利用分数阶导数模拟的粘弹材料振动模型

Vibration Model of Viscoelastic Materials Simulated by Using Fractional-Order Derivative

利用分数阶导数描述粘弹材料的本构关系,使用关于应变的分数阶导数的阶的积分,研究基于这样的本构关系的粘弹性杆-质量块的稳态振动分析,给出精确的幅频关系和相频关系,分析参数对粘弹性质、阻尼及共振现象的影响。结果显示这种本构关系能合理地体现材料的粘弹特性。

The constitutive relation of viscoelastic materials was characterized by using the fractional-order derivatives, where the integral on the order of fractional derivatives of strain was involved. The steady vibration analysis for viscoelastic rod-mass was conducted based on such constitutive equation, the accurate amplitude-frequency relation and phase-frequency relation were presented, and the effects of parameters on viscoelastic properties, damping and resonance phenomenon were analyzed. Results showed that such constitutive relation could reasonably reflect viscoelastic characterizations of materials.