Stability and Bifurcation Bahaviour of Electrostatic Torsional NEMS Varactor Influenced by Dispersion Forces

The influences of Casimir and van der Waals forces on the nano-electromechanical systems (NEMS) electrostatic torsional varactor are studied. A one degree of freedom, the torsional angle, is adopted, and the bifurcation behaviour of the NEMS torsional varactor is investigated. There are two bifurcation points, one of which is a Hopf bifurcation point and the other is an unstable saddle point. The phase portraits are also drawn, in which periodic orbits are around the Hopf bifurcation point, but the periodic orbit will break into a homoclinic orbit when meeting the unstable saddle point.

Stability and bifurcation behaviour of electrostatic torsional NEMS varactor influenced by dispersion forces

The influences of Casimir and van der Waals forces on the nano-electromechanical systems (NEMS) electrostatic torsional varactor are studied. A one degree of freedom, the torsional angle, is adopted, and the bifurcation behaviour of the NEMS torsional varactor is investigated. There are two bifurcation points, one of which is a Hopf bifurcation point and the other is an unstable saddle point. The phase portraits are also drawn, in which periodic orbits are around the Hopf bifurcation point, but the periodic orbit will break into a homoclinic orbit when meeting the unstable saddle point.

Similarity consideration of structural bifurcation buckling

Many structural bifurcation buckling problems exhibit a scaling or power law property. Dimensional analysis is used to analyze the general scaling property. The concept of a new dimensionless number, the response number-Rn, suggested by the present author for the dynamic plastic response and failure of beams, plates and so on, subjected to large dynamic loading, is generalized in this paper to study the elastic, plastic, dynamic elastic as well as dynamic plastic buckling problems of columns, plates as well as shells. Structural bifurcation buckling can be considered when Rn(n) reaches a critical value.

A New Designed Two-Dimensional Bifurcation Parallel-Plate Flow Chamber

解决平行平板流槽每次实验只能观测壁面培养细胞受一种剪应力作用的问题。作者在平行平板流槽的基础上,首次提出了一种改进后的流槽--二维平板分叉流槽。通过数值模拟,给出了流体作定常流动时,流速和壁面剪应力的分布。结果发现,利用这种二维平板分叉流槽可以研究壁面培养的细胞在不同大小剪应力作用下的力学行为。该研究结果为流槽的合理设计和使用,并分析剪应力空间分布对内皮细胞的影响有重要实际意义。

Two bifurcation transitions of the floating half zone convection in a fat liquid bridge of larger Pr

The transient process of the thermocapillary convection was obtained for the large Pu floating half zone by using the method of three-dimensional and unsteady numerical simulation. The convection transits directly from steady and axisymmetric state to oscillatory flow for slender liquid bridge, and transits first from steady and axisymmetric convection to the steady and non-axisymmetric convection, then, secondly to the oscillatory convection for the fatter liquid bridge. This result implies that the volume of liquid bridge is not only a sensitive critical parameter for the onset of oscillation, but also relates to the new mechanism for the onset of instability in the floating half zone convection even in case of large Prandtl number fluid.

Dynamic Stability of Electrostatic Torsional Actuators with van Der Waals Effect

electrostatic torsional nano-electro-mechanical systems (NEMS) actuators is analyzed in the paper. The dependence of the critical tilting angle and voltage is investigated on the sizes of structure with the consideration of vdW effects. The pull-in phenomenon without the electrostatic torque is studied, and a critical pull-in gap is derived. A dimensionless equation of motion is presented, and the qualitative analysis of it shows that the equilibrium points of the corresponding autonomous system include center points, stable focus points, and unstable saddle points. The Hopf bifurcation points and fork bifurcation points also exist in the system. The phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, as well as homoclinic orbits.

Refractive index and thickness analysis of natural silicon dioxide film growing on silicon with variable-angle spectroscopic ellipsometry

The refractive index and thickness of SiO2 thin films naturally grown on Si substrates were determined simultaneously within the wavelength range of 220-1100 nm with variable-angle spectroscopic ellipsometry. Different angles of incidence and wavelength ranges were chosen to enhance the analysis sensitivity for more accurate results. Several optical models describing the practical SiO2-Si system were investigated, and best results were obtained with the optical model, including an interface layer between SiO2 and Si, which proved the existence of the interface layer in this work as described in other publications.

Two Bifurcation Transition Processes in Floating Half Zone Convection of Larger Prandtl Number Fluid

Processes of the onset oscillation in the thermocapillaxy convection under the Earth's gravity are investigated by the numerical simulation and experiments in a floating half zone of large Prandtl number with different volume ratio. Both computational and experimental results show that the steady and axisymmetric convection turns to the oscillatory convection of m=1 for the slender liquid bridge, and to the oscillatory convection before a steady and 3D asymmetric state for the case of a fat liquid bridge. It implies that, there are two critical Marangoni numbers related, respectively, to these two bifurcation transitions for the fat liquid bridge. The computational results agree with the results of ground-based experiments.

Cellular Cell Bifurcation Of Cylindrical Detonations

Cellular cell pattern evolution of cylindrically-diverging detonations is numerically simulated successfully by solving two-dimensional Euler equations implemented with an improved two-step chemical kinetic model. From the simulation, three cell bifurcation modes are observed during the evolution and referred to as concave front focusing, kinked and wrinkled wave front instability, and self-merging of cellular cells. Numerical research demonstrates that the wave front expansion resulted from detonation front diverging plays a major role in the cellular cell bifurcation, which can disturb the nonlinearly self-sustained mechanism of detonations and finally lead to cell bifurcations.

Electromechanical influence of crack velocity at bifurcation for poled ferroelectric materials

The piezoelastodynamic field equations are solved to determine the crack velocity at bifurcation for poled ferroelectric materials where the applied electrical field and mechanical stress can be varied. The underlying physical mechanism, however, may not correspond to that assumed in the analytical model. Bifurcation has been related to the occurrence of a pair of maximum circumferential stress oriented symmetrically about the moving crack path. The velocity at which this behavior prevails has been referred to as the limiting crack speed. Unlike the classical approach, bifurcation will be identified with finite distances ahead of a moving crack. Nucleation of microcracks can thus be modelled in a single formulation. This can be accomplished by using the energy density function where fracture initiation is identified with dominance of dilatation in relation to distortion. Poled ferroelectric materials are selected for this study because the microstructure effects for this class of materials can be readily reflected by the elastic, piezoelectic and dielectric permittivity constants at the macroscopic scale. Existing test data could also shed light on the trend of the analytical predictions. Numerical results are thus computed for PZT-4 and compared with those for PZT-6B in an effort to show whether the branching behavior would be affected by the difference in the material microstructures. A range of crack bifurcation speed upsilon(b) is found for different r/a and E/sigma ratios. Here, r and a stand for the radial distance and half crack length, respectively, while E and a for the electric field and mechanical stress. For PZT-6B with upsilon(b) in the range 100-1700 m/s, the bifurcation angles varied from +/-6degrees to +/-39degrees. This corresponds to E/sigma of -0.072 to 0.024 V m/N. At the same distance r/a = 0.1, PZT-4 gives upsilon(b) values of 1100-2100 m/s; bifurcation angles of +/-15degrees to +/-49degrees; and E/sigma of -0.056 to 0.059 V m/N. In general, the bifurcation angles +/-theta(0) are found to decrease with decreasing crack velocity as the distance r/a is increased. Relatively speaking, the speed upsilon(b) and angles +/-theta(0) for PZT-4 are much greater than those for PZT-6B. This may be attributed to the high electromechanical coupling effect of PZT-4. Using upsilon(b)(0) as a base reference, an equality relation upsilon(b)(-) < upsilon(b)(0) < upsilon(b)(+) can be established. The superscripts -, 0 and + refer, respectively, to negative, zero and positive electric field. This is reminiscent of the enhancement and retardation of crack growth behavior due to change in poling direction. Bifurcation characteristics are found to be somewhat erratic when r/a approaches the range 10(-2)-10(-1) where the kinetic energy densities would fluctuate and then rise as the distance from the moving crack is increased. This is an artifact introduced by the far away condition of non-vanishing particle velocity. A finite kinetic energy density prevails at infinity unless it is made to vanish in the boundary value problem. Future works are recommended to further clarify the physical mechanism(s) associated with bifurcation by means of analysis and experiment. Damage at the microscopic level needs to be addressed since it has been known to affect the macrocrack speeds and bifurcation characteristics. (C) 2002 Published by Elsevier Science Ltd.

On the topological bifurcation of flows around a rotating circular cylinder

Flow fields around a rotating circular cylinder in a uniform stream are computed using a low dimensional Galerkin method. Results show that the formation of a Fopple vortex pair behind a stationary circular cylinder is caused by the structural instability in the vicinity of the saddle located at the rear of the cylinder. For rotating cylinder a bifurcation diagram with the consideration of two parameters, Reynolds number Re and rotation parameter a, is built by a kinematic analysis of the steady flow fields.

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220

Numerical analyses for the material bifurcation in plane sheet under tension

The various patterns (shear banding, surface wrinkling and necking) of material bifurcation in plane sheet under tension are investigated in this paper by means of a numerical method. It is found that numerical analysis can provide better ground for searching for the lowest critical loads. The inhomogeneity caused by void damage and the nonuniformity in the stress distribution across sheet thickness are proved to have detrimental effects on the material bifurcation. Nevertheless, material stability can be promoted by any means of depressing void damage or alleviating stress, even locally across the thickness. Besides, the peculiar behaviour of material bifurcation under slight biaxiality state is demonstrated. Copyright (C) 1996 Elsevier Science Ltd

Hopf bifurcation in wakes behind a rotating and translating circular cylinder

A low-dimensional Galerkin method, initiated by Noack and Eckelmann [Physica D 56, 151 (1992)], for the prediction of the flow field around a stationary two-dimensional circular cylinder in a uniform stream at low Reynolds number is generalized to the case of a rotating and translating cylinder. The Hopf bifurcation describing the transition from steady to time-periodic solution is investigated. A curve indicating the transitional boundary is given in the two-dimensional parameter plane of Reynolds number Re and rotating parameter alpha. Our results show that rotation may delay the onset of vortex street and decrease the vortex-shedding frequency. (C) 1996 American Institute of Physics.

Distribution, stability, bifurcations and catastrophe of steady rotation of a symmetrical heavy gyroscope with viscous-liquid-filled cavity

The number, the angles of orientation and the stability in Rumyantsev Movchan's sense of oblique steady rotations of a symmetric heavy gyroscope with a cavity completely filled with a uniform viscous liquid, possessing a fixed point 0 on its symmetric axis. are given for various values of the parameters. By taking the square of the upright component of the angular momentum M2 as a control parameter, three types of bifurcation diagrams of the steady rotations, two types of jumps and two kinds of local catastrophes, one being the symmetric reduced cusp type and the other being of the symmetric reduced butterfly type, are obtained. By taking account of the M2-damping owing to the moment of unavoidable faint friction, two different modes for the gyroscope, initially in a stable quasi-steady upright rotation with a nutation angle theta(s) equal to zero, to topple over are found.