Micro-mechanical stages with enhanced range

We present concepts and an optimization-based methodology for the design of micro-mechanical stages that have not only high precision but also an enhanced range. Joint-free distributed compliant designs provide high precision and easy manufacturability at macro and micro scales. The range of motion is enhanced by using displacement-amplifying compliant mechanisms (DaCMs). The main issue addressed in this paper is how to retain the decoupling between the X and Y motions in the stage when it is equipped with DaCMs. The natural frequency of the stage is also not compromised in enhancing the range. The optimized design has 2.5 times more range than the designs reported in the literature. Furthermore, the sensitivity improved by a factor of two when the stage is optimized for an accelerometer.

A Nearly Exact Reformulation of the Girsanov Linearization for Stochastically Driven Nonlinear Oscillators

The Girsanov linearization method (GLM), proposed earlier in Saha, N., and Roy, D., 2007, ``The Girsanov Linearisation Method for Stochastically Driven Nonlinear Oscillators,'' J. Appl. Mech., 74, pp. 885-897, is reformulated to arrive at a nearly exact, semianalytical, weak and explicit scheme for nonlinear mechanical oscillators under additive stochastic excitations. At the heart of the reformulated linearization is a temporally localized rejection sampling strategy that, combined with a resampling scheme, enables selecting from and appropriately modifying an ensemble of locally linearized trajectories while weakly applying the Girsanov correction (the Radon-Nikodym derivative) for the linearization errors. The semianalyticity is due to an explicit linearization of the nonlinear drift terms and it plays a crucial role in keeping the Radon-Nikodym derivative ``nearly bounded'' above by the inverse of the linearization time step (which means that only a subset of linearized trajectories with low, yet finite, probability exceeds this bound). Drift linearization is conveniently accomplished via the first few (lower order) terms in the associated stochastic (Ito) Taylor expansion to exclude (multiple) stochastic integrals from the numerical treatment. Similarly, the Radon-Nikodym derivative, which is a strictly positive, exponential (super-) martingale, is converted to a canonical form and evaluated over each time step without directly computing the stochastic integrals appearing in its argument. Through their numeric implementations for a few low-dimensional nonlinear oscillators, the proposed variants of the scheme, presently referred to as the Girsanov corrected linearization method (GCLM), are shown to exhibit remarkably higher numerical accuracy over a much larger range of the time step size than is possible with the local drift-linearization schemes on their own.

Extended Kalman filters using explicit and derivative-free local linearizations

We propose three variants of the extended Kalman filter (EKF) especially suited for parameter estimations in mechanical oscillators under Gaussian white noises. These filters are based on three versions of explicit and derivative-free local linearizations (DLL) of the non-linear drift terms in the governing stochastic differential equations (SDE-s). Besides a basic linearization of the non-linear drift functions via one-term replacements, linearizations using replacements through explicit Euler and Newmark expansions are also attempted in order to ensure higher closeness of true solutions with the linearized ones. Thus, unlike the conventional EKF, the proposed filters do not need computing derivatives (tangent matrices) at any stage. The measurements are synthetically generated by corrupting with noise the numerical solutions of the SDE-s through implicit versions of these linearizations. In order to demonstrate the effectiveness and accuracy of the proposed methods vis-à-vis the conventional EKF, numerical illustrations are provided for a few single degree-of-freedom (DOF) oscillators and a three-DOF shear frame with constant parameters.

A finite element analysis of dynamic fracture initiation by ductile failure mechanisms in a 4340 steel

In some recent dropweight impact experiments [5] with pre-notched bend specimens of 4340 steel, it was observed that considerable crack tunneling occurred in the interior of the specimen prior to gross fracture initiation on the free surfaces. The final failure of the side ligaments happened because of shear lip formation. The tunneled region is characterized by a flat, fibrous fracture surface. In this paper, the experiments of [5] (corresponding to 5 m/s impact speed) are analyzed using a plane strain, dynamic finite element procedure. The Gurson constitutive model that accounts for the ductile failure mechanisms of micro-void nucleation, growth and coalescence is employed. The time at which incipient failure was observed near the notch tip in this computation, and the value of the dynamic J-integral, J d, at this time, compare reasonably well with experiments. This investigation shows that J-controlled stress and deformation fields are established near the notch tip whenever J d , increases with time. Also, it is found that the evolution of micro-mechanical quantities near the notch root can be correlated with the time variation of J d .The strain rate and the adiabatic temperature rise experienced at the notch root are examined. Finally, spatial variations of stresses and deformations are analyzed in detail.

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are Investigated.

Two-Stage Extended Kalman Filters with Derivative-Free Local Linearizations

This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts. DOI: 10.1061/(ASCE)EM.1943-7889.0000255. (C) 2011 American Society of Civil Engineers.

Weakly corrected numerical solutions to stochastically driven nonlinear dynamical systems

A method to weakly correct the solutions of stochastically driven nonlinear dynamical systems, herein numerically approximated through the Eule-Maruyama (EM) time-marching map, is proposed. An essential feature of the method is a change of measures that aims at rendering the EM-approximated solution measurable with respect to the filtration generated by an appropriately defined error process. Using Ito's formula and adopting a Monte Carlo (MC) setup, it is shown that the correction term may be additively applied to the realizations of the numerically integrated trajectories. Numerical evidence, presently gathered via applications of the proposed method to a few nonlinear mechanical oscillators and a semi-discrete form of a 1-D Burger's equation, lends credence to the remarkably improved numerical accuracy of the corrected solutions even with relatively large time step sizes. (C) 2015 Elsevier Inc. All rights reserved.

Microstructural evolution and mechanical properties of Mg composites containing nano-B4C hybridized micro-Ti particulates

In this work, the microstructural evolution and mechanical properties of extruded Mg composites containing micro-Ti particulates hybridized with varying contents of nano-B4C are investigated, and compared with Mg-5.6Ti. Microstructural characterization showed the presence of uniformly distributed micro-Ti particles embedded with nano-B4C particulates that resulted in significant grain refinement. Electron back scattered diffraction (EBSD) analyses of Mg-(5.6Ti + x-B4C)(BM) hybrid composites showed that the addition of hybridized particle resulted in relatively more recrystallized grains, realignment of basal planes and extension of weak basal fibre texture when compared to Mg-5.6Ti. The evaluation of mechanical properties indicated improved strength with ductility retention in Mg-(5.6Ti + x-B4C)(BM) hybrid composites. When compared to Mg-5.6Ti, the superior strength properties of the Mg-(5.6Ti + xB(4)C)(BM) hybrid composites are attributed to the presence of nano-reinforcements, the uniform distribution of the hybridized particles, better interfacial bonding between the matrix and the reinforcement particles and the matrix grain refinement achieved by nano-B4C addition. The ductility enhancement obtained in hybrid composites can be attributed to the fibre texture spread and favourable basal plane orientation achieved due to nano B4C addition. (C) 2013 Elsevier B.V. All rights reserved.

Magnetic field induced tailoring of mechanical behavior of fluid filled micro porous carbon nanotube foam

Compressive loading of the carbon nanotube (CNT) has attracted much attention due to its entangled cellular like structure (CNT foam). This report investigates the mechanical behavior of magnetorheological fluid impregnated micro porous CNT foam that has not been realized before at this scale. Compressive behavior of CNT foam is found to greatly depend on the variation in both fluid viscosity as well as magnetic field intensity. Moreover, maximum achieved stress and energy absorption in CNT foam followed a power law behavior with the magnetic field intensity. Magnetic field induced movement of both CNT and iron oxide particles along the field direction is shown to dominate compressive behavior of CNT foam over highly attractive van der Waals forces between individual CNT. Therefore, this study demonstrates a method for tailoring the mechanical behavior of the fluid impregnated CNT foam. (C) 2014 AIP Publishing LLC.

Modelling, Design and Analysis of Low Frequency Platform for Attenuating Micro-Vibration in Spacecraft

One of the most important factors that affect the pointing of precision payloads and devices in space platforms is the vibration generated due to static and dynamic unbalanced forces of rotary equipments placed in the neighborhood of payload. Generally, such disturbances are of low amplitude, less than 1 kHz, and are termed as ‘micro-vibrations’. Due to low damping in the space structure, these vibrations have long decay time and they degrade the performance of payload. This paper addresses the design, modeling and analysis of a low frequency space frame platform for passive and active attenuation of micro-vibrations. This flexible platform has been designed to act as a mount for devices like reaction wheels, and consists of four folded continuous beams arranged in three dimensions. Frequency and response analysis have been carried out by varying the number of folds, and thickness of vertical beam. Results show that lower frequencies can be achieved by increasing the number of folds and by decreasing the thickness of the blade. In addition, active vibration control is studied by incorporating piezoelectric actuators and sensors in the dynamic model. It is shown using simulation that a control strategy using optimal control is effective for vibration suppression under a wide variety of loading conditions.

Effect Of Electroslag Refining On Microstructure And Mechanical-Properties Of Is-7670 Alloy

The electroslag refining technique is one of the modern tools which is capable of imparting superior mechanical and chemical properties to metals and alloys. Refining usually results in the elimination of a number of casting or solidification defects, such as shrinkage porosity, gas porosity, pipe, micro- and macro segregation. Remelting also imparts a directional grain structure apart from refining the size of the inclusions, grains and precipitates. This technique has over the years been used widely and successfully to improve the mechanical and chemical properties of steels and alloy steels which are used in the nuclear, missile, aerospace and marine industries for certain critical applications. But the application of ESR to aluminium and its alloys is only recent. This paper investigates the response of an aluminium alloy (corresponding to the Indian Specification IS: 7670) to ESR. Based on theoretical considerations and microstructural evidence it elucidates how ESR of aluminium alloys differs from that of ferrous alloys. The improvement achieved in mechanical properties of the alloy is correlated with the microstructure.

Ring Resonators and Micro Fluidics: Novel Design for Drug/Disease Detection

MEMS systems are technologically developed from integrated circuit industry to create miniature sensors and actuators. Originally these semiconductor processes and materials were used to build electrical and mechanical systems, but expanded to include biological, optical fluidic magnetic and other systems 12]. Here a novel approach is suggested where in two different fields are integrated via moems, micro fluidics and ring resonators. It is well known at any preliminary stage of disease onset, many physiological changes occur in the body fluids like saliva, blood, urine etc. The drawback till now was that current calibrations are not sensitive enough to detect the minor physiological changes. This is overcome using optical detector techniques 1]. The basic concepts of ring resonators, with slight variations can be used for optical detection of these minute disease markers. A well known fact of ring resonators is that a change in refractive index will trigger a shift in the resonant wavelength 5]. The trigger for the wavelength shift in the case discussed will be the presence of disease agents. To trap the disease agents specific antibody has to be used (e. g. BSA).