Coja Michael, Kari Leif
The Marcus Wallenberg Laboratory for Sound and Vibration Research (MWL), Department of Engineering Mechanics, KTH Royal Institute of Technology, 100 44 Stockholm, Sweden.
Polymers (Basel). 2021 May 23;13(11):1703. doi: 10.3390/polym13111703.
A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range-20 to 2000 Hz-and for a wide pre-compression domain-from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and frequency dependence are solved by applying a transformation of the pre-compressed isolator into a globally equivalent linearized, homogeneous, and isotropic form, thereby reducing the original, mathematically arduous, and complex problem into a vastly simpler assignment while using a straightforward waveguide approach to satisfy the boundary conditions by mode-matching. A fractional standard linear solid is applied as the visco-elastic natural rubber model while using a Mittag-Leffler function as the stress relaxation function. The dynamic stiffness is found to depend strongly on the frequency and pre-compression. The former is resulting in resonance phenomena such as peaks and troughs, while the latter exhibits a low-frequency magnitude stiffness increase in addition to peak and trough shifts with increased pre-compressions. Good agreement with nonlinear finite element results is obtained for the considered frequency and pre-compression range in contrast to the results of standard waveguide approaches.
建立了一种用于预压缩圆柱形天然橡胶隔振器的波导模型，该模型适用于20至2000 Hz的宽频率范围以及从无预压缩到使用中的最大预压缩（即20%）的宽预压缩域。通过将预压缩隔振器转换为全局等效的线性化、均匀且各向同性形式，解决了同时对预压缩和频率依赖性进行建模的问题，从而将原本数学上艰巨且复杂的问题简化为一个非常简单的任务，同时使用直接的波导方法通过模式匹配来满足边界条件。使用分数标准线性固体作为粘弹性天然橡胶模型，同时使用米塔格 - 莱夫勒函数作为应力松弛函数。发现动态刚度强烈依赖于频率和预压缩。前者导致共振现象，如峰值和谷值，而后者除了随着预压缩增加峰值和谷值发生偏移外，还表现出低频幅值刚度增加。与标准波导方法的结果相比，在所考虑的频率和预压缩范围内，与非线性有限元结果取得了良好的一致性。
