Wenjing Ye

Optimal shape design of an electrostatic comb drive in microelectromechanical systems

Polynomial driving-force comb drives are synthesized using numerical simulation. The electrode shapes are obtained using the indirect boundary element method. Variable-gap comb drives that produce combinations of linear, quadratic, and cubic driving-force profiles are synthesized. This inverse problem is solved by an optimization procedure. Sensitivity analysis is carried out by the direct differentiation approach (DDA) in order to compute design sensitivity coefficients (DSCs) of force profiles with respect to parameters that define the shapes of the fingers of a comb drive. The DSCs are then used to drive iterative optimization procedures. Designs of variable-gap comb drives with linear, quadratic, and cubic driving force profiles are presented in this paper.

On the squeeze-film damping of micro-resonators in the free-molecule regime

Predicting air damping of micromachined mechanical resonators is crucial in the design of high Q devices for various applications. In the past, most of the work focused on devices in which the rarefaction effects of air are not significant. For such cases, continuum theory with suitable boundary conditions (either non-slip or slip) is often adequate. In this work, we investigate the air damping on oscillating structures in the free-molecule regime in which classical continuum theory is no longer valid. Such a study is important for devices operated at a very low pressure or for those whose characteristic length is of the nanometer scale. First, a careful examination of the related previous theoretical studies has been conducted. Mistakes and limitations have been found and reported in this paper. Next, a molecular dynamics simulation code has been developed and used in predicting quality factors of an oscillating microbeam operated at low pressures. Simulation results have shown an excellent agreement with experimental data. Finally, we investigate the effects of the Stokes number and the gap to oscillation amplitude ratio on the energy dissipation and quality factor of the microbeam.

Recent Advances and Emerging Applications of the Boundary Element Method

Sponsored by the U.S. National Science Foundation, a workshop on the boundary element method (BEM) was held on the campus of the University of Akron during September 1–3, 2010 (NSF, 2010, “Workshop on the Emerging Applications and Future Directions of the Boundary Element Method,” University of Akron, Ohio, September 1–3). This paper was prepared after this workshop by the organizers and participants based on the presentations and discussions at the workshop. The paper aims to review the major research achievements in the last decade, the current status, and the future directions of the BEM in the next decade. The review starts with a brief introduction to the BEM. Then, new developments in Greens functions, symmetric Galerkin formulations, boundary meshfree methods, and variationally based BEM formulations are reviewed. Next, fast solution methods for efficiently solving the BEM systems of equations, namely, the fast multipole method, the pre-corrected fast Fourier transformation method, and the adaptive cross approximation method are presented. Emerging applications of the BEM in solving microelectromechanical systems, composites, functionally graded materials, fracture mechanics, acoustic, elastic and electromagnetic waves, time-domain problems, and coupled methods are reviewed. Finally, future directions of the BEM as envisioned by the authors for the next five to ten years are discussed. This paper is intended for students, researchers, and engineers who are new in BEM research and wish to have an overview of the field. Technical details of the BEM and related approaches discussed in the review can be found in the Reference section with more than 400 papers cited in this review.

Theoretical and Numerical Studies of Noncontinuum Gas-Phase Heat Conduction in Micro/Nano Devices

This article presents a comprehensive study of various modeling techniques for noncontinuum gas-phase heat conduction encountered in micro/nano devices over a broad range of Knudsen number. A new slip model is proposed for slip flows and an analytical approach is developed for collisionless steady-state heat conduction inside a fully diffuse enclosure. Excellent agreements with direct simulation Monte Carlo (DSMC) simulations have been achieved for both of them. For problems in the transition regime and/or with partially thermal accommodated walls, the DSMC method is employed. Some noncontinuum phenomena such as the steady gas flows induced by the nonuniform temperature field are observed.

A low-power resonant micromachined compass

This paper describes a micromachined magnetic field sensor based on magnetic resonant structures. A micromechanical resonator fabricated using surface micromachining techniques is modified so as to incorporate a magnetic material. The shift of the fundamental mechanical resonant frequency of the device, caused by the interaction of the external magnetic field and the magnetic component of the resonant system, is used to determine the amplitude or the direction of the external field. We have designed, fabricated and tested two types of micromachined magnetic field sensors relying on the proposed principle of operation. The fabrication of the sensors follows CMOS-compatible and low temperature processes based on surface micromachining. Devices have been fabricated which exhibit a minimum resolution of 45° at 30 µT or less, at an excitation voltage of 10 V, demonstrating their utility as a magnetic compass. The power consumed to actuate the resonator is on the order of 20 nW. A theoretical model of the magnetic field sensor was developed using vibration analysis and nonlinear deflection theory. Good agreement was observed between the predicted and observed behavior of the compass.

Elimination of rigid body modes from discretized boundary integral equations

Abstract Free rigid body modes in Neumann problems are typically eliminated by suitably restraining the body. An alternative approach, here called “regularization”, involves first computing the singular stiffness matrix and then suitably modifying it using ideas from linear algebra. This idea has been suggested by Verchery (1990) for symmetric matrices. This paper is concerned with regularization of nonsymmetric stiffness matrices that arise from the boundary element method (BEM) for linear elasticity. Existence and uniqueness issues, as well as properties of the displacement field, for elasticity problems with tractions prescribed at every point on the boundary, are discussed in this paper.

The impact of subcontinuum gas conduction on topography measurement sensitivity using heated atomic force microscope cantilevers

Nanometer-scale topographical imaging using heated atomic force microscope (AFM) cantilevers, referred to here as thermal sensing AFM (TSAFM), is a promising technology for high resolution topographical imaging of nanostructured surfaces. Heated AFM cantilevers were developed for high-density data storage, where the heated cantilever tip can form and detect 20 nm indents made in a thermoplastic polymer. The scan height of the cantilever heater platform is typically near 500 nm, but could be made much smaller to improve reading sensitivity. Under atmospheric conditions the continuum models used in previous studies to model the gas phase heat transfer are invalid for the smallest operating heights. The present study uses a molecular model of subcontinuum heat transfer coupled with a finite difference simulation to predict the behavior of a TSAFM system. A direct simulation Monte Carlo model and a kinetic theory based macromodel are separately developed and used to model subcontinuum gas conduction. For the ...

Octant flux splitting information preservation DSMC method for thermally driven flows

We present the octant flux splitting DSMC method as an efficient method for simulating non-equilibrium flows of rarefied gas, particularly those arising from thermal loading. We discuss the current state-of-the-art flux splitting IP-DSMC technique and show that it fails to capture the shear stresses created by thermal gradients. We present the development of the octant flux splitting IP-DSMC as well as degenerate 2D, 1D, and 0D forms and apply the method to a number of problems including thermal transpiration, with satisfactory results.

Complex variable formulations for usual and hypersingular integral equations for potential problems : with applications to corners and cracks

This paper first presents an unified discussion of real and complex boundary integral equations (BIEs) for two-dimensional potential problems. Relationships between real and complex formulations, for both usual and hypersingular BIEs, are discussed. Potential problems in bounded as well as in unbounded domains are of concern in this work. Quantities of particular interest are derivatives of the primary field that exhibit discontinuities across corners, as well as stress intensity factors at the tips of mode III cracks. The latter problem in an application of a recent generalization of the well-known Plemelj-Sokhotsky formulae. Numerical implementations and results for interior problems in bounded domains, as well as for crack problems in unbounded domains, are presented and discussed.

Numerical Simulation of Effective Phase Velocity and Attenuation of Shear Elastic Wave Propagation in Unidirectional Composite Materials

In this paper, a simple simulation approach is presented for calculating the effective phase velocity and attenuation coefficient of elastic shear waves propagating in composite materials with randomly distributed unidirectional inclusions. As an application of the developed numerical approach, the phase velocities and attenuation coefficients of the coherent waves in four different types of composite material are simulated for various incident frequencies up to π. Numerical results are compared with theoretical predictions obtained from three representative theoretical models. While all theoretical results agree very well with numerical values at low incident frequencies, the discrepancies increase with the increased incident frequency and volume fraction of inclusions. It has been found that within the frequency and volume fraction ranges considered in this work, the generalized self-consistent model by Kanaun and Levin [18] seems to provide the most accurate estimations.