磁流变粘弹性夹层板随机激励下的微振动响应特性  

Micro-vibration response characteristics of a randomly excited sandwich plate with MR visco-elastomer

作　　者：应祖光[1] 陈海锋[1] 

机构地区：[1]浙江大学航空航天学院力学系,杭州310027

出　　处：《振动与冲击》2012年第19期6-9,14,共5页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(11072215);浙江省教育厅科研项目(Y200907048);中央高校基本科研业务费专项资金

摘　　要：分析研究磁流变粘弹性夹层板在支座随机激励下的微振动响应特性,给出磁流变粘弹性材料的磁控动力学本构关系,建立粘弹性夹层板关于纵横位移的耦合运动微分方程。根据Galerkin法,将位移在空间上展开,转化该偏微分方程为常微分方程组,导出关于板挠度的多自由度振动方程。根据随机振动理论,得到板系统的频响函数、响应功率谱密度和对于微振动的均方根速度响应谱等表达式,从而发展该粘弹性夹层板的随机微振动响应分析方法。数值结果说明粘弹性夹层板可有效地控制其微振动响应,通过外加磁场调节磁流变粘弹性材料的损耗因子及存模系数等,可改进夹层板的微振动控制性能。The micro-vibration response of a sandwich plate with magnetorheological （MR） visco-elastomer under random support motion excitations was studied to illustrate its response reduction capacity. The dynamic behavior of the MR visco-elastomer was described with a complex modulus depending on vibration frequency and controlled with external magnetic fields. The differential equations of motion of the sandwich plate were derived from the dynamic equilibrium, constitutive and geometric relations. The plate displacements were expanded as series of spacial harmonic functions, and Galerkin method was used to convert the partial differential equations of motion into ordinary differential equations. The multi-degree-of-freedom vibration equations for the plate deflection were obtained. Based on the theory of random vibration, the expressions of frequency-response function, response power spectral density and root-mean-square velocity spectrum for the micro-vibration of the plate were derived. Then, the random micro-vibration response analysis method for the viscoelastic sandwich plate was developed. Finally, numerical results were given to illustrate the micro-vibration response reduction capacity of the viscoelastic sandwich plate. Its micro-vibration control performance was improved by adjusting the loss factor and storage modulus of the MR visco-elastomer with the external magnetic field.

关 键 词：夹层板 磁流变粘弹性体 随机激励 微振动 

分 类 号：O324[理学—一般力学与力学基础] O326[理学—力学]