Self-induced parametric amplification in ring resonating gyroscopes
Self-induced parametric amplification in ring resonating gyroscopes
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DOI：
10.1016/j.ijnonlinmec.2017.01.011
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发表时间：
2017-09-01
影响因子：
3.2
通讯作者：
Shaw, Steven W.
中科院分区：
文献类型：
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作者：
Polunin, Pavel M.;Shaw, Steven W.
我们研究了自诱导参量放大，所产生的色散非线性耦合系统中的退化模式与圆对称旋转对称轴。这种现象首先在微机电环/盘陀螺仪中观察到，其中它使用纯无源非线性效应提供增强的读出增益[Nitzan等人。[22]，2015]。这项调查的目的是提供一个基本的描述这种现象，这是一个例子，非线性动力学可以提高一个实际设备的性能。为了描述这种行为，我们考虑由电极围绕的薄环的面内振动，该薄环围绕其对称轴以比其振动频率小得多的速率ω旋转，如在应用中的情况。重点是对退化的椭圆模式，其中之一是作为驱动模式，另一个作为传感模式的传感器。这些模式耦合通过惯性（科里奥利）和几何非线性效应，所描述的一般形式的动能和势能，占有限变形运动学，以及静电效应。我们调查的具体影响，这种耦合系统的性能和灵敏度时，用作传感器的自旋速率。具体而言，我们表明，驱动模式振动具有足够高的振幅影响的感测模式的动态行为的形式的参数泵浦，这导致感测模式响应的相当大的放大。由于该响应幅度与Ω成比例，因此其导致陀螺仪相对于外部角速率的灵敏度大幅增加。我们还说明了当Ω/Ω（n）= 0时，在模型中可以忽略感测模态振动对驱动模态动力学的影响。
We investigate self-induced parametric amplification that arises from dispersive nonlinear coupling between degenerate modes in systems with circular symmetry that rotate about the axis of symmetry. This phenomenon was first observed in micro-electromechanical ring/disk gyroscopes, where it provided enhanced readout gain using purely passive nonlinear effects [Nitzan et al. [22], 2015]. The goal of this investigation is to provide a fundamental description of this phenomenon, which is an example where nonlinear dynamics can improve the performance of a practical device. To describe this behavior, we consider the in-plane vibrations of a thin ring surrounded by electrodes that rotates about its symmetry axis at a rate Omega much smaller than its vibration frequencies can, as is the case in applications. The focus is on the pair of degenerate elliptical modes, one of which is taken as the drive mode and the other as the sense mode for the sensor. These modes are coupled through both inertial (Coriolis) and geometric nonlinear effects, as described by general forms of the kinetic and potential energies that account for finite deformation kinematics, as well as electrostatic effects. We investigate the specific effects of this coupling on the system performance and its sensitivity when used as a sensor for the spin rate. Specifically, we show that drive mode vibrations with sufficiently high amplitude affect the sense mode dynamic behavior in the form of parametric pumping, which leads to a considerable amplification of the sense mode response. As this response amplitude is proportional to Omega it results in a substantial increase of the gyroscope sensitivity with respect to the external angular rate. We also illustrate that the effects of the sense mode vibrations on the drive mode dynamics can be neglected in the model when Omega/omega(n)