基础激励下分数阶线性系统的响应特性分析

发布时间：2018-04-27 03:13

本文选题：分数阶微积分 + 基础激励　；参考：《物理学报》2016年08期

【摘要】：本文研究了基础激励下含分数阶阻尼的线性系统的响应特性.当基础激励为简谐激励时,通过待定系数方法求得系统的动力传递系数;当基础激励为非简谐周期激励时,首先将激励展开成傅里叶级数,然后根据线性系统的叠加原理求得激励中各阶频率成分所引起的动力传递系数,并根据展开的傅里叶级数解决了数值运算中的不可导问题.用数值仿真的方法对解析结果进行了验证,两者符合良好,证明了解析分析的正确性.研究表明,基础激励引起的动力传递系数依赖于分数阶阻尼阶数的值,通过调节阻尼阶数可以控制动力传递系数的大小.对于基础激励为非简谐的周期激励情况,当激励频率一定时,激励中的高阶频率成分引起的动力传递系数可能大于激励中的低阶频率成分引起的动力传递系数.因此,激励中的高阶频率成分所起的作用是不可忽略的.
[Abstract]:In this paper, the response characteristics of linear systems with fractional damping under fundamental excitation are studied. When the foundation excitation is harmonic excitation, the dynamic transfer coefficient of the system is obtained by the undetermined coefficient method, and when the foundation excitation is anharmonic periodic excitation, the excitation is first expanded into Fourier series. Then according to the superposition principle of the linear system, the dynamic transfer coefficients caused by the frequency components in the excitation are obtained, and the non-differentiable problem in the numerical calculation is solved according to the expanded Fourier series. The numerical simulation method is used to verify the analytical results, which are in good agreement with each other, and the correctness of the analytical analysis is proved. The results show that the dynamic transfer coefficient caused by the foundation excitation depends on the value of the fractional damping order and the magnitude of the dynamic transfer coefficient can be controlled by adjusting the damping order. When the excitation frequency is fixed, the dynamic transfer coefficient caused by the high-order frequency component may be larger than that caused by the low-order frequency component. Therefore, the role of high-order frequency components in excitation can not be ignored.
【作者单位】：中国矿业大学机电工程学院;上海交通大学机械与动力工程学院;中国矿业大学江苏省矿山机电装备重点实验室;
【基金】：国家自然科学基金(批准号:51305441) 江苏省高校优势学科建设工程资助的课题~~
【分类号】：O32

【相似文献】