Effect of Pressure on Fluid Damping in MEMS Torsional Resonators with Flow Ranging from Continuum to Molecular Regime

High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q ∝P ^–r , with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h ₀/L<0.01). As this ratio increases, the range of validity decreases.     

聚酯-聚酯多嵌段共聚物的合成及其动态力学性能

聚酯-聚醚多嵌段共聚物的动态力学性能谱上有两个T_8,不宜做阻尼材料。本文报道聚对苯二甲酸乙二醇酯(PET)-端羟基聚己二酸乙二醇酯(PEA)共聚物(简称嵌段共聚酯),比聚醚-聚酯多嵌段共聚物有更好的相容性。我们研究了PEA的分子量,间苯二甲酸的用量对嵌段共聚酯的结晶度,以及结晶度对嵌段共聚酯的动态力学性能的影响。     

Photovoltaic and spectral properties of tetraphenyloporphyrin and metallotetraphenyloporphyrin dyes

Spectroscopical properties and photocurrent (or photovoltage) of tetraphenyloporphyrins and metallotetraphenyloporphyrins in nematic liquid crystal have been studied. Photoelectric response has been measured in an electrochemical cell made of the semitransparent semiconducting and golden electrodes with porphyrin dyes embedded in liquid crystal. Fluorescence, time-resolved luminescence in microsecond time scale and photoacoustic spectra have also been measured. The competition between radiative, non-radiative processes and charge transfer is discussed. It has been shown that effectivity of porphyrins for photocurrent generation depends on the presence/absence of central metal in the macrocycle of porphyrin skeleton and the kind of metal. The schematic model of the contributions of the dye molecule and semiconducting electrode in the electron transfer process is shown.     

Decay rates of energy of the 1D damped original nonlinear wave equation

We consider the decay rate of energy of the 1D damped original nonlinear wave equation. We first construct a new energy function. Then, employing the perturbed energy method and the generalized Young’s inequality, we prove that, with a general growth assumption on the nonlinear damping force near the origin, the decay rate of energy is governed by a dissipative ordinary differential equation. This allows us to recover the classical exponential, polynomial, or logarithmic decay rate for the linear, polynomial or exponentially degenerating damping force near the origin, respectively. Unlike the linear wave equation, the exponential decay rate constant depends on the initial data, due to the nonlinearity.     

A bi-virus competing model with time-varying susceptibility and repeated infection

This paper introduces a bi-virus model with time-varying susceptibility. The model describes the case that there coexist two viruses and the time-varying susceptibility due to repeated infections. For different parameters, we investigate the stability of various equilibriums. Under appropriate conditions the two viruses show competitive relationship, that is, one virus will eventually become a pandemic, and the other virus will eventually disappear. For this case, we further study the dynamical behavior of virus transmission. The model shows some new phenomena, that is, the outbreak of the virus will be delayed appropriately, giving people an illusion. Finally, we present a numerical example to illustrate the effectiveness of the theoretical results.     

Integral conditions on the asymptotic stability for the damped linear oscillator with small damping

The equation is considered under the assumption . It is proved that is sufficient for the asymptotic stability of , and is best possible here. This will be a consequence of a general result on the intermittent damping, which means that is controlled only on a sequence of non-overlapping intervals.

     

Effect of surfactants on the stability of thin liquid film flow on a rotating disk

The effect of surfactants on surface instabilities of thin liquid film flow on a rotating disk was studied at different flow rates Q (0.5相似文献   

NFR (Natural Frequency Region) approach for dynamic evaluation of anti-vibration systems with rebound resilience method

There is no universal method to perform dynamic analysis on solid rubber anti-vibration systems. In this article, an equivalent damping ratio is introduced to account for rubber hysteresis using a resilience experiment. A new concept, NFR (Natural Frequency Region), is defined for dynamic evaluation based on natural characteristics of a rubber anti-vibration system itself. Two typical industrial products were selected to verify the proposed NFR approach. The verification procedure involves three parts: natural frequencies, harmonic spectra and impact responses. The dynamic responses from both simulation and experiment have been compared and have not only demonstrated that the proposed approach is reliable but that it could also be used to guide the design of rubber anti-vibration systems in industry. The key points for applying this approach are also presented through the verification procedure.     

Bounded invariant verification for time-delayed nonlinear networked dynamical systems

We present a technique for bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections. The underlying problem in precise bounded-time verification lies with computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. For large networks, computing this sensitivity with precision guarantees is challenging. We introduce the notion of input-to-state (IS) discrepancy of each module or subsystem in a larger nonlinear networked dynamical system. The IS discrepancy bounds the distance between two solutions or trajectories of a module in terms of their initial states and their inputs. Given the IS discrepancy functions of the modules, we show that it is possible to effectively construct a reduced (low dimensional) time-delayed dynamical system, such that the trajectory of this reduced model precisely bounds the distance between the trajectories of the complete network with changed initial states. Using the above results we develop a sound and relatively complete algorithm for bounded invariant verification of networked dynamical systems consisting of nonlinear modules interacting through possibly delayed signals. Finally, we introduce a local version of IS discrepancy and show that it is possible to compute them using only the Lipschitz constant and the Jacobian of the dynamic function of the modules.     

Immersed boundary method for unsteady kinetic model equations

Predicting unsteady flows and aerodynamic forces for large displacement motion of microstructures requires transient solution of Boltzmann equation with moving boundaries. For the inclusion of moving complex boundaries for these problems, three immersed boundary method flux formulations (interpolation, relaxation, and interrelaxation) are presented. These formulations are implemented in a 2‐D finite volume method solver for ellipsoidal‐statistical (ES)‐Bhatnagar‐Gross‐Krook (BGK) equations using unstructured meshes. For the verification, a transient analytical solution for free molecular 1‐D flow is derived, and results are compared with the immersed boundary (IB)‐ES‐BGK methods. In 2‐D, methods are verified with the conformal, non‐moving finite volume method, and it is shown that the interrelaxation flux formulation gives an error less than the interpolation and relaxation methods for a given mesh size. Furthermore, formulations applied to a thermally induced flow for a heated beam near a cold substrate show that interrelaxation formulation gives more accurate solution in terms of heat flux. As a 2‐D unsteady application, IB/ES‐BGK methods are used to determine flow properties and damping forces for impulsive motion of microbeam due to high inertial forces. IB/ES‐BGK methods are compared with Navier–Stokes solution at low Knudsen numbers, and it is shown that velocity slip in the transitional rarefied regime reduces the unsteady damping force. Copyright © 2015 John Wiley & Sons, Ltd.