方形硅膜的共振频率对离面力的依赖性：应用于MEMS梯度仪
Resonance frequency dependence on out-of-plane forces for square silicon membranes: applications to a MEMS gradiometer
摘要：
由于膜可以作为传感头应用于各种器件中，因此膜的动态特性一直是人们研究的对象。已经提出了一些方法来解决确定谐振频率及其对由施加在膜表面上的力引起的应力的依赖性的问题。矩形薄膜在均匀面内力作用下的振动问题是众所周知的。然而，当力是平面外而不是平面内时的共振频率行为没有被很好地理解和记录。在以前的工作中，已经开发了一种梯度计，该梯度计使用具有固定在其上的磁体的硅方形膜作为传感器头。该器件报告频率与面外磁力的二次相关性。在这项工作中，模拟获得的基本弯曲模式的频率上的应力的依赖性已被执行。研究了面内力和面外力对膜的影响。正如所料，平方根依赖已被发现的平面内的力量。然而，当考虑平面外力时，问题更加复杂。平面外力引起初始二次相关性，该二次相关性从某个应力值变成平方根相关性。随着固定在膜上的磁体的表面的增加，二次范围增加，频率的变化率减小。研究解决了这些问题，实验和模拟结果进行了比较，实验和模拟结果之间有很好的一致性
英文摘要：
The dynamic properties of membranes have been object of many researches since they can be used as sensor heads in different devices. Some methods have been proposed to solve the problem of determining the resonance frequencies and their dependence on the stress caused by forces applied on the membrane surface. The problem of the vibrating rectangular membrane under a stress caused by a uniform in-plane force is well known. However, the resonance frequency behaviour when the force is out-of-plane instead of in-plane, is not so well understood and documented. A gradiometer which uses a silicon square membrane with a magnet fixed on it as a sensor head has been developed in a previous work. This device reports a quadratic dependence of the frequency on the out-of-plane magnetic force. In this work, simulations to obtain the dependence of the frequency of the fundamental flexural mode on the stress have been performed. It has been studied the influence of in-plane and out-of-plane forces applied to the membrane. As expected, a square root dependence has been found for in-plane forces. Nevertheless, the problem is more complex when out-of plane forces are considered. Out-of-plane forces gives rise to an initial quadratic dependence which turns into a square root dependence from a certain stress value. The quadratic range increases and the rate of change of the frequency decreases as the surface of the magnet fixed on the membrane increases. The study has addressed these problems and both, experimental and simulated results have been compared and a good agreement between experimental and simulated results has been found
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