The dynamic response and bifurcations of a harmonic oscillator with a hysteretic restoring force and sinusoidal excitation are investigated. A multilinear model of hysteresis is presented. A hybrid system approach is used to formulate and study the problem. A novel method for obtaining exact transient and steady state response of the system is discussed. Simple periodic orbits of the system are analyzed using the KBM method and an analytic criterion for existence of bound and unbound resonance is derived. Results of KBM analysis are compared with those from numerical simulations. Stability and bifurcations of higher period orbits are studied using Poincar´e maps. The Poincar´e map for the system is constructed by composing the corresponding maps for the individual subsystems of the hybrid system. The novelty of this work lies in a.) the study of a multilinear model of hysteresis, and, b.) developing a methodology for obtaining the exact transient and steady state response of the system.

Shape memory alloys (SMAs) are an important class of smart materials that have the ability to remember a shape. Current practical uses of SMAs are limited to below 100 degrees C which is the limit for the transformation temperatures of most commercially successful SMAs such as NiTi and Cu-based alloys. In recent years, the CoNiGa system has emerged as a new ferromagnetic shape memory alloy with some compositions exhibiting high martensitic transformation temperatures which makes CoNiGa a potential high temperature shape memory alloy (HTSMA). In this study, the microstructural evolution and martensitic transformation characteristics of CoNiGa (mainly Co46Ni27Ga27 and Co44Ni26Ga30 in at.percent) HTSMAs were investigated in as-cast and hot-rolled conditions as a function of different heat treatments. Heat treatment conditions were selected to introduce single, two, and three phase structures, where two precipitate phases (ductile Y and hard Y') do not martensitically transform. Calorimetry, X-ray analysis, scanning and transmission electron microscopy, thermo-mechanical process and cycling techniques are applied to understand the structural and chemical factors influencing the thermal stability and transformation characteristics. The main findings include improvement of ductility, most cyclically stable compositions with narrow transformation hysteresis (<40 degrees C) and transformation temperatures in the range of 100 degrees C to 250 degrees C, formation of new phases and their effects, and associated compositional changes in the matrix, on the transformation temperatures and on the microstructural evolution. In addition, Ms temperature depends linearly on the valence electron concentration (e/a) of the matrix, only if the Ga content is constant, and the samples with narrow transformation hysteresis demonstrate reversible martensitic transformation in constant-stress thermal cycling experiments.

Η παρούσα διδακτορική διατριβή περιγράφει το σχεδιασμό και την ανάπτυξη ενός εκπτυσσόμενου Ενδομυελικού Ήλου Επιμήκυνσης των Μακρών Οστών των Κάτω Άκρων. Η επιμήκυνση των κάτω άκρων είναι μία χειρουργική διαδικασία βαθμιαίας επιμήκυνσης των μακρών οστών των κάτω άκρων και των μαλακών μορίων που τα περιβάλουν. Γενικά, η επιμήκυνση των κάτω άκρων στοχεύει στην εξίσωση των σκελών ή αύξηση του μήκους των οστών και στα δύο άκρα. Η τεχνική αύξησης του μήκους των οστών των κάτω άκρων επινοήθηκε από τις αρχές του περασμένου αιώνα [1] και έχει καταξιωθεί στη μοντέρνα χειρουργική από τις αρχές του 1960, λόγω της ενασχόλησης του G.A.Ilizarov. Ο επιστήμονας και χειρουργός G.A.Ilizarov αφιέρωσε όλη τη θεωρητική και πρακτική του έρευνα [2] στη βελτίωση της διαδικασίας επιμήκυνσης των οστών και την ανάπτυξη εξωτερικής συσκευής σταθεροποίησης που φέρει το όνομα του. Η μέθοδος αυτή καθώς και η συσκευή Ilizarov χρησιμοποιήθηκαν πάρα πολύ για να διορθώσουν τόσο βλάβες όσο και παραμορφώσεις των κάτω άκρων. Η ευελιξία αυτής της συσκευής την κάνει ένα εξαιρετικό εργαλείο το οποίο μπορεί να χρησιμοποιηθεί για τη διόρθωση διαφόρων βλαβών όπως π.χ. σταθεροποίηση συνθέτων καταγμάτων, στροφικές διορθώσεις, διορθώσεις οστών με διαφορές μήκους. Τόσο όμως η συσκευή του Ilizarov όσο και οι υπόλοιποι μονόπακτοι εξωτερικοί σταθεροποιητές που παρουσιάσθηκαν αργότερα παρουσιάζουν μειονεκτήματα [3] όπως είναι π.χ. οι σύνθετες χειρουργικές διαδικασίες, οι συνδέσεις και οι βελόνες που διαπερνούν το δέρμα και που οδηγούν σε μολύνσεις, η μειωμένη δυνατότητα φόρτισης και η ταλαιπωρία λόγω του μεγέθους του σταθεροποιητή ειδικά στις περιπτώσεις εκείνες που η ευελιξία του σταθεροποιητή δεν είναι απαραίτητη. Πολλοί ασθενείς που χρειάζονται μία διόρθωση του μήκους ενός άκρου χωρίς άλλες παραμορφώσεις θα μπορούσαν να βοηθηθούν και από μία συσκευή μικρότερης ευελιξίας χωρίς τα μειονεκτήματα των εξωτερικών μονόπακτων σταθεροποιητών. / The technique to increase the length of the long bones is the subject of research for the orthopedic surgeons for many years. The technique is used for the treatment of a limb shortening due to malformation or to a deficit for other reasons e.g. the fracture of a long bone after a car accident, osteomyelitis, or malignancy. The procedure to increase the length of a bone is difficult and may become quite hazardous for the soft tissues surrounding the area. The two parts of the bone are stabilized to eliminate the possibility of relative torsion and bending. Then they align axially with respect to each other and move with a constant rate of elongation of 1mm per day. The elongation is usually achieved by 4 steps of 0,25mm every 6 hours. The application of internal distraction osteogenesis using shape memory alloys has all the advantages of internal osteosynthesis. The only part of these mechanisms that is found externally is the activation mechanism that is connected by the necessary cables of activation with the interior of the bone where the internal distraction device is placed. The basic problem of all designs is the high constructional complexity of activation and control of shift of the two parts of the bone, something that makes this systems non user friendly and with continuous fractures and blockings of the elements of the mechanisms. In the present work, all the advantages of the mechanism of internal distraction osteogenesis are combined with the fundamental advantage; the simplicity of manufacture of the mechanism and the simplicity of operation via the restriction of the moving elements.

Shape memory materials have been known for many years to possess the unique ability of memorising their shape at some temperature. If these materials are pre-strained into the plastic range, they tend to recover their original un-strained shapes via phase transformation when subjected to heat stimulation. In recent years, this shape memory effect (SME) or strain recovery capability has been explored in aerospace structures for actuating the real-time movement of structural components. Among all the shape memory materials, the nickel-titanium based shape memory alloy (SMA) has by far received the most attention because of its high recovery capabilities. Since SMAs are usually drawn into the form of wires, they are particularly suitable for being integrated into fibre-reinforced composite structures. These integrated composite structures with SMA wires are thus called smart adaptive structures. To achieve the SME, these wires are normally embedded in the host composite structures. In returning to their unstrained shape upon heat application, they tend to exert internal stresses on the host composite structures in which they are embedded. This action could result in a controlled change in shape of the structural components. Although there has been a significant amount of research dedicated to characterising and modelling the SME of SMA wires, little experimental work had been done to offer an in-depth understanding of the mechanical behaviour of these smart adaptive polymeric composite structures. This project examined the deflection and shape change of carbon/epoxy and glass/epoxy cantilever beams through heating and cooling of internal nitinol SMA wires/strips. The heat damage mechanism and cyclic behaviour are major factors in the operation of such a system and need to be clearly understood in order to develop and gain confidence for the possible implementation of future smart actuating systems. Therefore, the objectives of the proposed research were to investigate (i) effect of embedding SMA, wires on mechanical properties of host composite, (ii) assessment of single-cycle and multiple-cycle actuation performance of smart beams, and (iii) thermal effects of excessive heat on the surrounding composite matrix.

SMA belongs to a class of so-called “smart materials” which possess properties that can be controlled by application of various types of stimuli – stress, temperature, electric field or magnetic field. In particular, SMA is a smart material which undergoes a temperature- or stress-dependent phase transformation giving it the property of remembering its original shape. Once deformed (up to a certain recoverable strain), SMA returns to its original shape upon heating. In this thesis, a study of SMA models and techniques to improve the performance of SMA actuators was carried out. In general, an SMA model is required for 3 main purposes: simulation, analysis and for model-based hysteresis compensation. In this work, the reduced-order form of John Shaw’s partial-differential equation model is chosen for implementation and simulation. The reduced-order form is used because its simpler structure makes it more useful for real-time control applications. The parameters were estimated for the John Shaw model followed by its implementation in MATLAB. From the view of control applications, a limitation of the John Shaw model is the inability to reproduce the so-called ‘minor loop behavior’ which is observed when the material is subject to cycling resulting in incomplete phase transformations. Modeling minor loop behavior is particularly important in closed-loop strain (or position) control applications since achieving a specific target strain between the two (load-dependent) extremes requires partial phase transformation. Herein, the governing equations are modified to include minor loop behavior. This behavior was tested using damped signals which would be expected to trigger minor loops in the actual SMA and reasonable match is observed from the simulations. The use of SMA actuators is limited by the relatively slow response time compared to other smart materials. The conventional current saturation (CS) scheme limits the maximum current into the wire at the manufacturer-specified safe current values in order to protect the wire from damage due to overheating. However, this is a conservative limit on the maximum current and hence, the response is artificially slowed. In order to improve the response time, a model-based temperature saturation (MBTS) scheme was developed, in which current is saturated based on model-predicted temperature. The MBTS scheme allows much higher currents to be applied to the wire, while ensuring that the wire is not damaged. Based on simulations using the reduced-order John Shaw model, it is observed that better tracking occurs using the MBTS scheme in the actuation scheme as compared to the CS scheme.

The objective of this work is to characterize and understand structure- mechanical property relationships in (meth)acrylate networks. The networks are synthesized from mono-functional (meth)acrylates with systematically varying sidegroup structure and multi-functional crosslinkers with varying mole fraction and functionality. Fundamental trends are established between the network chemical structure, crosslink density, glass transition temperature, rubbery modulus, failure strain, and toughness. The glass transition temperature of the networks ranged from -29 to 112 °C, and the rubbery modulus ranged from 2.8 to 129.5 MPa. At low crosslink density (Er < 10 MPa) network chemistry has a profound effect on network toughness. At high crosslink densities (Er > 10 MPa), network chemistry has little influence on material toughness. The characteristic ratio of the mono-functional (meth)acrylates components is unable to predict trends in thermoset toughness as a function of chemical structure, as is accomplished for thermoplastics. The cohesive energy density is a better tool for prediction of network mechanical properties. Due to superior mechanical properties, networks with phenyl ring sidegroups are further investigated to understand the effect of phenyl ring distance on toughness. This work provides a fundamental basis for designing (meth)acrylate shape memory polymer networks with specific failure strain, toughness, glass transition temperature, and rubbery modulus.

The past twenty years have seen the successful characterization and computational modeling efforts by the smart materials community to better understand the Shape Memory Alloy (SMA). Commercially available numerical analysis tools, coupled with powerful constitutive models, have been shown to be highly accurate for predicting the response of these materials when subjected to predetermined loading conditions. This thesis acknowledges the development of such an established analysis framework and proposes an expanded design framework that is capable of accounting for the complex coupling behavior between SMA components and the surrounding assembly or system. In order to capture these effects, additional analysis tools are implemented in addition to the standard use of the non-linear finite element analysis (FEA) solver and a full, robust SMA constitutive model coded as a custom user-defined material subroutine (UMAT). These additional tools include a computational fluid dynamics (CFD) solver, a cosimulation module that allows separate FEA and CFD solvers to iteratively analyze fluid-structure interaction (FSI) and conjugate heat transfer (CHT) problems, and the addition of the latent heat term to the heat equations in the UMAT to fully account for transient thermomechanical coupling. Procedures for optimizing SMA component and assembly designs through iterative analysis are also introduced at the highest level. These techniques are implemented using commercially available simulation process management and scripting tools. The expanded framework is demonstrated on example engineering problems that are motivated by real morphing structure applications, namely the Boeing Variable Geometry Chevron (VGC) and the NASA Shape Memory Alloy Hybrid Composite (SMAHC) chevron. Three different studies are conducted on these applications, focusing on component-, assembly-, and system-level analysis, each of which may necessitate accounting for certain coupling interactions between thermal, mechanical, and fluid fields. Output analysis data from each of the three models are validated against experimental data, where available. It is shown that the expanded design framework can account for the additional coupling effects at each analysis level, while providing an efficient and accurate alternative to the cost- and time-expensive legacy design-build-test methods that are still used today to engineer SMA actuated morphing aerostructures.

Tez (Yüksek Lisans) - Süleyman Demirel Üniversitesi, Fen Bilimleri Enstitüsü, Fizik Anabilim Dalı, 2007. / Bibliyografya var.

Thesis (M.S.)--Auburn University, 2008. / Abstract. Vita. Includes bibliographical references (p. 70).

Thesis (Ph.D)--Electrical and Computer Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Gall, Ken; Committee Chair: May, Gary S; Committee Member: Brand, Oliver; Committee Member: Degertekin, F Levent; Committee Member: Milor, Linda S. Part of the SMARTech Electronic Thesis and Dissertation Collection.