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.     

Simulation of thermoacoustic waves by a pressure-based algorithm for compressible flows

A modified SIMPLEC method which can solve compressible flows at low Mach number is introduced and used to study thermoacoustic waves induced by a rapid change of temperature at a solid wall and alternatingdirection flows generated by thermoacoustic effects in a tapered resonator.The results indicate that the algorithm adopted in this paper can be used for calculating compressible flows and thermoacoustic waves.It is found that the pressure and velocity in the resonator behave as standing waves,and the tapered resonator can suppress highfrequency harmonic waves as observed in a cylindrical resonator.     

Dynamic analysis of a novel wide-tunable microbeam resonator with a sliding free-of-charge electrode

In this paper, a MEMS-based resonator with a novel effective stiffness tunability is presented. The performance of the proposed resonator is based on the transversal vibration of the two porous cantilever microbeams with a rectangular microplate at the end of the structure. The microplate as a free-of-charge slider electrode is in contact with two other fixed substrate electrodes via the thin layer of dielectric material. Applying a constant DC voltage to the two fixed electrodes leads to the movement of free electrons in the slider and eventually to the formation of two series capacitors. As a result, the slider meets a nonlinear electrostatic force proportional to the square of the applied DC voltage. It will act as a nonlinear spring with a tunable stiffness during the oscillation of the resonator. The coupled nonlinear equations governing the longitudinal and transversal vibration of the resonator are extracted in the presence of the nonlinear voltage-sliding spring. Its steady-state solution is obtained based on a physically based learning method that makes it possible to obtain frequency response for the first harmony as well as for the higher harmonies and to predict primary and secondary resonances in different harmonies of the response. The effect of the applied tuning DC voltage, the geometrical parameters of the resonator, and the cantilever's porosity on the dynamic response of the resonator are investigated. It is shown that the tuning stiffness of this voltage-sliding spring provides a highly effective solution to realize an extreme tunable range. In the end, a modified tunable structure is introduced in which the folded beams are replaced with common ones. The modified resonator by making the nonlinear behavior of the resonator least can improve its performance significantly.

     

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。     

Reprogrammable logic-memory device of a mechanical resonator

From the viewpoint of application of nonlinear dynamics, we report multifunctional operation in a single microelectromechanical system (MEMS) resonator. This paper addresses a reprogrammable logic-memory device that uses a nonlinear MEMS resonator with multi-states. In order to develop the reprogrammable logic-memory device, we discuss the nonlinear dynamics of the MEMS resonator with and without control input as logic and memory operations. Through the experiments and numerical simulations, we realize the reprogrammable logic function that consists of OR/AND gate by adjusting the excitation amplitude and the memory function by storing logic information in the single nonlinear MEMS resonator.     

Coupled mode theory for acoustic resonators

We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator–waveguide systems. In higher than one dimension the method represents acoustic coupled mode theory in which the scattering solution within an open resonator is found in the form of expansion over the eigenmodes of the closed resonator decoupled from the waveguides. The problem of finding the transmission spectra is reduced to solving a set of linear equations with a non-Hermitian matrix whose anti-Hermitian term accounts for coupling between the resonator eigenmodes and the scattering channels of the waveguides. Numerical applications to acoustic two-, and three-dimensional resonator–waveguide problems are considered.     

Voltage–amplitude response of alternating current near half natural frequency electrostatically actuated MEMS resonators

This paper uses the Reduced Order Model (ROM) method to investigate the nonlinear-parametric dynamics of electrostatically actuated MEMS cantilever resonators under soft Alternating Current (AC) voltage of frequency near half natural frequency of the resonator. The voltage is between the resonator and a ground plate, and provides a nonlinear parametric actuation for the resonator. Fringe effect and damping forces are included. The resonator is modeled as an Euler–Bernoulli cantilever. Two methods of investigations are compared, Method of Multiple Scales (MMS), and Reduced Order Model. Moreover, the instabilities (bifurcation points) are predicted for both cases, when the voltage is swept up, and when the voltage is swept down. Although MMS and ROM are in good agreement for small amplitudes, MMS fails to accurately predict the behavior of the MEMS resonator for greater amplitudes. Only ROM captures the behavior of the system for large amplitudes. ROM convergence shows that five terms model accurately predicts the steady-states of the resonator for both small and large amplitudes.     

Nonlinear dynamic response of beam and its application in nanomechanical resonator

Nonlinear dynamic response of nanomechanical resonator is of very important characteristics in its application. Two categories of the tension-dominant and curvature-dominant nonlinearities are analyzed. The dynamic nonlinearity of four beam structures of nanomechanical resonator is quantitatively studied via a dimensional analysis approach. The dimensional analysis shows that for the nanomechanical resonator of tension-dominant nonlinearity, its dynamic nonlinearity decreases monotonically with increasing axial loading and increases monotonically with the increasing aspect ratio of length to thickness; the dynamic nonlinearity can only result in the hardening effects. However, for the nanomechanical resonator of the curvature-dominant nonlinearity, its dynamic nonlinearity is only dependent on axial loading. Compared with the tension-dominant nonlinearity, the curvature-dominant nonlinearity increases monotonically with increasing axial loading; its dynamic nonlinearity can result in both hardening and softening effects. The analysis on the dynamic nonlinearity can be very helpful to the tuning application of the nanomechanical resonator.     

Dynamics of a close-loop controlled MEMS resonator

The dynamics of a close-loop electrostatic MEMS resonator, proposed as a platform for ultra sensitive mass sensors, is investigated. The parameter space of the resonator actuation voltage is investigated to determine the optimal operating regions. Bifurcation diagrams of the resonator response are obtained at five different actuation voltage levels. The resonator exhibits bi-stability with two coexisting stable equilibrium points located inside a lower and an upper potential wells. Steady-state chaotic attractors develop inside each of the potential wells and around both wells. The optimal region in the parameter space for mass sensing purposes is determined. In that region, steady-state chaotic attractors develop and spend most of the time in the safe lower well while occasionally visiting the upper well. The robustness of the chaotic attractors in that region is demonstrated by studying their basins of attraction. Further, regions of large dynamic amplification are also identified in the parameter space. In these regions, the resonator can be used as an efficient long-stroke actuator.     

Effect of movability of the resonator center on the operation of a hemispherical resonator gyro

It was established in [2] that resonator deformation according to the second mode shape of a thin hemispherical shell results in a displacement of the center of mass if the resonator is unbalanced, i.e., if the distribution of mass over the surface of the hemisphere deviates from axial symmetry. In the same paper, it was shown that this displacement of the center of mass makes the instrument sensitive to linear vibrations. The present paper deals with linear vibration caused in the presence of unbalance by the working vibrations themselves and by the forces used to maintain the latter. The linear vibration is considered in the form of beam vibrations of the resonator stem. The study is aimed at determining the influence of the coupling between the working and beam vibrations on the instrument readings. We obtain a formula relating the hemispherical resonator gyro drift to the unbalance and the eccentricity, which, in particular, can be caused by the gravity component normal to the sensitivity axis. The drift considered here is essentially caused by the fact that deformation of the resonator supports also results in deformation of the electric control field in the gap between the electrodes. The resulting additional forces cause the effect studied in this paper. The drift magnitude depends on how the control of the phase state of the resonator is chosen. In what follows, to be definite, we consider the control in fast-time mode, i.e., at the natural vibration frequency. A similar effect takes place for any other type of control of waves in the resonator.     

Tuning linear and nonlinear characteristics of a resonator via nonlinear interaction with a secondary resonator

Nonlinear Dynamics - We conside the dynamics of a nonlinear resonator that is nonlinearly coupled to a linear resonator that has a relatively short decay time. In this case, the secondary (linear)...     

通流面积可变型消声器及其在管道噪声控制中的应用

对利用共振消声器进行管道噪声控制问题作了理论分析,讨论了通流面积可变型消声器的特性及在管道噪声消声控制中的应用问题,消声控制实验的消声量约38dB.     

Inertial amplified resonators for tunable metasurfaces

Meccanica - In this work, we propose an inertial amplified resonator (IAR) as a building block of a tunable locally resonant metasurface. The IAR consists in a mass–spring resonator coupled...     

Understanding of the flow behaviour on a Helmholtz resonator excited by grazing flow

In this study, a large eddy simulation of the three-dimensional shear flow over a flow-excited Helmholtz resonator has been implemented. The simulations have been performed over a wide range of flow speeds to analyse the effect of the inlet flow properties on the excitation condition. For validation proposes, the results obtained from the numerical simulations have been compared with published experimental data and show that numerical modelling provides an accurate representation of the pressure fluctuations inside the cavity. The main objective of this paper is to gain an understanding of the flow features over a flow-excited Helmholtz resonator. To this end, using the numerical model, the interaction of a turbulent boundary layer with a Helmholtz resonator has been considered, and the characteristics of the flow inside the resonator and over the orifice for various flow conditions are also analysed.     

Resonance Absorption of Gravity Waves

Fluid Dynamics - The problem of absorption by a resonator of a gravity wave that propagates on the surface of an incompressible fluid is solved. The resonator is small as compared with the...     

一种基于硅基波导的新型谐振式集成光学陀螺

介绍了一种基于单偏振波导环形谐振腔的新型集成光学陀螺及单偏振环形波导谐振腔的实现方法。其中单偏振光波导由SiO2衬底层、锗掺杂SiO2波导芯层和SiO2上包层组成,整个结构可用硅热氧化技术和PECVD技术生长在硅衬底上。用BPM(束传播法)对设计的单偏振环形谐振腔的传输特性进行仿真分析。结果表明,当入射光波长为1550nm时,此单偏振波导谐振腔对TM模式传输光的消光比是25dB/cm,而对TE模式传输光的传输损耗是0.05dB/cm,谐振腔的精细度可达到35。单偏振波导谐振腔的这些特点适于集成光学陀螺的应用要求,由其研制的集成光学陀螺的分辨率可达到16(°)/h。     

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.     

Dynamic analysis of a dielectric elastomer-based microbeam resonator with large vibration amplitude

A non-linear vibration equation with the consideration of large amplitude, gas damping and excitation is developed to investigate the dynamic performance of a dielectric elastomer (DE)-based microbeam resonator. Approximate analytical solution for the vibration equation is obtained by applying parameterized perturbation method (PPM) and introducing a detuning variable. The analysis exhibits that active tuning of the resonant frequency of the resonator can be achieved through changing an applied electrical voltage. It is observed that increasing amplitude will increase the natural frequency while it will decrease the quality factor of the resonator. In addition, it is found that the initial pre-stretching stress and the ambient pressure can significantly alter the resonant frequency of the resonator. The analysis is envisaged to provide qualitative predictions and guidelines for design and application of DE-based micro resonators with large vibration amplitude.     

Field analysis and complex resonance frequency of the quasi-TE0,1,1-mode in an inhomogeneously filled resonator with losses

The object of the present investigation is the determination of the field intensity and the resonance frequency of the quasi-TE_0,1,1-mode (with rotational symmetry) in an inhomogeneously filled resonator. The resonator is filled with a number of concentrically located tubes consisting of different materials, which may be lossy. The top and the bottom walls of the resonator are electrically perfectly conducting; at the side wall an impedance boundary condition is employed. Numerical results for a case of practical interest in magnetic resonance experiments are obtained.     

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.