Modal Interactions in Resonant Microscanners

The fast response of micromirrors and their ability to achieve large scanning angles and low wavelength sensitivity, has made them an appealing substitute for traditional scanning and display technologies. To achieve large rotation angles, while minimizing the voltage requirements, the microscanner is excited at its resonance frequency and then used to steer a light beam along a surface. In this work, we develop a comprehensive model of a torsional microscanner. Based on the eigenvalue problem, we reduce the model to a 2-DOF lumped-mass model that captures the significant dynamics of the microscanner. We use the method of multiple scales to derive an approximate analytical solution of the microscanner response to combined DC and resonant AC voltage excitation. We examined the characteristics of the solution and found that, for a range of DC voltage, a two-to-one internal resonance occurs between the first two modes. Therefore, the energy fed to the first (torsional) mode may be channeled to the second (bending) mode causing an undesirable steady-state response. This phenomenon results in significant degradation in the microscanner performance, therefore, the designer needs to identify it, design around it, or control it.

Friction Induced Brake Vibrations at Low Speeds: Experiments, State-Space Reconstruction and Implications on Modeling

Today, low frequency disc-brake noises are commonly explained as self-sustained stick-slip oscillations. Although, at a first glance this explanation seems reasonable, there are indices that cast doubt on it. For instance, the basic frequency of the observed oscillations does not scale with the disc-speed as it is with stick-slip oscillations and the classical model does not explain the observed ending of the vibrations beyond a certain speed. Indeed, our experimental studies on groaning noises reveal two different vibration patterns: stick-slip vibrations at almost vanishing relative speed and a second, differing vibration pattern at low to moderate relative speeds. Yet, these two patterns produce a very similar acoustic impression. While the experiment provides a vast amount of data, the dimension and structure of the underlying oscillation is not known a priori – hence, constructing phenomenological minimal models usually must rely on assumptions, e.g. about the number of DOF, etc. Due to noise and complexity, the measured raw data did only allow for a first straight forward insight, rendering further analysis necessary. Hence, time-delay embedding methods together with a principle component analysis were used to reconstruct a pseudo-phase space together with the embedded attractor to analyse for the system's dimension and to separate signal from noise.

Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

Impact Properties of Syntactic Foams and Effect of Microballoon Wall Thickness

Hollow particle (microballoon) filled polymeric composites, called syntactic foams, are tested for impact properties in the present work. Izod type pendulum impact testing is carried out on eight types of foams, which are made of four types of microballoons used in volume fractions of 0.5 and 0.6. Variation in the volume fraction of microballoons leads to a difference in the total energy absorbed during fracture of different types of foams. Results show that syntactic foams containing microballoons of lower density show lower impact strength because of the lower strength of these microballoons. An increase in microballoon volume fraction leads to decreased energy absorption and strength.

Constitutive Gradients and Pore Tolerance in Two Weldments

The mechanical constitutive behavior of welded components is difficult to characterize at any size scale, but particularly challenging in the case of sub-millimeter welds such as produced by laser welding. Recently emerging digital image correlation (DIC) techniques provide a means for extracting local constitutive response. The tensile stress-strain response of laser welded austenitic 304L is evaluated in the present study. Weld fusion zones were found to have slightly higher yield strengths than the corresponding basemetal, and retained significant ductility (~45%). In this ductile, flaw tolerant stainless steel, the local weld ductility was essentially unaffected by the presence of weld-root porosity which was induced only by pulsed laser welding. In contrast, in a parallel study on the local constitutive properties of a welded Ni-Gd-Mo-Gd alloy with much less macroscopic ductility, the presence of weld root porosity was found to localize strain only in the vicinity of the largest pores, causing premature failure at low macroscopic strains.

Dynamic Stability of a Base-Excited Thin Beam With Top Mass

This paper deals with a base-excited clamped-clamped vertical thin beam carrying a top mass. The thin beam is considered to be inextensible and initially not perfectly straight. Based on Taylor series expansions of the inextensibility constraint and the exact curvature, and by using one or more basis functions, a semi-analytical model is derived. This model is numerically validated through a comparison with quasi-static and modal analysis results obtained using finite element modelling. The steady-state nonlinear dynamics of the base-excited beam are investigated using numerical continuation of periodic solutions and bifurcations. Using these numerical tools, the dynamic stability of the beam is investigated for various parameter settings, including the effect of nonlinear damping. The continuation of bifurcations appears to be very suitable to determine whether or not parametric resonance occurs for certain parameter settings.

Static and Dynamic Techniques for Residual Stress Measurements in Microelectromechanical Systems

A major concern in the development of microelectromechanical systems (MEMS) is the presence of residual stress. Residual stress, which is produced during the fabrication of multi-layer thin-film structures, can significantly affect the performance of microscale devices. Though experimental measurement techniques are accurate, actual stress measurements can vary dramatically from run to run and wafer to wafer. For this reason, modeling of this stress is a challenging task. Past work has focused on experimental, static techniques for determining residual stress levels in single-layer and bi-layer structures. In this effort, two different experimental techniques are used for determining residual stress levels in four-layer piezoelectrically driven cantilever and clamped-clamped structures. One of the techniques is based on wafer bow measurements, and the other technique is a dynamic technique that is based on parameter identification from nonlinear frequency-response data. The devices studied, which consist of a piezoelectric layer or lead zirconate titanate (PZT) layer, are fabricated with varying lengths, widths, and material layer thickness. The results obtained from the static and dynamic techniques are compared and discussed.

Novel Friction Test Structures for Microelectromechanical Systems

Novel friction test structures that are suitable for determining the friction coefficient of vertical surfaces in microelectromechanical systems (MEMS) devices are fabricated and used to carry out friction measurements on smooth and rough deep reactive ion etched (DRIE) silicon surfaces. The results obtained for rough surfaces show that the friction coefficient decreases as the sliding contact is put through the first eight to ten cycles, before it reaches a steady-state value that closely matches the friction coefficient of the smooth surface.

Characterization of Defect Nucleation and Propagation in Fe2O3+FCC-Al Nanocomposites During Uniaxial Tensile and Compressive Deformations

The objective of this research is to analyze uniaxial tensile and compressive mechanical deformations of α-Fe2O3 + fcc Al nanoceramic-metal composites using classical molecular dynamics (MD). Specifically, variations in the nucleation and the propagation of defects (such as dislocations and stacking faults etc.) with variation in the nanocomposite phase morphology and their effect on observed tensile and compressive strengths of the nanocomposites are analyzed. For this purpose, a classical molecular dynamics (MD) potential that includes an embedded atom method (EAM) cluster functional, a Morse type pair function, and a second order electrostatic interaction function is developed, see Tomar and Zhou (2004) and Tomar and Zhou (2006b). The nanocrystalline structures (nanocrystalline Al, nanocrystalline Fe2O3 and the nanocomposites with 40% and 60% Al by volume) with average grain sizes of 3.9 nm, 4.7 nm, and 7.2 nm are generated using a combination of the well established Voronoi tessellation method with the Inverse Monte-Carlo method to conform to prescribed log-normal grain size distributions. For comparison purposes, nanocrystalline structures with a specific average grain size have the same grain morphologies and the same grain orientation distribution. MD simulations are performed at the room temperature (300 K). Calculations show that the deformation mechanism is affected by a combination of factors including the fraction of grain boundary (GB) atoms and the electrostatic forces between atoms. The significance of each factor is dependent on the volume fractions of the Al and Fe2O3 phases. Depending on the relative orientations of the two phases at an interface, the contribution of the interface to the defect formation varies. The interfaces have stronger effect in structures with smaller average grain sizes than in structures with larger average grain sizes.

Modeling of Eddy Current Damper Composed of Spherical Magnet and Conducting Shell

If a conducting plate moves through a nonuniform magnetic field, eddy currents are induced in the conducting plate. The eddy currents produce a magnetic force of drag, known as Fleming's left-hand rule. This rule means that a magnetic field perpendicular to the direction of movement generates a magnetic damping force. We have fabricated the eddy current damper composed of the spherical magnet and the conducting shell. The spherical magnet produces the axisymmetric magnetic field, and the shape of the conducting shell appears to combine a semispherical shell conductor and a cylinder conductor. When the eddy current damper works, the conducting shell is fixed in space, and the spherical magnet moves under the conducting shell. In this case, since there are magnetic flux densities perpendicular to the direction of movement, eddy currents flow inside the conducting shell, and then a magnetic force is produced. The reaction force of this magnetic force acts on the spherical magnet. In our study, eddy current dampers composed of a magnet and a conducting plate have been modeled using infinitesimal loop coils. As a result, magnetic damping forces are obtained. Our modeling has three merits as follows: the equation of a magnetic damping force is simple in the equation, we can use the static magnetic field obtained using FEM, the Biot-Savart law or experiments and the equation automatically satisfies boundary conditions using infinitesimal loop coils. In this study, we explain simply the principle of this method, and model an eddy current damper composed of a spherical magnet and a conducting shell. The analytical results of the modeling agree well with the experimental results.