Modeling the CO 2

This paper presents an investigation of the density-driven problem that rises during the CO2 sequestration into saline aquifer. The lattice Boltzmann method (LBM) is implemented in a way to solve this mixing problem (the brine problem along with the solute transport). The CO2-brine interface was located at the top of the considered domain. Different Rayleigh numbers were used in order to investigate this problem. When Rayleigh number is low, we got steady-state concentration contours describing a Rayleigh-Bénard type of convection. Moreover, when the Rayleigh number was selected to be big enough, we observe that the system is less stable and a convective fingering is initiated. This instability is caused by a higher density difference between the brine and the sequestrated CO2. Note here that the turbulence is not taken into account in the study. After the onset this convective instability, the brine with a high CO2 concentration migrates down into the porous medium. This study is based on a statistical LBM theory without assuming periodicity in any directions and without considering any type of disturbances in order to turnon the instability behavior

Stability analysis of periodic orbits in a class of duffing-like piecewise linear vibrators

In this paper, we study the dynamical behavior of a Duffing-like piecewise linear (PWL) springmass-damper system for vibration-based energy harvesting applications. First, we present a continuous time single degree of freedom PWL dynamical model of the system. From this PWL model, numerical simulations are carried out by computing frequency response and bifurcation diagram under a deterministic harmonic excitation for different sets of system parameter values. Stability analysis is performed using Floquet theory combined with Fillipov method.Postprint (published version

A hybrid piezoelectric–electromagnetic nonlinear vibration energy harvester excited by fluid flow

Energy harvesting mechanisms can be used to extract energy from ambient surroundings to power small electronic devices, which has a significant advantage in realizing self-sustaining wireless devices. The proposed design of this study uses the internal fluid flow within a pipe and takes advantage of the fluid-structure interaction through flow-induced vibration of a bluff body. The hybrid harvester uses the vibration to convert electrical energy through a piezoelectric material and an electromagnetic oscillator that can be tuned to resonate at the oscillation frequency. A numerical solver was used to estimate harvestable voltage for this submerged hybrid energy harvester model by using ordinary differential equations. A computational study was used to optimize the performance of the bluff bodies under the influence of the vortices for circular, triangular, ellipse, and quadrilateral shapes. Wake development was seen in the circular and triangular shapes with the ellipse having the lowest turbulence kinetic energy among the shapes. Structural deflection of the beam under resonance was compared for the different shapes, which displayed better results for triangular and elliptical bluff bodies.This work is supported by International Research Collaboration Co-Funds (IRCC-2020-017) from Qatar University.Scopu

An Electrostatically Actuated MEMS Arch Band-Pass Filter

This work presents an investigation of the dynamics of micromachined arches resonators and their potential to be utilized as band-pass filters. The arches are actuated by a DC electrostatic load superimposed to an AC harmonic load. The dynamic response of the arch is studied analytically using a Galerkin-based reduced-order model when excited near its fundamental and third natural frequencies. Several simulation results are presented demonstrating interesting jumps and snap-through behavior of the arches and their attractive features for uses as band-pass filters, such as their sharp roll-off from pass bands to stop bands and their flat response

Free Vibration Characteristics of Rectangular Membranes Assuming Rounded-Edges Boundary

This study examines the vibratory characteristics of rectangular membranes having an outer rounded-edges periphery. This class of membranes with rounded outer corners has a great advantage over membranes with a rectangular platform wave propagation at the boundary being greatly diffused. As a result, such membranes have a great potential for use in practical engineering applications, especially in waveguides-based structures. Based on an effective 2D Differential-Quadrature numerical method, the frequencies and respective modeshapes of a rectangular membrane with rounded-edges are computed. This method is shown to yield better versatility, efficiency and less computational execution than other discretization methods. The simulated results, showing complex mode exchanges occurring for the higher order modes, demonstrate advantageous use for such membrane patterns in the design of tunable waveguides

Analysis of the lateral vibrations of an unbalanced Jeffcott rotor

This paper examines experimentally and analytically the lateral vibrations of a Jeffcott rotor running at various unbalance states. Using a Bently Nevada RK-4 rotor kit, three states of eccentric mass unbalance were assumed in this study: 0.4g, 0.8g and 1.2g. Measurements of the startup data and the steady state data at rigid and flexible rotor condition were collected using a setup that mimics the vibration monitoring industrial practices. Lagrange method was assumed to construct a linear mathematical model of the investigated rotor, based on rigid rotor assumptions, that can predict analytically the lateral vibrations. The dynamic characteristics of the system, including the linearized bearing induced stiffness, were solely extracted from startup data. It was concluded that the developed twodegrees- of-freedom model was able to predict the lateral vibration at the rigid condition with an error around 5%. Whereas it failed to predict the response at flexible condition with matching accuracy. Unlike the majority of the work done in this field where complex, nonlinear mathematical model were used to model real systems, this work validates the applicability of using simple mathematical models in predicting the response of a real rotorsystem with an acceptable accuracy

Comprehensive Analytical Approximations of the Pull-In Characteristics of an Electrostatically Actuated Nanobeam under the Influences of Intermolecular Forces

In this paper, analytical closed-form expressions to accurately estimate the pull-in characteristics of an electrostatically-actuated doubly-clamped nanobeam are derived and examined. In this regard, a coupled electro-mechanical problem for the nano-actuator is first presented assuming a single mode approximation while taking into account all the possible structural, electrical and nanoscale effects: the fringing of the electrical actuating force, the geometric mid-plane stretching and intermolecular (van der Walls and Casimir) forces. The complicated nonlinear resultant equations are numerically approximated in order to derive the closed-form expressions for the important nano-actuator pull-in characteristics: i.e., the detachment length, the minimum reachable gap size before the collapse and the respective pull-in voltage. The resulting closed-form expressions are first quantitatively validated with other previously published results, and comparisons showed an acceptable agreement. Unlike the reported expressions in the literature, the proposed closed-form expressions in this work are proper approximations, fairly accurate and, more importantly, provide a quick estimate of the critical design pull-in parameters of the nano-actuator. In addition, the analysis of these expressions demonstrated that the consideration of the intermolecular forces together with the fringe effect tends to significantly reduce the threshold pull-in voltage, whereas the mid-plane stretching parameter tends to the contrary to increase the voltage at the pull-in collapse. The derived expressions of these analytical/approximate solutions could hopefully be appropriately used by NEMS engineers as simple/quick procedures for successful design and fabrication of electrostatically-actuated nano-devices

Modeling the Structural-Thermal-Electrical Coupling in an Electrostatically Actuated MEMS Switch and Its Impact on the Switch Stability

Modeling and analysis for the static behavior and collapse instabilities of a MEMS cantilever switch subjected to both electrical and thermal loadings are presented. The thermal loading forces can be as a result of a huge amount of switching contact of the microswitch. The model considers the microbeam as a continuous medium and the electric force as a nonlinear function of displacement and accounts for its fringing-field effect. The electric force is assumed to be distributed over specific lengths underneath the microbeam. A boundary-value solver is used to study the collapse instability, which brings the microbeam from its unstuck configuration to touch the substrate and gets stuck in the so-called pinned configuration. We have found negligible influence of the temperature on the static stability of the switch. We then investigate the effect of the thermal heating due to the current flow on the cantilever switch while it is in the on position (adhered position). We also found slight effect on the static stability of the switch

Proceedings of IMECE2008

ABSTRACT We present modeling and analysis for the static behavior and collapse instabilities of doubly-clamped and cantilever microbeams subjected to capillary forces. These forces can be as a result of a volume of liquid trapped underneath the microbeam during the rinsing and drying process in fabrication. The model considers the microbeam as a continuous medium, the capillary force as a nonlinear function of displacement, and accounts for the mid-plane stretching nonlinearity. The capillary force is assumed to be distributed over a specific length underneath the microbeam. The Galerkin procedure is used to derive a reduced-order model consisting of a set of nonlinear algebraic and differential equations that describe the microbeams static and dynamic behaviors. We study the collapse instability, which brings the microbeam from its unstuck configuration to touch the substrate and gets stuck in the so-called pinned configuration. We calculate the pull-in length that distinguishes the free from the pinned configurations as a function of the beam thickness and gap width for both microbeams. Comparisons are made with analytical results reported in the literature based on the Ritz method for linear and nonlinear beam models. The instability problem, which brings the microbeam from a pinned to adhered configuration is also investigated. For this case, we use a shooting technique to solve the boundary-value problem governing the deflection of the microbeams. The critical microbeam length for this second instability is also calculated