Theses and Dissertations at Montana State University (MSU)
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/733
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Item Application of boundary integral equation method to two-dimensional frictional contact problems(Montana State University - Bozeman, College of Engineering, 1987) Dandekar, Bhushan WasudeoItem Increase of frictional resistance in closed conduit systems fouled with biofilms(Montana State University - Bozeman, College of Engineering, 2000) Groenenboom, Mark DouglasItem A finite element approach to predicting vibrothermographic heat detections of fully embedded delaminations within composite plates(Montana State University - Bozeman, College of Engineering, 2013) Cook, Corey Joseph; Chairperson, Graduate Committee: Ahsan MianVibrothermography is a Nondestructive Evaluation (NDE) technique which is particularly well suited for locating discontinuities, such as cracks and sub-surface delaminations within composite structures. The Vibrothermographic method relies on high-amplitude vibrational excitations within a structure to cause frictional rubbing along flaw surfaces. Frictional heat energy dissipated between flaw surfaces diffuses through the material of the structure to a surface where heat signatures are monitored using infra-red thermographic camera technologies. Vibrothermographic testing methods, developed in the late 1970's with the advent of improved IR camera technologies, have been somewhat slow to develop, due in part to a lack of understanding of the physics surrounding damaged areas of structures. The focus of this research is on the use of Finite Element (FE) Analysis, using ANSYS® software, to simulate the Vibrothermographic method. One goal of the research is to produce algorithms predicting the likely-hood of thermal detection of numerous delamination flaws within a fiberglass/epoxy composite plate. The FE modeling attempts accurately characterize harmonic responses surrounding the "damaged" regions (flaw areas) of the plate. Harmonic response analyses are performed on the FE plate model, and nodal harmonic displacement data is subsequently utilized within transient analysis sub-modeling procedures. Each of the nine delamination flaws are analyzed within these sub-modeling procedures and the rates at which frictional heat energy dissipation, due rubbing, occur at the flaw faces are derived. Each delamination sub-model is subjected to a high-resolution frequency sweep analysis, where frequency dependent heat generation data is collected over a frequency bandwidth of 800-30000Hz. The latter portion of the paper discusses the use of a novel finite element approach to estimating the likely hood of thermal detections for the flaws. The approach uses generic finite element model to predict thermal detection times for an expansive set of flaw and testing parameters. A response surface method of curve-fitting is applied to the collected detection time data, and the resulting equation is subsequently used to predict the heat-signature detectability for each flaw. The results of this method are ultimately compared to empirical vibrothermographic frequency-sweep data, and a preliminary assessment of the viability of the approach is made.Item Development of effective numerical schemes for frictional heat generation and diffusion in vibrothermography(Montana State University - Bozeman, College of Engineering, 2012) Platt, Darren Joseph; Chairperson, Graduate Committee: Ahsan MianVibrothermography is a non-destructive testing (NDT) method that utilizes high frequency acoustic vibrations to cause flaw faces to rub together and generate frictional heat which is then detectable using an IR camera. This testing process was first investigated over 20 years ago, however it has been slow to develop due to the lack of understanding of the mechanical processes behind the heat generation and the inability to effectively control flaw heating. Vibrothermography is particularly suitable for composite materials due to their tendency to develop subsurface delaminations between laminating plies, which are undetectable using most other NDT methods. Increased use of composite materials in structures such as airplane components and wind turbine blades has contributed to a revived interest in vibrothermography. This paper investigates the use of the finite element analysis (FEA) method to model vibrothermographic systems. Physical samples of glass epoxy composites that contained large delaminations were tested using vibrothermography to create an empirical data set that is used to verify an FE model of a similar system The resulting surface temperatures in the FE model were compared to those observed in the physical test. Both the strengths and shortcomings of using FEA to model these systems are discussed and the proposals for how to improve the model accuracy are provided. The second of half of the paper describes the use FEA to create thermal models of vibrothermographic systems in order to generate a detection model that will indicate the excitation time required to detect a flaw according to it's size, depth, and heat generation rate. The model also accounts for measurement noise and camera distance, and is found to be accurate for flaws with short detection times, and less reliable for those with longer times. The connection between model accuracy and detection time is explained by the inherent issue of problem conditioning. Possible resolutions to this problem are described and further work is proposed on how to improve model accuracy.Item Classical mechanics with dissipative constraints(Montana State University - Bozeman, College of Letters & Science, 2009) Harker, Shaun Russell; Chairperson, Graduate Committee: Tomas GedeonThe aim of this thesis is to consider the mathematical treatment of mechanical systems in the presence of constraints which are energetically dissipative. Constraints may be energetically dissipative due to impacts and friction. In the frictionless setting, we generalize Hamilton's principle of stationary action, central to the Lagrangian formulation of classical mechanics, to reflect optimality conditions in constrained spaces. We show that this generalization leads to the standard measure-theoretic equations for shocks in the presence of unilateral constraints. Previously, these equations were simply postulated; we derive them from a fundamental variational principle. We also present results in the frictional setting. We survey the extensive literature on the subject, which focusses on existence results and numerical schemes known as time- stepping algorithms. We consider a novel model of friction (which is more dissipative than standard Coulomb friction) for which we can give better well-posedness results than what is currently available for the Coulomb theory. To this end, we study multi-valued maps, differential inclusions, and optimization theory. We construct a differential inclusion we call the feedback problem, for which the multi-valued map is the solution set of a convex program. We give existence and uniqueness results regarding this feedback problem. We cast the persistent contact evolution problem of our novel model of friction into the form of a feedback problem to derive an existence result.