随机激励下一类含分数阶阻尼的轮胎的振动响应  

Vibration Responses of Rubber Tires With Fractional Damping Under Stochastic Excitation

作　　者：范院琴 徐伟[1] 韩群[1] 杨勇歌 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《应用数学和力学》2014年第12期1330-1340,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11172233;11302169)~~

摘　　要：基于随机平均法研究了Kanai-Tajimi噪声激励下含分数阶阻尼的轮胎动力学系统的响应.首先将地震波近似为Kanai-Tajimi噪声,结合点接触模型和分数阶导数模型,建立轮胎的动力学方程,然后运用随机平均法求解振动位移的稳态概率密度函数的解析解,最后通过Monte-Carlo数值模拟验证了该方法的有效性.利用振动位移的概率密度求解聚丁二烯橡胶、丁基B252橡胶轮胎振动位移的均值与方差,并以此为依据考察这两类橡胶的减振性能.研究结果表明,轮胎振动位移的均值和方差随橡胶的储能模量的增大而增大,随耗散模量的增大而减小,这说明减小橡胶的储能模量或增大耗散模量可有效改善轮胎的减振性能.所得结果可为轮胎的设计与制造提供一定的理论基础.The vertical dynamic responses of rubber tires with fractional damping under the Kanai-Tvjimi noise excitation were investigated with the stochastic averaging method. Firstly, the earthquake wave was appro-uated with the Kanai-Tajimi noise, and the differential equation for tire vibration was established through combination of the point contact model with the frac- tional derivative model. Then, the stochastic averaging method was used to solve the stationary probability density analytically. In turn, validity of the proposed method was verified against the Monte-Carlo numerical simulation results. The probability density was applied to determine the mean values and variances of vibration displacements of the 2 kinds of tires made of polybuta- diene and butyl B252 rubbers, respectively. The results show that the mean value and variance of vibration displacement increase with the rubber＇ s storage modulus and decrease with its dissipation modulus. That means, the lower the rubber＇ s storage modulus is or the higher its dissi- pation modulus is, the better the vibration damping effect of the resulting tire will be. The work provides a theoretical reference for the design and manufacture of rubber tires.

关 键 词：分数阶阻尼 橡胶材料 随机平均法 粘弹材料 

分 类 号：O246[理学—计算数学]