声表面波谐振器频率-温度行为分析

声表面波（SAW）器件以其优良的性能广泛应用于雷达、通讯和日常用品等领域。然而,随着器件工作频率的不断升高,温度对器件频率稳定性的影响也越来越严重。因此,研究声表面波器件的温度效应,并在变温情况下保持SAW器件的频率稳定性至关重要。本文采用增量型的拉格朗日方程分析受温度影响的声表面波频率漂移问题。用频率-温度系数（TCF）作为评价频率-温度行为的标准。设计了一个具有温度补偿层的双层SAW谐振器模型,降低了器件的频率-温度系数。通过尺寸优化,LiNbO3-AlN结构的SAW谐振器在25℃（参考温度）下的频率温度系数TCF接近0ppm/℃。SAW谐振器的波长为4μm,谐振频率为1214.9MHz。     

声表面波谐振器频率-温度行为分析

声表面波（SAW）器件以其优良的性能广泛应用于雷达、通讯和日常用品等领域。然而,随着器件工作频率的不断升高,温度对器件频率稳定性的影响也越来越严重。因此,研究声表面波器件的温度效应,并在变温情况下保持SAW器件的频率稳定性至关重要。本文采用增量型的拉格朗日方程分析受温度影响的声表面波频率漂移问题。用频率-温度系数（TCF）作为评价频率-温度行为的标准。设计了一个具有温度补偿层的双层SAW谐振器模型,降低了器件的频率-温度系数。通过尺寸优化,LiNbO3-AlN结构的SAW谐振器在25℃（参考温度）下的频率温度系数TCF接近0ppm/℃。SAW谐振器的波长为4μm,谐振频率为1214.9MHz。     

在旋转的半无限LiNbO3上传播的声表面波

声表面波(SAW)陀螺具有无源、无线、单层平面结构等优点。以目前国外研究小组所用的铌酸锂为对象，对含陀螺效应的声表面波的波动方程进行求解。用编制的程序进行了数值计算并绘制了基体绕各不同坐标轴旋转时，陀螺效应对铌酸锂表面传播的声表面波速度及对机电耦合系数影响的相关曲线，并对结果进行了分析。     

硅微机械谐振式陀螺仪

介绍了硅微机械谐振式陀螺仪的工作原理，给出了硅微机械谐振式陀螺仪的动力学方程详尽推导。针对此方程进行仿真研究，对结构设计参数进行了估计。研究表明，硅微机械谐振式陀螺仪是一种很有发展前途的新型陀螺仪。     

微静电陀螺仪再平衡回路设计

微静电陀螺仪依靠可控的静电力,将高速旋转的陀螺转子稳定地悬浮在高真空的电极腔中心,是一种能实现两自由度角速率测量的新型微机电陀螺。针对大角度、高角速率的捷联式惯性导航系统应用,对陀螺仪再平衡回路进行了设计。讨论了陀螺仪的动力学特性,给出了补偿负刚度特性的方法,采用双频波特图对系统稳定性进行了分析,给出了再平衡回路的性能仿真结果。仿真与分析表明,陀螺仪允许的最大输入角速度为768(°)/s,标度系数为6.44mV/((°)·s-1)。     

Gradient surface ply model of SH wave propagation in SAW sensors

Investigation of the propagation of the wave in SAW sensors is a basis for the research and design of the sensors. With the advance of the sensor, both the effect of environment on the surface ply and the geometry of waveguide are complicated. To consider the complication, a model with gradient surface ply and multilayer waveguide of SH wave propagation in sensor is proposed. The equation of wave velocity is derived by a transfer matrix method. Through the equation, the function of wave velocity increment via the change of parameters in the surface ply is obtained. The effect of the inhomogeneity on the function is also studied. Finally, some influencing factors of the behavior of the sensor are discussed. This study was supported by the National Natural Science Foundation of China (No. 59635140), the Doctoral Education Foundation of the Ministry of Education of China and Aeronautics Foundation of China.     

MEMS硅微陀螺仪系统级建模与仿真研究

根据MEMS陀螺仪敏感哥式加速度、测量角速度的原理,建立MEMS陀螺系统级行为模型是分析MEMS陀螺仪内部的驱动、检测和信号解调等行为过程及改进陀螺整个系统的性能的重要方法。根据MEMS陀螺的动力学方程及其内部组成,将MEMS陀螺分成驱动电路、传感器、信号调理电路等三部分,建立了MEMS陀螺系统级模拟行为模型,运用相关检测技术对角速度信号进行了提取,并对模型进行了仿真验证。仿真结果验证了所设计模型的有效性,所建模型可以用于MEMS陀螺的特性和性能分析。     

Control of nonlinear vibrations of vibrating ring microgyroscope

The influence of the basement rotation on the variations in the spectrum of vibration frequencies of thin elastic shells and rings was known already at the end of the 19th century [1]. The physical phenomenon of inertness of elastic waves occurring free vibrations of an axisymmetric body, first explained in [2], were practically used in developing new types of gyros [2–6]. The foundations of the theory of wave gyros were laid in [2, 4], and the errors of such gyroscopes for various shapes of the vibrating resonator were studied in [2, 4, 7, 8]. It was shown that the error of the resonator manufacturing (the variable density, thickness, anisotropy of the material elastic properties, etc.) [2, 8] and the geometric nonlinearity of the resonator flexural vibrations studied in [2, 7] lead to splitting of the natural frequency of flexural vibrations [2], which is reflected in the wave picture of the resonator vibrations and characterizes the gyroscope precision.In the present paper, we study the errors of the vibrating microgyroscope which arise because of nonlinear elastic properties of the ring resonator material. We construct a control of the potential on the electrodes which allows one to maintain the prescribed amplitude of the normal resonator deflection and compensate for the gyroscope errors arising because of the nonlinear elastic properties of the material.     

Geometrical nonlinearity stabilizes a wave solid-state gyro

It was recognized long ago that quasi-harmonic standing waves in a thin-walled axisymmetric resonator, mounted on a rotating platform, are subject to a precession. This significant phenomenon is naturally associated with a concept of a solid-state wave gyro, or an inertial instrument used to measure angular rotation rate, as if any wave may be interpreted as a material particle moving in a rotating frame of reference. Because there are no typical mechanical parts, these wave sensors can be utilized with a lot of advantages. To run such a gyro in vita, one should excite and keep on by certain means a standing wave in the thin-walled axisymmetric resonator. Up to now, there are known two ways how to do it, and namely, using either external or parametric resonant mechanisms of excitation. Although both cases necessarily require an additional feedback control device in order to stabilize instable or other parasite oscillations of the resonator. This paper, following the study of nonlinear waves in a thin circular ring, demonstrates that the solid-state wave gyro may be naturally stabilized just at the expense of the geometrical nonlinearity by combining advantages of both the positional resonant excitation and the parametric resonance.     

A nonlinear analysis of surface acoustic waves in isotropic elastic solids

With the fast evolution of wireless and networking communication technology, applications of surface acoustic wave (SAW), or Rayleigh wave, resonators are proliferating with fast shrinking sizes and increasing frequencies. It is inevitable that the smaller resonators will be under a strong electric field with induced large deformation, which has to be described in wave propagation equations with the consideration of nonlinearity. In this study, the formal nonlinear equations of motion are constructed by introducing the nonlinear constitutive relation and strain components in a standard procedure, and the equations are simplified by the extended Galerkin method through the elimination of harmonics. The wave velocity of the nonlinear SAW is obtained from approximated nonlinear equations and boundary conditions through a rigorous solution procedure. It is shown that if the amplitude is small enough, the nonlinear results are consistent with the linear results, demonstrating an alternative procedure for nonlinear analysis of SAW devices working in nonlinear state.     

半球谐振陀螺的机理分析

—本文论述了半球谐振陀螺的组成；用能量法建立了旋转轴对称壳体的动力学方程，研究了半球谐振频率；推导了半球谐振子四波腹振型的形成，同时分析半球谐振子环向振型的进动性，说明了不同的拾振原理。     

硅微型两自由度振动轮式陀螺仪的研究

本文详细介绍了一种利用微电子加工工艺制作的硅微型两自由度振动轮式陀螺仪的新结构 ,分析了该种陀螺仪的工作原理 ,推导了陀螺仪动力学方程 ,并讨论了梳状谐振器的工作机理和陀螺仪模拟力反馈的闭环控制方案 ;目前已制作完成了该型陀螺仪的原理样机     

微机械陀螺温度混合线性回归补偿方法

环形振动微机电陀螺受温度影响较大,并且还具有很强的自回归特性。针对传统的分段拟合等温度模型均难以精确补偿陀螺受温度影响的问题,提出了一种基于混合线性回归的温度补偿模型。该方法根据混合线性回归模型的特点将陀螺自身的影响以及温度变化等因素考虑到温度补偿模型中,采用多元线性回归方法确定各项的系数,通过对残差的正态检验确定模型是否能够较好的符合陀螺数据的变化规律。验证试验结果表明:补偿后的均值可以减小1～2个数量级,并且该温度误差补偿方法重复性好,具有重大的工程应用参考价值。     

激光器光谱线宽对布里渊光纤谐振腔谐振特性的影响

针对激光器光谱线宽不可能严格为零的问题,在激光相干理论的基础上,采用光波场叠加的方法计算了布里渊光纤谐振腔的循环光强,详细分析了激光器光谱线宽对布里渊光纤谐振腔谐振谱线宽度和精细度的影响,并进一步分析了光谱线宽对谐振腔受激布里渊散射阈值的影响,最后,引入了线宽压缩的概念分析了布里渊光纤陀螺的灵敏度。分析表明,除了耦合器插入损耗外,激光器光谱线宽也是影响精细度的重要因素,具体影响程度与激光器光谱线宽及谐振腔本征谱线宽度间的相对大小有关,受激布里渊散射阈值随激光器线宽的增加而近似线性增加,另外在其他参数相同的情况下,布里渊光纤陀螺的灵敏度比谐振式光纤陀螺高大约三个数量级。本文为布里渊光纤陀螺的光源选择及光路参数的优化设计过程提供了理论依据。     

Propagation characteristics of thermoelastic waves in piezoelectric (6 mm class) rotating plate

The propagation of Lamb waves in a homogeneous, transversely isotropic (6 mm class), piezothermoelastic plate rotating with uniform angular velocity about normal to its boundary has been investigated. The generalized (non-classical) theories of thermoelasticity in contrast to Sharma and Pal [Sharma, J.N., Pal, M., 2004. Lamb wave propagation in transversely isotropic piezothermoelastic plate. J. Sound Vib. 270, 587–610] have been used to investigate the problem. The surfaces of the plate are subjected to stress free, thermally insulated/isothermal and electrically shorted boundary conditions. Secular equations for wave propagation modes in the plate are derived from a coupled system of governing partial differential equations of linear piezothermoelasticity. After obtaining the complex characteristic roots with the help of Descartes' algorithm, the transcendental secular equations have been solved by functional iteration numerical technique to compute phase velocity and attenuation coefficient. Finally, in order to illustrate the analytical development, numerical solution of secular equations is carried out for PZT-5A piezo-thermoelastic material. The corresponding simulated results of various physical quantities such as phase velocity, attenuation coefficients, specific loss factor of energy dissipation, thermo-mechanical coupling factor and relative frequency shifts have been presented graphically for both rotating and non-rotating plates for comparison purpose. There is a scope for extension of the present work to other classes of piezo/pyroelectric crystals. The study will be useful in design and construction of gyroscope, rotation sensors, temperature sensors and other pyro/piezoelectric surface acoustic wave (SAW) devices.     

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave, also known as surface acoustic wave(SAW), solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth. Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation. A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates. It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius, confirming the existence of surface acoustic waves is irrelevant to coordinate system. On the other hand, the solutions can be treated as plane waves in regions far away from the source. Furthermore, the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.     

Investigation of the effect of the Coriolis force on a thin fluid film on a rotating disk

The effect of the Coriolis force on the evolution of a thin film of Newtonian fluid on a rotating disk is investigated. The thin-film approximation is made in which inertia terms in the Navier–Stokes equation are neglected. This requires that the thickness of the thin film be less than the thickness of the Ekman boundary layer in a rotating fluid of the same kinematic viscosity. A new first-order quasi-linear partial differential equation for the thickness of the thin film, which describes viscous, centrifugal and Coriolis-force effects, is derived. It extends an equation due to Emslie et al. [J. Appl. Phys. 29, 858 (1958)] which was obtained neglecting the Coriolis force. The problem is formulated as a Cauchy initial-value problem. As time increases the surface profile flattens and, if the initial profile is sufficiently negative, it develops a breaking wave. Numerical solutions of the new equation, obtained by integrating along its characteristic curves, are compared with analytical solutions of the equation of Emslie et al. to determine the effect of the Coriolis force on the surface flattening, the wave breaking and the streamlines when inertia terms are neglected.     

硅微机械谐振陀螺仪的非线性分析

给出了硅微机械谐振陀螺仪的结构,介绍了硅微机械谐振陀螺仪的工作原理,详细推导并给出了陀螺仪的输出频率和标度因数非线性的计算公式;基于影响谐振陀螺仪标度因数的参数,分析了由谐振器的振幅和梳齿静电驱动力引起的硅微机械谐振陀螺仪的非线性特性,给出了振动幅度与谐振频率关系的表达式.实验结果表明,陀螺仪的整体性能主要取决于谐振器振动幅度的稳定性.     

Investigation of flexural wave band gaps in a locally resonant metamaterial with plate-like resonators

This paper presents an investigation of flexural wave band gaps in locally resonant metamaterials (LRMs). An LRM is a periodic structure consisting of repeated unit cells containing a local resonator. Due to the local resonance occurring in the unit cell, the LRM induces a band gap (a frequency band in which no waves propagate). Discrete-like or beam-like resonators have generally been used to realise LRMs in previous research. By extending the beam-like resonator configuration, this paper studies LRMs with a plate-like resonator to exploit its advantages with respect to large design freedom. In order to understand flexural wave band gaps in an LRM with plate-like resonators, parametric studies are conducted with the development of a finite element model. Further, the influences of the plate-like resonator design parameters on flexural wave band gaps are investigated. Based on the parametric studies, the rules governing band gap properties are determined. Finally, tailoring flexural wave band gaps by adjusting the parameters is discussed.     

Non-contact boundary layer profiler using low-coherence self-referencing velocimetry

A spatially self-referencing velocimetry system based on low-coherence interferometry has been developed. The measurement technique is contactless and relies on the interference between back-reflected light from an arbitrary reference surface and seeding particles in the flow. The measurement location and the flow velocity are measured relative to the reference surface’s location and velocity, respectively. Scanning of the measurement location along the beam direction does not require mechanical movement of the sensor head. The reference surface (which can move or vibrate relative to the sensor head) can be either an external object or the surface of a body over which measurements are to be performed. The absolute spatial accuracy and the spatial resolution only depend on the coherence length of the light source (tens of microns for a superluminescent diode). The prototype is an all-fiber assembly. An optical fiber of arbitrary length connects the self-contained optical and electronics setup to the sensor head. Proof-of-principle measurements in water (Taylor–Couette flow) and in air (Blasius boundary layer) are reported in this paper.