Influence of the resonator angular displacements in a hemispherical resonator gyro on the coupling between the working and beam-type vibrations

In [1], we have studied how the coupling between the working and beam type vibrations of the resonator affects the hemispherical resonator gyro operation. We show that such a coupling arises if the resonator is unbalanced. The beam type vibrations are considered as translational displacements of the resonator hemisphere in the plane orthogonal to the symmetry axis. In the present paper, we take into account the fact that the hemisphere translational displacement is accompanied by its rotation about the axis perpendicular to the displacement line. We show that in this case a more accurate balancing of the resonator is required to eliminate the coupling between the two vibration modes.     

比力对半球谐振陀螺仪解算精度的影响

为了分析半球谐振陀螺仪非敏感轴X、Y轴存在比力输入时,对输出角速率解算精度的影响,首先,利用环形谐振子的动力学方程,得到了径向振动方程。然后,分析了存在比力输入时,谐振子唇沿中心将偏移激励器和位移传感器所确定的圆心,并根据闭环检测原理,推导了陀螺仪解算角速率误差的表达式,仿真计算了相对偏移量对输出结果的影响程度。最后,利用分度头进行了非敏感轴的多位置翻滚试验,验证了输出中存在与非敏感轴比力输入有关的误差。     

Amplitude control contour in a hemispherical resonator gyro with automatic compensation for difference in <Emphasis Type="Italic">Q</Emphasis>-factors

For the normal operation of a hemispherical resonator gyro, its circuit must contain a control contour maintaining the resonator vibrations in the form of a standing wave with a prescribed amplitude. A turn of the basement leads to a turn of the standing wave, which permits using the resonator as a gyro. A turn of the standing wave may arise without a turn of the basement if the resonator has difference in Q-factors, i.e., if the damping constant of the standing wave depends on its orientation. This is one important source of device errors. Some information about the difference in Q-factors can be obtained by analyzing how the control signal maintaining the prescribed amplitude depends on the wave orientation. The larger the damping constant, the larger control signal is required to maintain the wave with the largest amplitude.In the present paper, we consider a version of the amplitude control contour in which the control signal maintaining the amplitude is supplemented with signal compensating for difference in Q-factors of the resonator. The compensating signals are produced by time integration of the control signal multiplied by certain trigonometric functions of the wave orientation angle. In this case, we decrease the level of dynamic errors of the amplitude maintenance contour, which arise in the usual circuit with each change of the wave orientation in the resonator, and simultaneously eliminate the drift caused by difference in Q-factors.     

Influence of surface micro-beams with large deflection on the resonance frequency of a quartz crystal resonator in thickness-shear mode vibrations

We study the dynamic behavior of a quartz crystal resonator(QCR)in thickness-shear vibrations with the upper surface covered by an array of micro-beams(MBs)under large deflection.Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator,dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations.It is found that the frequency shift produces a little right(left)translation for increasing elastic modulus(length/radius ratio)of MBs.Moreover,the frequency right(left)translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one.     

On flexural vibration of hemispherical shell

This paper makes detailed analyses for the flexural vibration(frequency)of the hemispherical shell and presents the varying laws of frequency with the varying boundary angles and the wall thickness of the above shell.It is an important value to develop the instrument,such as hemispherical resonator gyro(HRG),whose sensing component is a hemispherical shell.     

Multi-frequency vortex-induced vibrations of a long tensioned beam in linear and exponential shear flows

The multi-frequency vortex-induced vibrations of a cylindrical tensioned beam of aspect ratio 200, free to move in the in-line and cross-flow directions within first a linearly and then an exponentially sheared current are investigated by means of direct numerical simulation, at a Reynolds number equal to 330. The shape of the inflow profile impacts the spectral content of the mixed standing-traveling wave structural responses: narrowband vibrations are excited within the lock-in area, which is limited to a single region lying in the high flow velocity zone, for the linear shear case; in contrast, the lock-in condition occurs at several spanwise locations in the exponential shear case, resulting in broadband responses, containing a wide range of excited frequencies and spatial wavenumbers. The broadband in-line and cross-flow vibrations occurring for the exponential shear current have a phase difference that lies within a specific range along the entire span; this differs from the phase drift noted for narrowband responses in linear shear flow. Lower vibration amplitudes, time-averaged and fluctuating in-line force coefficients are observed for the exponential shear current. The cross-flow force coefficient has comparable magnitude for both inflow profiles along the span, except in zones where the broadband vibrations are under the lock-in condition but not the narrowband ones. As in the narrowband case, the fluid forces associated with the broadband responses are dominated by high frequencies related to high-wavenumber vibration components. Considerable variability of the effective added mass coefficients along the span is noted in both cases.     

半球谐振陀螺（HRG）信号处理技术

半球谐振陀螺是一种高精度的振动陀螺,其信号处理技术是实现陀螺功能并取得预期性能的关键之一。本导出了半球振子振动位移信号的表达形式,提出了信号处理的基本方法并进行了详细的计算。其结果为自主设计半球谐振陀螺信号处理电路提供了依据。     

Nonlinear dynamic analysis of a photonic crystal nanocavity resonator

A nonlinear dynamic model of a one-dimensional photonic crystal nanocavity resonator is presented. It considers the internal tensile stress and the geometric characteristics of a photonic crystal with rectangular(and circular) holes. The solution of the dynamic model shows that the internal tensile stress can suppress the hardening and softening behaviors of the resonator. However, the stress can reduce the amplitude, which is not conducive to an improvement of the sensitivity of the sensor. It is demonstrated that with an optimized beam length, the normalized frequency drift of the beam can be stabilized within 1% when the optical power increases from 2 mW to 6 mW. When the hole size of the resonator beam is close to the beam width, its increase can lead to a sharp rise of the resonant frequency and the promotion of hardening behavior. Moreover,the increase in the optical power initially leads to the softening behavior of the resonator followed by an intensification of the hardening behavior. These theoretical and numerical results are helpful in understanding the intrinsic mechanism of the nonlinear response of an optomechanical resonator, with the objective of avoiding the nonlinear phenomena by optimizing key parameters.     

Investigation of the vibrational characteristics of a Helmholtz resonator with vibrations of finite amplitude

An investigation has been made of the elastic and dissipative characteristics of a Helmholtz resonator. On the basis of an analysis of the equation of the free vibrations in the resonator, and of an experimental investigation of the damping of the vibrations, it is shown that the elastic characteristic of the resonator can be regarded as linear and the dissipative characteristic, as quadratic.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 185–186, September–October, 1976.     

基于二维质点振动模型的半球谐振陀螺谐振子进动分析

半球谐振陀螺是基于固体波的进动效应进行角速度检测的一种全固态陀螺。为分析半球谐振子中固体波的进动效应,基于虚功原理,建立了理想条件下半球谐振陀螺谐振子中固体波进动的动力学模型。针对进动波的动力学模型过于复杂、难于分析的缺陷,提出采用相似系统的分析方法,将该动力学模型等效为二维空间质点的简谐振动模型;采用快变量与慢变量分离的方法,对等效模型进行了参数分析,通过与实际的半球谐振陀螺信号处理系统采集的李沙育图形进行对比,验证了等效简谐振动模型的有效性和正确性。     

Vibration analysis of undamped,suspended multi-beam absorber systems

The vibration analysis of an Euler-Bernoulli beam with an attached rotary unit is first carried out assuming no unbalance. For comparison purposes, two different beam end boundary conditions are considered: a simply-supported and a clamped-clamped condition. The problem is then extended to the vibration behavior of the initial beam when subjected to a harmonic load due to an unbalance in the rotary unit. To absorb the ensuing vibrations, a secondary passive beam system is suspended from the primary beam which consists of two continuous leaf springs and three discrete masses. The absorption frequency is obtained by exploring the deflection norm of the primary beam versus dimensionless frequencies of the system. To ensure the appropriateness of the procedure for similar multi-beam absorber systems, an experimental set-up is established and analytical results are verified.     

Axisymmetric vibrations of a cylindrical resonator measured by holographic interferometry

A circular, cylindrical, ultrasonic resonator excited at one of its resonant frequencies is studied by holographic interferometry. Displacement distributions associated with the axisymmetric oscillations of the resonator are measured with the aid of time-average holograms, and are compared with a simple one-dimensional theory of rod vibrations, corrected for radial inertia. Analysis shows the overall error bounds on measured displacements to be ±9 percent of the maximum displacement at the resonator tip. Although the accuracy of measurements could be increased by refinements in experimental techniques, the work reported here represents substantial improvement in measuring the vibratory motion characteristics of ultrasonic devices over the point-by-point technique used heretofore.     

广义边界梁的动力学建模与动态特征

对于广义边界条件Euler-Bernoulli梁,采用相对描述方式建立了可描述梁整体运动和相对变形的几何非线性及其线性化动力学模型,应用线性变换得到了该类梁的线性经典动力学方程,得到了广义边界条件下梁的横向振动代数特征方程、特征函数及特征值的退化表达式.算例分析了边界小扰动对固支-固支梁横向振动特征的影响规律.     

Interaction of the thermovibrational and thermocapillary convection mechanisms

Thermal convection in microgravity induced by the combined action of thermocapillary forces and vibrations is considered. In the high-frequency approximation the thermovibrational forces are written for the case in which isothermal mixing of the fluid is unimportant. The authors' own work and new results of investigating the effect of vibration on thermocapillary instability, of numerically modeling the heat and mass transfer in open cavities and of experiments on the vibrational suppression of surface deformation are reviewed. The prospects for the practical application of the results obtained are discussed.     

An image encryption algorithm based on compound homogeneous hyper-chaotic system

A new dynamic model of a rotating flexible beam with a concentrated mass located in arbitrary position is derived based on the absolute nodal coordinate formulation, and its modal characteristics are investigated in this paper. To consider the concentrated mass at an arbitrary location of the beam, a Dirac’s delta function is used to express the mass per unit length of the beam. Based on the proposed dynamic model, the frequency analysis is performed. The nonlinear equation is transformed into the linear one via employing the linear perturbation analysis method. The stiffness matrix of static equilibrium of the system under the deformed condition is obtained, in which the effect of coupling between the longitudinal deformation and transversal deformation is included. This means even if only the chordwise bending equation is solved, the longitudinal vibration effect can be still considered. As we know, once the longitudinal deformation is large, it will significantly affect the chordwise bending vibration. So the proposed model in this paper is more accurate than the traditional dynamic models which are usually lack of the coupling terms between the longitudinal deformation and transversal deformation. In fact, the traditional dynamic models for the chordwise vibration analysis in the existing literature are usually linear due to neglecting the coupling terms, and consequently, they are only suitable for the modal characteristic analysis of a beam under small deformations. In order to get some general conclusions of the natural frequencies and mode shapes, the equation which governs the chordwise bending vibration of the rotating beam is transformed into a dimensionless form. The dynamic model presented in this paper is nonlinear and can be conveniently used to analyze the modal characteristics of a rotating flexible beam with large deformations. To demonstrate the power of the new dynamic model presented in this paper, the dynamic simulations involving the comparisons between the different frequencies obtained using the model proposed in this paper and the models in the existing literature and the investigating in frequency veering and mode shift phenomena are given. The simulation results show that the angular velocity of the flexible beam will give rise to the phenomena of the natural frequency loci veering and the associated mode shift which is verified in the previous studies. In addition, the phenomena of the natural frequency loci veering rather than crossing can be observed due to the changing of the magnitude of the concentrated mass or of the location of the concentrated mass which are found for the first time. Furthermore, there is an interesting phenomenon that the natural frequency loci will veer more than once due to different types of mode coupling between the bending and stretching vibrations of the rotating beam. At the same time, the mode shift phenomenon will occur correspondingly. Additionally, the characteristics of the vibration nodes are also investigated in this paper.     

Torsional dynamics of the Birnboim-Schrag multiple lump resonator studied using TV-holography

We have studied the torsional dynamics of the Birnboim-Schrag multiple lump resonator (MLR) using TV holography. The relative torsional displacement amplitudes have been determined for all resonator lumps at their five resonance modes. Due to the low vibration amplitudes for the highest frequency mode, we only give a rough estimate of the relative torsional displacements for this resonance. For some lumps, the observed relative displacement amplitudes deviate by as much as a factor of 2 from the predictions of the dumbbell theory commonly used to analyze MLR dynamics. The experimental data agree well with the recent theoretical analysis carried out by Mikkelsen et al. (1992).     

基于剪切变形的矩形梁剪力滞求解方法

Timoshenko梁通过假设截面的剪切刚度和附加平均剪切转角变形的方式来近似修正初等梁中未考虑剪切变形能的问题,这与梁剪应力沿梁高变化的实际不符。本文基于材料力学剪应力计算式和相应的剪切变形理论,从剪切变形与梁的位移关系入手,导出矩形梁考虑剪切变形时的纵向位移沿梁高方向的函数关系式,证明该位移可分解为纯弯曲引起的位移和剪力引起的剪力滞翘曲位移之和。应用剪力滞广义坐标与广义力的概念,基于能量变分原理得到等截面梁剪力滞控制微分方程组及其通解形式。对均布荷载作用下矩形简支梁的算例分析表明,本文算法与弹性力学精确解对比,两者的应力和挠度剪力滞系数求解结果非常接近,本文算法有足够的精度,且比弹性力学简单。     

Analysis of thickness-shear and thickness-twist modes of AT-cut quartz acoustic wave resonator and filter

The thickness-shear(TS) and thickness-twist(TT) vibrations of partially electroded AT-cut quartz plates for acoustic wave resonator and filter applications are theoretically studied. The plates have structural variations in one of the two in-plane directions of the plates only. The scalar differential equations derived by Tiersten and Smythe for electroded and unelectroded AT-cut quartz plates are used, resulting in free vibration resonant frequencies and mode shapes for both fundamental and overtone families of modes. The trapped modes with vibrations, mainly confined in the electroded areas, are found to exist in both the resonator and the filter structures. The numerical results for the trapped modes are presented for different aspect ratios of electrodes and material properties, providing a reference to the design and optimization of quartz acoustic wave resonators and filters.     

钝圆柱头质量对简支梁的弹性次碰撞研究

该文采用赫兹碰撞理论、三维动力有限元方法和自行研制的次碰撞实验装置,研究了钝圆柱头质量一次坠落碰撞简支钢梁过程的次碰撞现象、次碰撞过程的持续时间和次碰撞发生的条件．实验测试和数值模拟均清楚地观察到了复杂的次碰撞现象．研究结果表明：（1）当梁初始处于静止状态时,将实验测试和数值模拟结果与理论分析结果对比后发现,首个次碰撞过程由局部接触变形主导,并可以采用 Hertz弹性碰撞理论来描述;（2）实验和数值模拟结果展现了与首个次碰撞过程特征迥异的后续次碰撞过程,后续次碰撞过程的持续时间出现大范围的随机变化;（3）进一步分析发现,后续次碰撞过程由局部接触变形和梁的整体变形运动共同主导,梁的整体变形运动使得碰撞力响应变得异常复杂;（4）通过数值计算结果发现,当出现次碰撞现象时,碰撞位移响应中的一阶模态幅值占比会突然降低,相位角发生明显的变化;（5）数值计算结果表明,次碰撞发生的条件与质量比、碰撞初速度、碰撞动量、碰撞位置、测试梁长度和厚度等有关;（6）次碰撞发生的条件若用质量比来度量,则发现存在一个质量比阀值．上述研究表明,局部接触变形和梁的整体变形运动相互作用,产生了复杂的耦合效应,使得次碰撞现象呈现了丰富的力学行为．因此,进一步通过理论、实验和数值仿真研究复杂的次碰撞现象,对于深入理解柔性结构的碰撞行为很有必要．     

中性线修正型变截面梁类构件压电控制

传统绝对节点坐标法(absolute nodal coordinate formulation,ANCF)在变截面梁类构件建模过程中常以几何中位线等效构造单元中性线,难以对变截面单元位移场状态进行精确描述.为解决此类问题,本文以中细型变截面梁类构件为研究对象,深入考虑变截面结构几何因素及复合材料属性对变截面梁类构件中性...