MEMS Huygens Clock Based on Synchronized Micromechanical Resonators

With the continuous miniaturization of electronic devices,microelectromechanical system(MEMS)oscillators that can be combined with integrated circuits have attracted increasing attention.This study reports a MEMS Huygens clock based on the synchronization principle,comprising two synchronized MEMS oscillators and a frequency compensation system.The MEMS Huygens clock improved shorttime stability,improving the Allan deviation by a factor of 3.73 from 19.3 to 5.17 ppb at 1 s.A frequency compensation system based on the MEMS oscillator’s temperature-frequency characteristics was developed to compensate for the frequency shift of the MEMS Huygens clock by controlling the resonator current.This effectively improved the long-term stability of the oscillator,with the Allan deviation improving by 1.6343105 times to 30.9 ppt at 6000 s.The power consumption for compensating both oscillators simultaneously is only 2.85 mW·℃^(-1).Our comprehensive solution scheme provides a novel and precise engineering solution for achieving high-precision MEMS oscillators and extends synchronization applications in MEMS.

NONLINEAR STOCHASTIC DYNAMICS: A SURVEY OF RECENT DEVELOPMENTS

This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and nonlinear stochastic control. Topics for future research are also suggested.

The collision efficiency of spherical dioctyl phthalate aerosol particles in the Brownian coagulation

The collision efficiency in the Brownian coagulation is investigated. A new mechanical model of collision between two identical spherical particles is proposed, and a set of corresponding collision equations is established. The equations are solved numerically, thereby obtaining the collision efficiency for the monodisperse dioctyl phthalate spherical aerosols with diameters ranging from 100 to 760 nm in the presence of van der Waals force and the elastic deformation force. The calculated collision efficiency, in agreement with the experimental data qualitatively, decreases with the increase of particle diameter except a small peak appearing in the particles with a diameter of 510 nm. The results show that the interparticle elastic deformation force cannot be neglected in the computation of particle Brownian coagulation. Finally, a set of new expressions relating collision efficiency to particle diameter is established.

Stochastic response of fractional-order van der Pol oscillator

We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Ito equation is deduced. We obtained the Fokker–Planck–Kolmogorov equation connected to the averaged Ito equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.

Effect of Diffusively Shaped Holes on the Turbulent Flow Field of a Film Cooling Plate

The gas turbine blades with diffusion film cooling holes are newlydeveloped blade struc- tures in the hydrogen combustion gas turbine,which has an extremely high inlet gas temperature (1700 deg. C). TheFluid Machinery Laboratory of Nagoya Institute o Technology conductedfirstly a new research o the turbulent flow field over the gasturbine blade with diffusion film cooling holes in Japan. Normal-typeand X-ray hot wires were applied in the measurement of the flowfield.

Exact solution and transient behavior for torsional vibration of functionally graded finite hollow cylinders

Exact solutions are obtained for transient torsio- nal responses of a finitely long, functionally graded hollow cylinder under three different end conditions, i.e. free-free, free-fixed and fixed-fixed. The cylinder with its external surface fixed is subjected to a dynamic shearing stress at the internal surface. The material properties are assumed to vary in the radial direction in a power law form, while keep invariant in the axial direction. With expansion in the axial direction in terms of trigonometric series, the governing equations for the unknown functions about the radial coordinate r and time t are deduced. By applying the variable substitution technique, the superposition method and the separation of variables consecutively, series-form solutions of the equations are obtained. Natural frequencies and the transient torsional responses are finally discussed for a functionally graded finite hollow cylinder.

A THEORETICAL SOLUTION OF CYLINDRICALLY ISOTROPIC CYLINDRICAL TUBE FOR AXISYMMETRIC PLANE STRAIN DYNAMIC THERMOELASTIC PROBLEM

A dynamic thermoelastic solution of a cylindrically isotropiccylindrical tube or solid cylinder with axisymmetric planedeformations is developed. Since there exist thermal boundaryconditions and trac- tions on the two surfaces of a cylindrical tube,the problem under consideration is with inhomogeneous bound- aryconditions. Therefore we introduce a special function to transformthe inhomogeneous boundary conditions to homogeneous ones for anunknown function. They by using the method of separation ofvariables, the un- known function can be expressed as themultiplication series of Bessel functions and unknown time functions.

A Forced System of Two Cylinders with Various Spacings

The spectrum characteristics and wake structures for a circular cylinder oscillating in a wake are investigated by use of the currently modified virtual boundary method. A forced system of two cylinders with a small spacing (the downstream one is made to oscillate in the transverse direction) is studied and interesting flow characteristics are observed. A vortex switch and the change of vortex modes (between 2S mode and 2P mode) are observed in the “lock in' region. Vortex bands are formed and lost with the increasing excitation frequency. Information concerning saddle points in the flow field is obtained for different excitation frequencies. For a forced system of two cylinders with a large spacing, the upstream cylinder sheds vortexes because there is no downstream cylinder oscillating in the wake. No distinct “lock in' response is found for the downstream cylinder.

Effect of Coagulation and Diffusion on Nanoparticle Distribution in a Fully Developed Turbulent Boundary Layer

Nanoparticle distributions in a fully developed turbulent boundary layer are simulated numerically using the moment method.The effects of Schmidt number and Damk(o)hler number on the nanoparticle distribution are studied.It is found that the particle number concentration and total particle mass increase from the wall to the outside.The difference of particle number concentration and total particle mass near the wall and near the outside becomes smaller with the increasing Schmidt number Sc.The particle diameter and geometric standard deviation increase from the wall to the outside at a fixed Damk(o)hler number Da,and grow with the increase of Da at the same lateral position.

FIRST-PASSAGE TIME OF QUASI-NON-INTEGRABLE-HAMILTONIAN SYSTEM

Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary order. An example is studied in detail and some numerical results are given to illustrate the above procedure.

Exact solution of free vibration of adjacent buildings interconnected by visco-elastic dampers

With consideration of a high-rise coupled building system,a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system.The general motion equation for the two beams interconnected by multiple viscous/visco-elastic dampers is rewritten into a non-dimensional form to identify the minimal set of parameters governing the dynamic characteristics.The corresponding exact solution suitable for arbitrary boundary conditions is presented.Furthermore,the methodology for computing the coefficients of the modal shape function is proposed.As an example,the explicit expression of the modal shape function is derived,provided only one damper is adopted to connect the adjacent buildings.Finally,to validate the proposed methodologies,three case studies are performed,in which the existence of the overdamping and the optimal damping coefficient are revealed.In the case of using one damper in connecting two similar buildings,the estimating equations for the first modal damping ratio are formulated.

Research on nucleation and coagulation of nanoparticles in parallel twin jets

The large eddy simulation method has been used to simulate the diffusion of H2SO4 vapor in the parallel twin jets. The distributions of number concentration and size of nanoparticles produced by nucleation and coagulation in sulfuric acid/water system are given. The functions of the sulfur content, relative humidity and jet Reynolds number are evaluated according to the distributions of number concentration and size of nanoparticles. The results show that the nucleation in sulfuric acid/water system produces large number of nanoparticles , and gas-to-nanoparticle conversion mostly takes place in the middle and interface of the twin jets. The coagulation process of particles reduces the number concentration, while increases the mean particle size. For the case with higher sulfur content, more number and smaller size nanoparticles are produced by nucleation and coagulation. There is also a larger number of nanoparticles for the cases with higher relative humidity and jet Reynolds number.

Stabilization of an abutment under a rigidly fixed bridge by holographical-speckle interferometry

Objective: There are no detailed reports of three-dimensional measurement of abutment teeth in mastication, because it is knotty to observe the rotation in chewing directly, and inexact to estimate indirectly. This work studies the three-dimensional stability of rigidly fixed bridge under the stresses of distributed loads and concentrated loads by optical method that gives the tip angle and rotation angle calculated directly based on measurement data. Methods: The specimen, taken from a 25-year-old male, was a left mandible without the second premolars and the first molars. As abutments, first premolar and second molar have complete periodontium. The specimen was soaked in formaldehyde solution. The bridge was fixed between two abutment teeth (first premolars and second molars), and the mandible was cemented in a steel box. The load was increased from 0 kg to 23 kg. Laser holographic technique was used to measure the three-dimensional bit shift of the dens, both buccolingual bit shift and mesiodistal bit shift, and determine tip angle and rotation angle. Results: The effects of stress distribution on the rigidly fixed bridge were evaluated, and stabilization of the bridge under the stresses of distributed loads and concentrated loads, respectively, were analyzed. The results showed that the tips of two abutments were very similar, and no distinct difference was observed between the distributed load and the concentrated load. However, the maximum rotation angle for the distributed load was two to four times as large as that for the concentrated load. In the experiment, the tip angle of the abutment teeth was no more than 0.65 degree, and the rotation angle was no more than 0.60 degree. All maximum angles occurred in the second molar. Conclusion: The fixed bridge is considered to be safe. In addition, a method for measuring the rotation angle was provided effectively.

Motion and orientation of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio

Lattice Boltzmann method was used to numerically investigate the motion and orientation distribution of cylindrical and cubic particles in pipe flow with high concentration and high particle to pipe size ratio. The transient impulse model of 3D collisions between particles and between particle and wall is proposed. The numerical results are qualitatively in agreement with and quantitatively comparable to the experiment data. The results show that the increases of both the cylindrical particle to pipe size ratio and the particle aspect ratio decrease the rotation about all axes. All rotations of cubic particles decrease with increasing the particle concentration. The cubic particles, rotating more drastically in the flow with large Reynolds number, rotate faster than the cylindrical particles with the same size. The cylindrical particles align with the flow direction more obviously with decreasing Reynolds numbers. However, the orientations of cubic particles are spread all over the range with no significant difference in magnitude, and the Reynolds numbers have no obvious effect on the orientations of cubic particles.

FORMATION AND EVOLUTION OF THE STREAMWISE VORTICES IN MIXING LAYERS

The evolution of the three-dimensional time-developing mixing layer was simulated numerically using the pseudo-spectral method. The initial perturbations consisted of the two-dimensional fundamental wave and the streamwise-invariant three-dimensional disturbance. A comparison of the formations of the streamwise vortices with different amplitude functions for three-dimensional disturbances was made. In one case the results are similar to that of Rogers and Moser (1992), whereas a different way in which the quadrupole forms and sudden expansion of the rib were observed in another case. The simulation also confirms that stretching by the forming roller rather than Rayleigh centrifugal instability is responsible for the formation of the rib. Finally, numerical flow visualization results were presented. (Edited author abstract) 9 Refs.

STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WITH ACTUATOR SATURATION

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First,a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged It stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle,respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control effciency.

Evaluation of an Asymmetric Bistable System for Signal Detection under Levy Stable Noise

We evaluate the performance of a typical asymmetric bistable system for detecting aperiodic signal under Levy stable noise.A Grünwald-Letnikov implicit finite difference method is employed to solve the fractional FokkerPlanck equation numerically.The noise-induced stochastic resonance(SR)and the parameter-induced SR both exist in the asymmetric bistable systems.The increase of the skewness parameterγmay deteriorate the system performance.However,by tuning the system parameters,the effects of asymmetry on the system performance can be reduced.

Effect of Surface Roughness and Reynolds Number on Self-Similarity of Velocity Profile in the Atmospheric Boundary Layer

Self-similarity of power law velocity profile of a simulated atmospheric boundary layer is studied experimentally. The results demonstrate that the self-similarity maintains very well along the streamwise direction for the same rough surface but changes significantly with the surface roughness at the same position. The self-similarity of the vertical velocity profiles is affected by enhancement of the free stream velocity when the roughness concentration is relatively denser.

ELASTODYNAMIC SOLUTION OF A NON-HOMOGENEOUS ORTHOTROPIC HOLLOW CYLINDER

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure.

A THEORETICAL SOLUTION OF CYLINDRICAL SHELLS FOR AXISYMMETRIC PLAIN STRAIN ELASTODYNAMIC PROBLEMS

A method is developed for the transient responses of axisymmetric plain strain problems of cylindrical shells subjected to dynamic loads. Firstly, a special Junction was introduced to transform the inhomogeneous boundary conditions into the homogeneous ones. Secondly, using the method of separation of variables, the quantity that the displacement subtracts the special function was expanded as the multiplication series of Bassel functions and time functions. Then by virtue of the orthogonal properties of Bessel Junctions, the equation With respect to the time variable was derived, of which the solution is easily obtained. The displacement solution was finally obtained by adding the two parts mentioned above. The present method can avoid the integral transform and is fit for arbitrary loads. Numerical results are presented for internally shocked isotropic and cylindrically isotropic cylindrical shells and externally shocked cylinders, as well as for an externally shocked, cylindrically isotropic cylindrical shell that is fixed at the internal surface.