VTechWorks Repository :: Browsing by Author "Cramer, Mark S."

Browsing by Author "Cramer, Mark S."

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Active vibration control of composite structures
Chang, Min-Yung (Virginia Tech, 1990-07-07)
The vibration control of composite beams and plates subjected to a travelling load is studied in this dissertation. By comparing the controlled as well as uncontrolled responses of classical and refined structural models, the influence of several important composite structure properties which are not included in the classical structural model is revealed. The modal control approach is employed to suppress the structural vibration. In modal control, the control is effected by controlling the modes of the system. The control law is obtained by using the optimal control theory. Comparison of two variants of the modal control approach, the coupled modal control (CMC) and independent modal-space control (IMSC), is made. The results are found to be in agreement with those obtained by previous investigators. The differences between the controlled responses as well as actuator outputs that are predicted by the classical and the refined structural models are outlined in this work. In conclusion, it is found that, when performing the structural analysis and control system design for a composite structure, the classical structural models (such as the Euler-Bernoulli beam and Kirchhoff plate) yield erroneous conclusions concerning the performance of the actual structural system. Furthermore, transverse shear deformation, anisotropy, damping, and the parameters associated with the travelling load are shown to have great influence on the controlled as well as uncontrolled responses of the composite structure.
Adaptive finite element simulation of incompressible viscous flow
Fithen, Robert Miller (Virginia Tech, 1993-08-05)
A finite element method is employed for solving two- and three-dimensional incompressible flows. The formulation is based on a segregated solution method. In this segregated formulation, the velocities and pressures are uncoupled and the equations for each are solved one after the other. This segregated solution method is numerically compared to the penalty method and to previous reported data to determine its validity. Next an iterative solution method which employs an element by - element data structure of the finite element method is developed. Two types of iterative methods are used. For a symmetric stiffness matrix, the conjugate gradient method is used. For an unsymmetric stiffness matrix, the bi-conjugate gradient method is used. Both iterative solution methods make use of a diagonal preconditioning method (Jacobi preconditioning). Several problems are solved using this segregated method. In two-dimensions, flow over a backward facing step and flow in a cavity are investigated. In three-dimensions, the problems include flow in a cavity at Reynolds number 100 and 1000, and flow in a curved duct. The simulation compares very well with previously reported data, where available.
Analysis of Instabilities in Microelectromechanical Systems, and of Local Water Slamming
Das, Kaushik (Virginia Tech, 2009-08-24)
Arch-shaped microelectromechanical systems (MEMS) have been used as mechanical memories, micro-sensors, micro-actuators, and micro-valves. A bi-stable structure, such as an arch, is characterized by a multivalued load deflection curve. Here we study the symmetry breaking, the snap-through instability, and the pull-in instability of bi-stable arch shaped MEMS under steady and transient electric loads. We analyze transient finite electroelastodynamic deformations of perfect electrically conducting clamped-clamped beams and arches suspended over a flat rigid semi-infinite perfect conductor. The coupled nonlinear partial differential equations (PDEs) for mechanical deformations are solved numerically by the finite element method (FEM) and those for the electrical problem by the boundary element method. The coupled nonlinear PDE governing transient deformations of the arch based on the Euler-Bernoulli beam theory is solved numerically using the Galerkin method, mode shapes for a beam as basis functions, and integrated numerically with respect to time. For the static problem, the displacement control and the pseudo-arc length continuation (PALC) methods are used to obtain the bifurcation curve of arch's deflection versus the electric potential. The displacement control method fails to compute arch's asymmetric deformations that are found by the PALC method. For the dynamic problem, two distinct mechanisms of the snap-through instability are found. It is shown that critical loads and geometric parameters for instabilities of an arch with and without the consideration of mechanical inertia effects are quite different. A phase diagram between a critical load parameter and the arch height is constructed to delineate different regions of instabilities. The local water slamming refers to the impact of a part of a ship hull on stationary water for a short duration during which high local pressures occur. We simulate slamming impact of rigid and deformable hull bottom panels by using the coupled Lagrangian and Eulerian formulation in the commercial FE software LS-DYNA. The Lagrangian formulation is used to describe planestrain deformations of the wedge and the Eulerian description of motion for deformations of the water. A penalty contact algorithm couples the wedge with the water surface. Damage and delamination induced, respectively, in a fiber reinforced composite panel and a sandwich composite panel and due to hydroelastic pressure are studied.
An analytical and experimental investigation of the response of elliptical composite cylinders
Meyers, Carol Ann (Virginia Tech, 1996)
An analytical and experimental investigation of the response of composite cylinders of elliptical cross-section to axial compression and internal pressure loadings is discussed. Nine eight-ply graphite-epoxy elliptical cylinders, three layups for each of three cross sectional aspect ratios, are specifically examined. The lay-ups studied are a quasi-isotropic (±45/0/90)_g, an axially-stiff (±45/0₂)_g, and a circumferentially-stiff (±45/90₂)_g. The elliptical cross sections studied are characterized by semi-minor axis (b) to semi-major axis (a) ratios of b/a = 0.70, 0.85, and 1.00 (circular). The cross sections are obtained by holding the semi-major axis constant for all cross sections, and only varying the semi-minor axis. The nominal semi-major axis for all specimens was 5.00 in. (127 mm), and all specimens were cut to the same length, which provided a length-to-radius ratio of 2.9 for the circular cylinders. For the elliptical cross section cylinders, the length to- radius ratios, L/R(s), ranged from two to slightly greater than six, where R(s) is the function describing the circumferential variation of the radius. A geometrically nonlinear special-purpose analysis, based on Donnell’s nonlinear shell equations, is developed to study the prebuckling responses of geometrically perfect cylinders. In this analysis the circumferentially-varying radius of curvature of the cylinder is expanded in a cosine series. While elliptical sections are studied here, it should be noted that such an expansion will accommodate any cross section with at least two axes of symmetry. The displacements are likewise expanded in a harmonic series using the Kantorovich method. The total potential energy, written in terms of the displacements, is then integrated over the circumferential coordinate. The variational process then yields the governing Euler-Lagrange equations and boundary conditions. This process has been automated using the symbolic manipulation package Mathematica ©. The resulting nonlinear ordinary differential equations are then integrated via the finite difference method. A geometrically nonlinear finite element analysis is also utilized to compare with the prebuckling solutions of the special-purpose analysis and to study the prebuckling and buckling responses of geometrically imperfect cylinders. The imperfect cylinder geometries are represented by an analytical approximation of the measured shape imperfections. An accompanying experimental program is carried out to provide a means for comparison between the real and theoretical systems using a test fixture specifically designed for the present investigation to allow for both axial compression and internal pressurization. A description of the test fixture is included. Three types of tests were run on each specimen: (1) low internal pressure with no axial end displacement, (2) low internal pressure with a low level compressive axial displacement and, (3) compressive axial displacement to failure, with no internal pressure. The experimental data from these tests are compared to predictions for both perfect and imperfect cylinder geometries. Prebuckling results are presented in the form of displacement and strain profiles for each of the three sets of load conditions. Buckling loads are also compared to predicted values based upon classical estimates as well as linear and nonlinear finite element results which include initial shape imperfections. Lastly, the postbuckling and failure characteristics observed during the tests are described.
Application of the vortex-lattice concept to flows with smooth- surface separation
Thrasher, David Fred (Virginia Polytechnic Institute and State University, 1984)
A nonlinear three-dimensional vortex-lattice method which treats the steady separated flow over prolate bodies with open separation moving through an inviscid incompressible fluid is developed. The strength and position of the body wake are found as part of the solution. Specifically, flows with smooth-surface separation are considered as opposed to flows with sharp-edge separation treated· with the vortex-lattice concept in the past. To demonstrate the technique, results for the flow over an inclinded ogive-cylinder are presented. In the case of attached flow, comparsions are presented of the results from the vortex-lattice method using optimal and average control point locations with the results of the source-distribution method and with experimental data. Significantly, the same panel arrangement is used in the calculations for both methods. The results demonstrate that the results of the present method is somewhat more sensitive to panel arrangement than are those of the source-distribution method. Also, the effect of control point location varies dramatically as the incidence of the body is changed. In the case of separated flow, comparsions of the results of the vortex-lattice method are made with experimental data and with the results of a typical two-dimensional analogy. The results demonstrate that the present method agrees most favorably with the experimental data windward of a separation line.
Arrival times for dissipative, nonlinear second-sound waves in solids
Tarkenton, G. M.; Cramer, Mark S. (American Physical Society, 1995-07-01)
We extend our original analysis begun in Tarkenton et al. [Phys. Rev. B 49, 11 794 (1994)] to include dissipative effects that are important in real cryogenic systems where nonlinear second sound exists. We present results concerning arrival times of thermal pulses propagated in cryogenic crystals, namely the behavior of the arrival times as a function of pulse amplitude. These arrival times show some surprising effects due to competing nonlinear terms: after decreasing with increasing amplitude, as one would expect, the arrival times start to lengthen due to nonlinear effects and finally saturate at a level slightly above the shortest arrival times. All these surprising effects arise from competing nonlinear terms in the expression for the wave speed. We finally relate these results to the experiment we proposed in our original paper.
Assessment of lateral and torsional stiffness characteristics of medium rise concrete buildings
Mirtaheri, Masoud (Virginia Polytechnic Institute and State University, 1982)
Little is known of the actual performance of existing buildings for normally Structural Engineers do not require that their structures be tested once they are built. The wide availability of computer programs to aid Structural Engineers in design and analysis is a great advantage over previous computational tools but the very precision of computer output can give the designer a false sense of accuracy. If buildings of the future are to be safe and efficient, then an assessment of the accuracy of current analytical procedures is required. This study used some of the few published measurements of the lateral and torsional dynamic characteristics of buildings to establish accurate analytical models of the structures. These measurements, for five different buildings, consisted of data on their fundamental mode shapes and natural frequencies. Initially, estimates of these characteristics were obtained by inputting traditional evaluations of the stiffness parameters for a TABS-77 program. In general, the traditional assumptions did not result in an adequate prediction when compared with the known experimental results. Improvements were made in the analytical models by incorporating "non-structural" elements or by reducing the efficiency of certain members until the fundamental mode shapes and frequencies were matched. Implications of incorrect modelling at the design stage were investigated for both static and dynamic lateral loadings. This study shows that it is necessary to match both frequencies and mode shapes if an accurate analytical model is desired. Failure to match mode shapes can seriously affect the evaluation of loads carried by the structural elements when the building is subjected to lateral loads. Internal partitions and cladding not only add stiffness to the structure but also change the mode shape. Strong evidence is provided that these nonstructural elements do carry load and do provide stiffness. This study shows that shear lag exists in shear wall elevator cores commonly occurring in buildings and this should not be neglected. Large panels buildings apparently have significant joint rotation between panels and this should be accommodated in some manner in developing an analytical model. Considerable inaccuracies have been shown to exist in present design and practice and this study provides guidance for significantly improving present analytical modelling.
Bat swarming as an inspiration for multi-agent systems: predation success, active sensing, and collision avoidance
Lin, Yuan (Virginia Tech, 2016-02-22)
Many species of bats primarily use echolocation, a type of active sensing wherein bats emit ultrasonic pulses and listen to echoes, for guidance and navigation. Swarms of such bats are a unique type of multi-agent systems that feature bats's echolocation and flight behaviors. In the work of this dissertation, we used bat swarming as an inspiration for multi-agent systems to study various topics which include predation success, active sensing, and collision avoidance. To investigate the predation success, we modeled a group of bats hunting a number of collectively behaving prey. The modeling results demonstrated the benefit of localized grouping of prey in avoiding predation by bats. In the topics regarding active sensing and collision avoidance, we studied individual behavior in swarms as bats could potentially benefit from information sharing while suffering from frequency jamming, i.e., bats having difficulty in distinguishing between self and peers's information. We conducted field experiments in a cave and found that individual bat increased biosonar output as swarm size increased. The experimental finding indicated that individual bat acquired more sensory information in larger swarms even though there could be frequency jamming risk. In a simulation wherein we modeled bats flying through a tunnel, we showed the increasing collision risk in larger swarms for bats either sharing information or flying independently. Thus, we hypothesized that individual bat increased pulse emissions for more sensory information for collision avoidance while possibly taking advantage of information sharing and coping with frequency jamming during swarming.
Boundary-layer analysis and measurement of Newtonian and non-Newtonian fluids
Kim, Byung Kyu (1984)
The velocity fields around a circular cylinder in a crossflow of drag-reducing polymeric solutions and water were experimentally investigated using a laser-Doppler velocimeter. Measured boundary-layer velocity profiles indicated that the flow parameter controlling the drag on a bluff body in drag-reducing flows is the turbulence intensity rather than the Reynolds number. For turbulence intensity less than 0.7% polymer addition induced delayed separation. For turbulence intensity over 1% the opposite effect was true. Time-averaged velocity profiles of water did not show any significant difference between self-induced and forced oscillatory flows. Heat, mass and momentum transfer of Newtonian and power-law non-Newtonian fluids were theoretically investigated using an implicit finite-difference scheme. The results clearly· indicated that shear-dependent non-Newtonian viscosity controls the entire transport processes of the power-law fluids. For the major portion of the boundary layer, it was found that the more shear thinning the material exhibits, the lower the skin friction and the higher the heat transfer result. Accounting for the motion of the stagnation point provided an improved prediction of heat transfer for Newtonian fluid.
Buckling and postbuckling of flat and curved laminated composite panels under thermomechanical loadings incorporating non-classical effects
Lin, Weiqing (Virginia Tech, 1997-04-05)
Two structural models which can be used to predict the buckling, post buckling and vibration behavior of flat and curved composite panels under thermomechanical loadings are developed in this work. Both models are based on higher-order transverse shear deformation theories of shallow shells that include the effects of geometric nonlinearities and initial geometric imperfections. Within the first model (Model I), the kinematic continuity at the contact surfaces between the contiguous layers and the free shear traction condition on the outer bounding surfaces are satisfied, whereas in the second model (Model II), in addition to these conditions, the static interlaminae continuity requirement is also fulfilled. Based on the two models, results which cover a variety of problems concerning the postbuckling behaviors of flat and curved composite panels are obtained and displayed. These problems include: i) buckling and postbuckling behavior of flat and curved laminated structures subjected to mechanical and thermal loadings; ii)frequency-load/temperature interaction in laminated structures in both pre-buckling and post buckling range; iii) the influence of a linear/nonlinear elastic foundation on static and dynamic post buckling behavior of flat/curved laminated structures exposed to mechanical and temperature fields; iv) implication of edge constraints upon the temperature/load carrying capacity and frequencyload/ temperature interaction of flat/curved structures; v) elaboration of a number of methodologies enabling one to attenuate the intensity of the snap-through buckling and even to suppress it as well as of appropriate ways enabling one to enhance the load/temperature carrying capacity of structures.
The Cellular Automata Paradigm for the Parallel Solution of HeatTransfer Problems
Lowekamp, Bruce B.; Watson, Layne T.; Cramer, Mark S. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1994-04-01)
This paper describes the numerical solution of heat transfer problems using cellular automata. While traditional methods offer high performance on uniprocessor machines, their performance is limited on distributed memory multiprocessors by communication bottlenecks caused by the interdependence of the equations. Using a cellular automata formulation, these bottlenecks can be avoided, and performance greater than that obtained by parallelizing traditional algorithms can be achieved. This paper gives an overview of the cellular automata paradigm and specific examples of solutions to a hyperbolic and a parabolic problem. The accuracy of the method is verified by comparisons of the results with analytical solutions and with results produced by other techniques.
Chaos in Pulsed Laminar Flow
Kumar, Pankaj (Virginia Tech, 2010-08-09)
Fluid mixing is a challenging problem in laminar flow systems. Chaotic advection can play an important role in enhancing mixing in such flow. In this thesis, different approaches are used to enhance fluid mixing in two laminar flow systems. In the first system, chaos is generated in a flow between two closely spaced parallel circular plates by pulsed operation of fluid extraction and reinjection through singularities in the domain. A singularity through which fluid is injected (or extracted) is called a source (or a sink). In a bounded domain, one source and one sink with equal strength operate together as a source-sink pair to conserve the fluid volume. Fluid flow between two closely spaced parallel plates is modeled as Hele-Shaw flow with the depth averaged velocity proportional to the gradient of the pressure. So, with the depth-averaged velocity, the flow between the parallel plates can effectively be modeled as two-dimensional potential flow. This thesis discusses pulsed source-sink systems with two source-sink pairs operating alternately to generate zig-zag trajectories of fluid particles in the domain. For reinjection purpose, fluid extracted through a sink-type singularity can either be relocated to a source-type one, or the same sink-type singularity can be activated as a source to reinject it without relocation. Relocation of fluid can be accomplished using either "first out first in" or "last out first in" scheme. Both relocation methods add delay to the pulse time of the system. This thesis analyzes mixing in pulsed source-sink systems both with and without fluid relocation. It is shown that a pulsed source-sink system with "first out first in" scheme generates comparatively complex fluid flow than pulsed source-sink systems with "last out first in" scheme. It is also shown that a pulsed source-sink system without fluid relocation can generate complex fluid flow. In the second system, mixing and transport is analyzed in a two-dimensional Stokes flow system. Appropriate periodic motions of three rods or periodic points in a two-dimensional flow are determined using the Thurston-Nielsen Classification Theorem (TNCT), which also predicts a lower bound on the complexity generated in the fluid flow. This thesis extends the TNCT -based framework by demonstrating that, in a perturbed system with no lower order fixed points, almost invariant sets are natural objects on which to apply the TNCT. In addition, a method is presented to compute line stretching by tracking appropriate motion of finite size rods. This method accounts for the effect of the rod size in computing the complexity generated in the fluid flow. The last section verifies the existence of almost invariant sets in a two-dimensional flow at finite Reynolds number. The almost invariant set structures move with appropriate periodic motion validating the application of the TNCT to predict a lower bound on the complexity generated in the fluid flow.
Characterization and deterioration detection of portland cement concrete using ultrasonic waves
Al-Akhras, Nabil M. (Virginia Tech, 1995-11-10)
An experimental study was conducted to characterize Portland cement concrete (PCC), to detect deterioration induced by freeze/thaw and alkali-silica reaction, and to detect chloride presence in PCC using ultrasonic waves. The experimental program was initiated to investigate the effect of water to cement (w/c) ratio, aggregate type, and air entrainn1ent on measured ultrasonic wave velocity and signal energy. Three w/c ratios (0.35, 0.45, and 0.55) were evaluated. Two aggregate types, quartzite and limestone, were included in the PCC mixes separately. Mixes were prepared as non-air entrained and air entrained. Thus, a total of twelve batches were prepared to evaluate PCC using ultrasonic waves at two frequencies, 54 and 340 kHz. The experimental program to investigate freeze/thaw (FT) damage included the effect of curing time, w/c ratio, and aggregate type. The effect of curing time was investigated by exposing PCC specimens cured for 3 and 7 days to FT. Two w/c ratios were considered, 0.45 and 0.55. The effect of aggregate on detecting FT damage was investigated using two types of crushed stone aggregate, quartzite and limestone. Alkali-silica reaction (ASR) damage was investigated uSIng two w/c ratios, 0.35 and 0.45. Embedded composite strain gages were used to monitor the ASR deleterious deterioration. High alkali cement and active silica aggregate were used to produce ASR.
Characterization of high temperature creep in siliconized silicon carbide using ultrasonic techniques
Buttram, Jonathan D. (Virginia Tech, 1990-04-04)
Ultrasonic velocity and attenuation were both measured on samples containing various degrees of damage due to high temperature creep. These results were compared with parameters associated with creep damage such as strain and cavity formation, in order to better understand the mechanisms of creep in Si/SiC and to determine if ultrasonics can be used in evaluating the severity of damage. The data indicated that both ultrasonic velocity and attenuation are directly related to creep strain and can be used in evaluating creep damage. Ultrasonic velocity was found to be exponentially related to creep strain. Cavity formation was found not to significantly affect either of the measured ultrasonic properties. The results indicated that Si/SiC behaves as a two phase material in that high frequency ultrasound propagates primarily through the silicon carbide phase and not by the silicon phase.
Characterizing Magnetic Particle Transport for Microfluidic Applications
Sinha, Ashok (Virginia Tech, 2008-09-25)
Magnetic particles with active functional groups offer numerous advantages for use in μ-TAS (Micro Total Analytical Systems). The functional site allows chemical binding of the particle with the target species in the fluid sample. Selection of the functional group establishes the target molecule and vice versa under assumptions of highly specific biding. The particles hence act as mobile reaction substrates with high surface to volume ratios owing to their small size. The concept of action at a distance allows their use as agents for separation in microchannels based on relatively simple design. It is possible to manipulate magnetic particles and bound target species using an externally applied magnetic field. Hence, the particles can be effectively separated from the flow of a carrier fluid. Magnetic fields create dipolar interactions causing the particles to form interesting structures and aggregates. Depending upon the applied field, the microstructure evolution of the aggregate is interesting in its own right, e.g. related to improvements in material properties and bottom-up self assembly. The shape of the aggregates can be determined a priori if the interaction between the particles is well characterized. The dominant competing forces that influence magnetic particle dynamics in a flow are magnetic and viscous. There are a number of physical parameters such as viscosity, magnetic susceptibility, fluid velocity, etc. which are varied to study their individual effects. Initially dilute suspensions are studied experimentally and numerically using a particle based dynamics approach. Once established, a force model for particle interaction is investigated for concentrated suspensions. A Lagrangian particle tracking algorithm that returns positions of the particles is used for this work that focuses on studying the dynamics of these particles. A mathematical model is proposed and investigated for functionalization between magnetic and non-magnetic particles. Having characterized the collection of magnetic particles, the effect of relative concentrations is investigated on the collection of the non-magnetic species.
Comprehensive Theory of Heat Transfer in Heterogeneous Materials
Vogl, Gregory William (Virginia Tech, 2003-01-06)
For over forty years, researchers have attempted to refine the Fourier heat equation to model heat transfer in engineering materials. The equation cannot accurately predict temperatures in some applications, such as during transients in microscale (< 10^-12 s) situations. However, even in situations where the time duration is relatively large, the Fourier heat equation might fail to predict observed non-Fourier behavior. Therefore, non-Fourier models must be created for certain engineering applications, in which accurate temperature modeling is necessary for design purposes. In this thesis, we use the Fourier heat equation to create a general non-Fourier, but diffusive, equation that governs the matrix temperature in a composite material. The composite is composed of a matrix with embedded particles. We let the composite materials be governed by Fourier's law and let the heat transfer between the matrix and particles be governed by contact conductance. After we make certain assumptions, we derive a general integro-differential equation governing the matrix temperature. We then non-dimensionalize the general equation and show that our model reduces to that used by other researchers under a special limit of a non-dimensional parameter. We formulate an initial-boundary-value problem in order to study the behavior of the general matrix temperature equation. We show that the thermalization time governs the transition of the general equation from its small-time limit to its large-time limit, which are both Fourier heat equations. We also conclude that our general model cannot accurately describe temperature changes in an experimental sand composite.
Compressible Lubrication Theory in Pressurized Gases
Chien, Ssu-Ying (Virginia Tech, 2019-04-08)
Lubrication theory plays a fundamental role in all mechanical design as well as applications to biomechanics. All machinery are composed of moving parts which must be protected against wear and damage. Without effective lubrication, maintenance cycles will be shortened to impractical levels resulting in increased costs and decreased reliability. The focus of the work presented here is on the lubrication of rotating machinery found in advanced power systems and designs involving micro-turbines. One of the earliest studies of lubrication is due to Osborne Reynolds in 1886 who recorded what is now regarded as the canonical equation governing all lubrication problems; this equation and its extensions have become known as the Reynolds equation. In the past century, Reynolds equation has been extended to include three-dimensional effects, unsteadiness, turbulence, variable material properties, non-newtonian fluids, multi-phase flows, wall slip, and thermal effects. The bulk of these studies have focused on highly viscous liquids, e.g., oils. In recent years there has been increasing interest in power systems using new working fluids, micro-turbines and non-fossil fuel heat sources. In many cases, the design of these systems employs the use of gases rather than liquids. The advantage of gases over liquids include the reduction of weight, the reduction of adverse effects due to fouling, and compatibility with power system working fluids. Most treatments of gas lubrication are based on the ideal, i.e., low pressure, gas theory and straightforward retro-fitting of the theory of liquid lubrication. However, the 21st Century has seen interest in gas lubrication at high pressures. At pressures and temperatures corresponding to the dense and supercritical gas regime, there is a strong dependence on gas properties and even singular behavior of fundamental transport properties. Simple extrapolations of the intuition and analyses of the ideal gas or liquid phase theory are no longer possible. The goal of this dissertation is to establish the correct form of the Reynolds equation valid for both low and high pressure gases and to explore the dynamics predicted by this new form of the Reynolds equation. The dissertation addresses five problems involving our new Reynolds equation. In the first, we establish the form appropriate for the simple benchmark problem of two-dimensional journal bearings. It is found that the material response is completely determined by a single thermodynamic parameter referred to as the "effective bulk modulus". The validity of our new Reynolds equation has been established using solutions to the full Navier-Stokes-Fourier equations. We have also provided analytical estimates for the range of validity of this Reynolds equation and provided a systematic derivation of the energy equation valid whenever the Reynolds equation holds. The next three problems considered here derive local and global results of interest in high speed lubrication studies. The results are based on a perturbation analysis of our Reynolds and energy equation resulting in simplified formulas and the explicit dependence of pressure, temperature, friction losses, load capacity, and heat transfer on the thermodynamic state and material properties. Our last problem examines high pressure gas lubrication in thrust bearings. We again derive the appropriate form of the Reynolds and energy equations for these intrinsically three-dimensional flows. A finite difference scheme is employed to solve the resultant (elliptic) Reynolds equation for both moderate and high-speed flows. This Reynolds equation is then solved using perturbation methods for high-speed flows. It is found that the flow structure is comprised of five boundary layer regions in addition to the main ``core'' region. The flow in two of these boundary layer regions is governed by a nonlinear heat equation and the flow in three of these boundary layers is governed by nonlinear relaxation equations. Finite difference schemes are employed to obtain detailed solutions in the boundary layers. A composite solution is developed which provides a single solution describing the flow in all six regions to the same accuracy as the individual solutions in their respective regions of validity. Overall, the key contributions are the establishment of the appropriate forms of the Reynolds equation for dense and supercritical flows, analytical solutions for quantities of practical interest, demonstrations of the roles played by various thermodynamic functions, the first detailed discussions of the physics of lubrication in dense and supercritical flows, and the discovery of boundary layer structures in flows associated with thrust bearings.
Computational Analysis of Elastic Moduli of Covalently Functionalized Carbon Nanomaterials, Infinitesimal Elastostatic Deformations of Doubly Curved Laminated Shells, and Curing of Laminates
Shah, Priyal (Virginia Tech, 2017-04-05)
We numerically analyze three mechanics problems described below. For each problem, the developed computational model is verified by comparing computed results for example problems with those available in the literature. Effective utilization of single wall carbon nanotubes (SWCNTs) and single layer graphene sheets (SLGSs) as reinforcements in nanocomposites requires their strong binding with the surrounding matrix. An effective technique to enhance this binding is to functionalize SWCNTs and SLGSs by covalent attachment of appropriate chemical groups. However, this damages their pristine structures that may degrade their mechanical properties. Here, we delineate using molecular mechanics simulations effects of covalent functionalization on elastic moduli of these nanomaterials. It is found that Young's modulus and the shear modulus of an SWCNT (SLGS), respectively, decrease by about 34% (73%) and 43% (42%) when 20% (10%) of carbon atoms are functionalized for each of the four functional groups of different polarities studied. A shell theory that gives results close to the solution of the corresponding 3-dimensional problem depends upon the shell geometry, applied loads, and initial and boundary conditions. Here, by using a third order shear and normal deformable theory and the finite element method (FEM), we delineate for a doubly curved shell deformed statically with general tractions and subjected to different boundary conditions effects of geometric parameters on in-plane and transverse stretching and bending deformations. These results should help designers decide when to consider effects of these deformation modes for doubly curved shells. Composite laminates are usually fabricated by curing resin pre-impregnated fiber layers in an autoclave under prescribed temperature and pressure cycles. A challenge is to reduce residual stresses developed during this process and simultaneously minimize the cure cycle time. Here, we use the FEM and a genetic algorithm to find the optimal cycle parameters. It is found that in comparison to the manufacturer's recommended cycle, for a laminate with the span/thickness of 12.5, one optimal cycle reduces residual stresses by 47% and the total cure time from 5 to 4 hours, and another reduces the total cure time to 2 hours and residual stresses by 8%.
Coupled Electromechanical Peridynamics Modeling of Strain and Damage Sensing in Carbon Nanotube Reinforced Polymer Nanocomposites
Prakash, Naveen (Virginia Tech, 2017-09-05)
This work explores the computational modeling of electromechanical problems using peridynamics and in particular, its application in studying the potential of carbon nanotube (CNT) reinforced nanocomposites for the purpose of sensing deformation and damage in materials. Peridynamics, a non-local continuum theory which was originally formulated for modeling problems in solid mechanics, has been extended in this research to electromechanical fields and applied to study the electromechanical properties of CNT nanocomposites at multiple length scales. Piezoresistivity is the coupling between the electrical properties of a material and applied mechanical loads, more specifically the change in resistance in response to deformation. This can include both, a geometric effect due to change in dimensions as well as the change in resistivity of the material itself. Nanocomposites referred to in this work are materials which consist of CNTs dispersed in a binding polymer matrix. The origins of the extraordinary piezoresistive properties of nanocomposites lie at the nanoscale where the non-local phenomenon of electron hopping plays a significant role in establishing the properties of the nanocomposite along with CNT network formation and inherent piezoresistivity of CNTs themselves. Electron hopping or tunneling allows for a current to flow between neighboring CNTs even when they are not in contact, provided the energy barrier for electrons to hop is small enough. This phenomenon is highly nonlinear with respect to the intertube distance and is also dependent on other factors such as the potential barrier of the polymer matrix. To investigate this in more detail, peridynamic simulations are first employed to study the piezoresistivity at the CNT bundle scale by considering a nanoscale representative volume element (RVE) of CNTs within polymer matrix, and by explicitly modeling electron hopping effects. This is done by introducing electron hopping bonds and it is shown that the conductivity and the non-local length scale parameter in peridynamics (the horizon) can be derived from a purely physics based model rather than assuming an ad-hoc value. Piezoresistivity can be characterized as a function of the deformation and damage within the material and thereby used as an in-situ indicator of the structural health of the material. As such, a material system for which real time in-situ monitoring may be useful is polymer bonded explosives. While these materials are designed for detonation under conditions of a strong shock, they can be damaged or even ignited under certain low magnitude impact scenarios such as during accidental drop or transportation. Since these materials are a heterogeneous system consisting of explosive grains within a polymer matrix binder, it is proposed that CNTs can be dispersed within the binder medium leading to an inherently piezoresistive hybrid nanocomposite bonded explosive material (NCBX) material which can then be monitored for a continuous assessment of deformation and damage within the material. To explore the potential use of CNT nanocomposites for this novel application, peridynamic simulations are carried out at the microscale level, first under quasistatic conditions and subsequently under dynamic conditions to allow the propagation of elastic waves. Peridynamics equations, which can be discretized to obtain a meshless method are particularly suited to this problem as the explicit modeling of crack initiation and propagation at the microscale is essential to understanding the properties of this material. Moreover, many other parameters such as electrical conductivity of the grain and the properties of the grain-binder interface are studied to understand their effect on the piezoresistive response of the material. For example, it is found that conductivity of the grain plays a major role in the piezoresistive response since it affects the preferential pathways of current density depending on the relative ease of flow through grain vs. binder. The results of this work are promising and are two fold. Peridynamics is found to be an effective method to model such materials, both at the nanoscale and the microscale. It alleviates some of difficulties faced by traditional finite element methods in the modeling of damage in materials and can be extended to coupled fields with relative ease. Secondly, simulations presented in this work show that there is much promise in this novel application of nanocomposites in the field of structural health monitoring of polymer bonded explosives.
Crossflow stability and transition experiments in a swept-wing flow
Dagenhart, J. Ray (Virginia Tech, 1992-12-03)
An experimental examination of crossflow instability and transition on a 45° swept wing is conducted in the Arizona State University Unsteady Wind Tunnel. The stationary-vortex pattern and transition location are visualized using both sublimating-chemical and liquid-crystal coatings. Extensive hot-wire measurements are conducted at several measurement stations across a single vortex track. The mean and travelling-wave disturbances are measured simultaneously. Stationary-crossflow disturbance profiles are determined by subtracting either a reference or a span-averaged velocity profile from the mean-velocity data. Mean, Stationary-crossflow, and travelling-wave velocity data are presented as local boundary-layer profiles and as contour plots across a single stationary-crossflow vortex track. Disturbance-mode profiles and growth rates are determined. The experimental data are compared to predictions from linear stability theory. Comparison of measured and predicted pressure distributions shows that a good approximation of infinite swept-wing flow is achieved. A fixed-wavelength vortex pattern is observed throughout the visualization range. The theoretically-predicted maximum-amplified vortex wavelength is found to be approximately 25% larger than the observed wavelength. Linear-stability computations for the dominant stationary-crossflow vortices show that the N-factors at transition ranged from 6.4 to 6.8. The mean-velocity profiles vary slightly across the stationary-crossflow vortex at the first measurement station. The variation across the vortex increases with downstream distance until nearly all of the profiles become highly-distorted S-shaped curves. Local stationary-crossflow disturbance profiles having either purely excess or deficit values develop at the upstream measurement stations. Further downstream the profiles take on crossover shapes not anticipated by the linear theory. The maximum streamwise stationary-crossflow velocity disturbances reach +20% of the edge velocity just before transition. The travelling-wave disturbances have single lobes at the upstream measurement stations as expected, but further downstream double-lobed travelling-wave profiles develop. The maximum disturbance intensity remains quite low until just ahead of the transition location where it suddenly peaks at 0.7% of the edge velocity and then drops sharply. The travelling-wave intensity is always more than an order of magnitude lower than the stationary crossflow-vortex strength. The mean streamwise-velocity contours are nearly flat and parallel to the model surface at the first measurement station. Further downstream, the contours rise up and begin to roll over like a wave breaking on the beach. The stationary-crossflow contours show that a plume of low-velocity fluid rises near the center of the wavelength while high-velocity regions develop near the surface at each end of the wavelength. There is no distinct pattern to the low-intensity travelling-wave contours until a short distance upstream of the transition location where the travelling-wave intensity suddenly peaks near the center of the vortex and then falls abruptly. The experimental disturbance-mode profiles agree quite well with the predicted eigenfunctions for the forward measurement stations. At the later stations, the experimental mode profiles assume double-lobed shapes with maxima above and below the single maximum predicted by the linear theory. The experimental growth rates are found to be less than or equal to the predicted growth rates from the linear theory. Also, the experimental growth rate curve oscillates over the measurement range whereas the theoretically-predicted growth rates decrease monotonically.

Browsing by Author "Cramer, Mark S."

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