基于扫频响应反推黏弹性材料分数阶导数模型
Inverse Identification of the Fractional Derivative Model of Viscoelastic Materials Based on Sweeping Response

提出了基于测试获得的扫频响应反推黏弹性材料分数阶导数模型参数的方法。在同时考虑黏弹性材料阻尼和剩余等效黏性阻尼的基础上，建立了基础激励作用下黏弹性复合板动力学方程，给出了求解振动响应的方法。提出利用基于灵敏度的匹配计算实现分数阶导数模型参数辨识的方法。以贴敷ZN-1型黏弹性材料的悬臂钛板为例，辨识得到了该黏弹性材料的分数阶导数模型。将结果代入到黏弹性阻尼板振动响应分析模型中，通过理论与实验的对比，证明了辨识参数的合理性。
The fractional derivative model can effectively represent the mechanical behavior of the viscoelastic material in the time and frequency domain. The identification of fractional derivative model is of great importance for viscoelastic composite structure modeling as well as for damping reduction design. A method for identifying the fractional derivative model of viscoelastic materials based on sweeping response of composite structure was proposed. On the basis of considering both the viscoelastic material damping and the remaining equivalent viscous damping, the dynamic equation of viscoelastic composite plate under basement excitation is established and the method for solving the vibration response is also presented. Furthermore, a matching calculation method based on sensitivity is developed to identify the parameters of the fractional derivative model. The cantilevered titanium plate attached with ZN-1 viscoelastic material is chosen to display the proposed method and the parameters of fractional derivative model of this material are obtained. The identified parameters are substituted into the analysis model of the viscoelastic damping plate and the rationality of the identified results is verified by comparing the vibration responses obtained by theoretical calculation and experiments.