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一種描述磁流變彈性體滯回特性的分數階導數改進Bouc?Wen模型

Modified Bouc?Wen model based on a fractional derivative for describing the hysteretic characteristics of magnetorheological elastomers

  • 摘要: 為了準確表征大范圍應變幅值、激勵頻率和磁場下磁流變彈性體(Magnetorheological elastomer, MRE)的力學行為,本文引入黏彈性分數階導數,提出一種描述磁流變彈性體滯回特性的分數階導數改進Bouc?Wen模型。分析了各向同性與異性MRE的微觀形貌特征,對MRE進行了性能試驗,研究發現,MRE的儲能和損耗模量隨著應變幅值(0~100%)增大先不變后減小,隨著頻率(0~100 Hz)增大而增大,隨著磁場(0~545 mT)增大而增大。在此基礎上,基于分數階導數提出改進Bouc?Wen模型,在Simulink軟件中建立仿真模型,利用Oustaloup濾波器算法對分數階導數項近似計算,對比分析驗證了改進模型的有效性,各工況下仿真數據和試驗數據的吻合度均高于98%。結果表明:改進Bouc?Wen模型能準確地模擬MRE應力應變滯回曲線,擬合精度較Bouc?Wen模型明顯提升,改進模型在較寬的應變幅值、頻率和磁場范圍內是準確有效的,為實現MRE的工程應用打下基礎。

     

    Abstract: As a new type of magnetic sensitivity smart material, magnetorheological elastomers showing a good magnetorheological effect have been broadly applied in the field of intelligent structures and devices. A viscoelastic fractional derivative element was introduced into the stress?strain relationship of magnetorheological elastomers based on the Bouc?Wen model to accurately characterize the mechanical behavior of magnetorheological elastomers under a wide range of strain amplitude, excitation frequency, and magnetic field and to make it better applied in engineering practice. Further, a modified Bouc?Wen model based on a fractional derivative was proposed to describe the hysteresis characteristics of magnetorheological elastomers. The Bouc?Wen model has good universality and can accurately describe the hysteretic characteristics of the magnetorheological elastomer’s nonlinear viscoelastic region, but it cannot accurately simulate magneto-viscoelasticity and frequency dependence. The fractional derivative can express this characteristic with fewer parameters and higher accuracy. The micromorphology characteristics of isotropic and anisotropic magnetorheological elastomers were analyzed, and the performance tests of the magnetorheological elastomers were conducted. The storage and loss modulus of the magnetorheological elastomers initially remain unchanged and then decrease with an increase in strain amplitude (0–100%). Moreover, the storage and loss modulus of the magnetorheological elastomers increase with an increase in frequency (0–100 Hz) and magnetic flux density (0–545 mT). On this basis, a modified Bouc?Wen model was proposed based on the fractional derivative. The simulation model was established using the Simulink software, and the fractional derivative part of the modified model was approximately calculated using the Oustaloup filter algorithm. The effectiveness of the modified model was verified through a comparative analysis. The fitness values of simulation and experimental data under different loading conditions are higher than 98%. Results show that the modified Bouc?Wen model can accurately simulate the stress?strain hysteresis loops of the magnetorheological elastomers, and the fitting accuracy is significantly improved compared with that of the Bouc?Wen model. The modified model is accurate and effective in a wide range of strain amplitudes, frequencies, and magnetic fields, which can lay a foundation for the engineering application of magnetorheological elastomers.

     

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