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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Modeling the high-frequency complex modulus of silicone rubber using standing lamb waves and an inverse finite element method
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Modeling the high-frequency complex modulus of silicone rubber using standing lamb waves and an inverse finite element method

机译：利用驻波和逆有限元法模拟硅橡胶的高频复数模量

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摘要

To gain an understanding of the high-frequency elastic properties of silicone rubber, a finite element model of a cylindrical piezoelectric element, in contact with a silicone rubber disk, was constructed. The frequency-dependent elastic modulus of the silicone rubber was modeled by a four-parameter fractional derivative viscoelastic model in the 100 to 250 kHz frequency range. The calculations were carried out in the range of the first radial resonance frequency of the sensor. At the resonance, the hyperelastic effect of the silicone rubber was modeled by a hyperelastic compensating function. The calculated response was matched to the measured response by using the transitional peaks in the impedance spectrum that originates from the switching of standing Lamb wave modes in the silicone rubber. To validate the results, the impedance responses of three 5-mm-thick silicone rubber disks, with different radial lengths, were measured. The calculated and measured transitional frequencies have been compared in detail. The comparison showed very good agreement, with average relative differences of 0.7%, 0.6%, and 0.7% for the silicone rubber samples with radial lengths of 38.0, 21.4, and 11.0 mm, respectively. The average complex elastic moduli of the samples were (0.97 + 0.009i) GPa at 100 kHz and (0.97 + 0.005i) GPa at 250 kHz.
机译：为了了解硅橡胶的高频弹性，构建了与硅橡胶盘接触的圆柱形压电元件的有限元模型。硅橡胶的频率相关弹性模量通过在100至250 kHz频率范围内的四参数分数阶导数粘弹性模型进行建模。在传感器的第一径向共振频率的范围内进行计算。在共振时，硅橡胶的超弹性效应通过超弹性补偿功能进行建模。通过使用源自硅橡胶中固定兰姆波模式转换的阻抗谱中的过渡峰，将计算得到的响应与测量响应相匹配。为了验证结果，测量了三个具有不同径向长度的5毫米厚的硅橡胶盘的阻抗响应。已对计算和测量的过渡频率进行了详细比较。比较显示出很好的一致性，径向长度分别为38.0、21.4和11.0 mm的硅橡胶样品的平均相对差异分别为0.7％，0.6％和0.7％。样品的平均复弹性模量在100 kHz时为（0.97 + 0.009i）GPa，在250 kHz时为（0.97 + 0.005i）GPa。

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