固有频率、损耗因子、振型函数、动力响应与外激励频率及磁场强度间的关系。 3. 建立了磁流变液夹层简支梁有限元模型，分别形成了上下弹性层和中
3、间磁流变液层的单元矩阵，推导了磁流变液夹层简支梁的动力学方程，分析了上下面板为铝材的磁流变液夹层简支梁的振动特性以及简谐激励下磁流变液夹层梁的动力响应，分析了不同磁场强度和磁流变层厚度对动力响应的影响。 4. 进行了磁流变液夹层悬臂梁、简支梁结构在不同磁场作用下的动力学实验研究， 分析了磁流变液对夹层悬臂梁、 简支梁结构振动抑制的效果及影响。 本文的理论分析与试验结果吻合较好。随着外加磁场强度的增加，磁流变液夹层梁的固有频率和损耗因子均增大，振动响应明显减小，说明在外加磁场作用下磁流变液对夹层梁有显著的振动抑制作用。 关键词：磁流变液，夹层梁，固有频率，损耗因子，动力响应 磁流变液夹层梁的动力
4、学研究 ii ABSTRACT Smart material structure is a new structure developed to meet the high requirement in the fields of modern aeronautics, astronautics, electronics and mechanics. Magnetorheological fluid (MRF) is a kind of inteligent material. The devices made by using magnetorheological effect have a
5、 lot of advantages such as continuous controll ability, less noise, fast response, simplicity of structure, low power consumption and so on. Therefore MRF has a great potential application in engineering. The properties of MRF, such as viscosity, shear modulus and damping can be changed quickly, con
6、trollably and reversibly under the varying magnetic field. The MRF can be compounded with other elastic materials to form the MRF sandwich beams and plates. The stiffness and damping properties of such structures can be controlled through the different levels of applied magnetic field, which is grea
7、t worthy to control the working performance of aerospacecraft, vehicle and mechanical structures. The dynamics of MRF sandwich beam structures has been investigated theoretically and experimentally in this thesis. The main research includes as follows. 1. The MRF was supposed to be the linear viscoe
8、lastic materials. The stressstrain relationship of MRF was expressed by using the complex shear modulus. The flexural vibration model of the MRF sandwich beam structures has been developed. The vibration characteristics of beam structures with the simply supported and cantilevered conditions were an
9、alyzed. 2. A kind of beam structure with non-continously distributed MRF and its design method have been presented. The relationships of the natural frequencies, loss factors, mode shapes, and transverse vibration response with the excitation frequencies and applied magnetic field levels have been o
10、btained. 3. A finite element model of a simply supported MRF sandwich beam has been developed. The element matrices of up and down elastic material layers and 南京航空航天大学博士学位论文 iii internal MRF layer were formed to derive the dynamic equations of the MRF sandwich beam. The vibration properties and the
11、responses under the harmonic excitation of the simply supported MRF sandwich beam with up and down Aluminium layers were analyzed. The effects of the magnetic field level and height of MRF on the dynamic response were also analyzed. 4. The experimental investigation of dynamics of the MRF sandwich b
12、eam structures with the simply supported and cantilevered boundary conditions was conducted, under the different magnetic field levels. The effects of MRF on the vibration suppression of the beam structures were analyzed. The theoretical results agreed with the experimental results. The natural freq
13、uencies and loss factors of the MRF sandwich beam structures increased with the increment of the applied magnetic field levels, and the vibration response of the beam structures decreased obviously, which indicated that MRF had an effective vibration suppression of the sandwich beam structures under
14、 the applied magnetic field. Key words: magnetorheological fluid (MRF), sandwich beam, natural frequency, loss factor, dynamic response 磁流变液夹层梁的动力学研究 viii 图、表 清 单 图 2.1 磁流变液的剪切应力与剪切应变的关系.10 图 2.2 磁流变液的流变机理 . 11 图 3.1 磁流变液夹层梁示意图 .26 图 3.2 磁流变液夹层梁的单元变形.28 图 3.3 单元位移.28 图 3.4 应力分布图.30 图 3.5 磁流变液夹层梁的位移与受力示意图.33 图 3.6 磁流变液非连续分布的夹层梁示意图.43 图 3.7 N 段两端固支磁流变液夹层梁的边界条件 .44 图 3.8 夹层简支梁实验与计算固有频率的比较(B=0 ) .49 图 3.9 夹层简支梁的固有频率计算值(Hz) .
