This work is concerned with the theoretical development of dynamic equations for gyroelastic systems which are dynamic systems with four basic types of continuous mechanical influences, i.e. inertia, elasticity, damping, and gyricity or stored angular momentum. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing two different theories of elasticity, i.e. the classical and micropolar theories of elasticity, the energy expressions and equations of motion for the undamped classical and micropolar gyroelastic continua are derived. Whereas the micropolar gyroelastic continuum model with extra coefficients and degrees of freedom is primarily developed to account for the asymmetric elasticity, it also proves itself to be more comprehensive in describing the actual gyroscopic system or structure. The dynamic equations of the general three-dimensional gyroelastic continua are reduced to the case of a one-dimensional gyroelastic continua in the three-dimensional space, i.e. three-dimensional gyrobeams. Two different gyrobeam models are developed, one based on the classical beam torsion and bending theories and one based on the simplified micropolar beam torsion and bending theories. Finite element models corresponding to the classical and micropolar gyrobeams are built in MATLAB and used for numerical analysis. The classical and micropolar gyrobeam models are analyzed and compared, against the earlier gyrobeam models developed by other authors and also against each other, through numerical examples. It is shown that there are significant differences between the developed unrestricted classical gyrobeam model and the previously derived zero-order restricted classical gyrobeam models. These differences are more pronounced in the shorter beams and for the transverse gyricity case. The results also indicate that the unrestricted classical and micropolar gyrobeam models behave very diversely in a wide range of micropolar elastic constants even where the classical and micropolar elasticity models coincide. As a foundation for development of the above-mentioned theories, the correct approach for simplification of the micropolar elasticity to the classical elasticity, the simple torsion and bending theories for micropolar beams, and the correct approximation of infinitesimal rotations or microrotations are derived and presented.

This dissertation focuses on a novel approach for characterizing the mechanical behavior of an elastic body. In particular, we develop a mathematical tool for the estimation of residual stress field in an elastic body that has mechanical properties similar to that of the arterial wall, by making use of intravascular ultrasound (IVUS) imaging techniques. This study is a preliminary step towards understanding the progression of a cardiovascular disease called atherosclerosis using ultrasound technology. It is known that residual stresses play a significant role in determining the overall stress distribution in soft tissues. The main part of this work deals with developing a nonlinear inverse spectral technique that allows one to accurately compute the residual stresses in soft tissues. Unlike most conventional experimental, both in vivo and in vitro, and theoretical techniques to characterize residual stresses in soft tissues, the proposed method makes fundamental use of the finite strain non- linear response of the material to a quasi-static harmonic loading. The arterial wall is modeled as a nonlinear, isotropic, slightly compressible elastic body. A boundary value problem is formulated for the residually stressed arterial wall, the boundary of which is subjected to a constant blood pressure, and then an idealized model for the IVUS interrogation is constructed by superimposing small amplitude time harmonic infinitesimal vibrations on large deformations via an asymptotic construction of its solution. We then use a semi-inverse approach to study the model for a specific class of deformations. The analysis leads us to a system of second order differential equations with homogeneous boundary conditions of Sturm-Liouville type. By making use of the classical theory of inverse Sturm-Liouville problems, and root finding and optimization techniques, we then develop several inverse spectral algorithms to approximate the residual stress distribution in the arterial wall, given the first few eigenfrequencies of several induced blood pressures.

Doctor of Philosophy / The main issue to be articulated in this thesis is the proposition that Leibniz’s mature philosophy is best, or preferably, presented as a double-aspect ontology. All the arguments to be furnished herein support this case; however, their intrinsic weight and extent far exceeds that of the principal contention, so that the whole of Leibniz’s natural philosophy and metaphysics will be seen to be involved and to undergo some measure of re-orientation away from more traditional interpretive concerns. Part I follows Leibniz in his emendation of Aristotelian-Scholastic notions as a result of his need for a “higher, metaphysical principle” to remedy the defects of the ‘modern’ account of motion. From this flowed his new conception of substance. The fundamental premise of Leibniz’s metaphysics is that spirit and body lie in series. The cosmos presents itself as aspects of an unbroken continuum. Ineluctably our conclusions as to the ‘whole’ is therefore an intellectual reconstruction of the perspectives delivered to us by these aspects. This emerges most clearly from the phenomenotaxis which has been collated in this part of the thesis – apparently the first such exercise in the scholarly literature. All this involves a separation of domains which require appropriate levels of description to explain their autonomous features. A double-aspect theory seems indispensable to account for the one world to which these levels nonetheless refer. In Part II we engage with Leibniz’s conception of substance as a unit of force. From this protean idea (aka monad) the whole material and spiritual cosmos is derived. The basis of this theory is that to act is to be. Accordingly we arrive at an ontology of agency. The nature of a monad is to exert Daseinstreben, the equivalent of individuation. Included in its definition is an absolute freedom to act. God’s “concession” of existence therefore refers to the autonomous collectivisation of monads into universes eligible for actualisation. Accordingly Leibniz arrives at a theory of a self-constructing universe. Post-Arnauld, Leibniz discarded the complete concept, having realised that contingency breaks open the system of determinism. Accordingly Leibniz replaced the ‘sum of predicates’ doctrine with the law of the series. In this conception monads collect the asymmetrical and irreversible information relevant to their internal states; for it transpires that freely executed choices guarantee avoidance of indiscernibles. The section therefore presents a schema of the ten main issues entangled in the conception of agency as well as an analytical chart of the structure of monads. In Part III, the “Labyrinth of the Continuum” resolves the perspectives on the world. Leibniz declares his colours unambiguously – realism concerns the world of facts, idealism the realm of foun-dations. The Principle of Continuity covers a vast range of indeterminate parts which serve as the foundations of real parts. We investigate some case studies, e.g. petites perceptions and especially the Pacidius, in which the conception of an agent-in-motion is studied in depth to reveal Leibniz’s extraordinary conclusions on change. We also consider Shapes, Limits and Boundaries which are relevant to the theory of the self-constructing universe (infolding and unfolding order); and finally his models of self-similarity and scale invariance. PART IV is concerned with grounding existents from the principle of sufficient reason. The virtue claimed here for the double-aspect theory is the possibility of penetrating into the thought of an exceptionally complex thinker through more than one portal. It yields a greater variety of facets, an inner coherence and a much richer texture of thought than the traditional insistence on just one primary aspect reveals.

Thesis (Ph.D.) - James Cook University, 2003. / Typescript (photocopy). Appendices: leaves 156-172. Bibliiography: leaves 149-155.

Thesis (Ph.D.) - Carleton University, 2005. / Includes bibliographical references (p. 341-348). Also available in electronic format on the Internet.

Thesis (Ph.D)--Mechanical Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Jianmin Qu; Committee Member: David McDowell; Committee Member: Elisa Riedo; Committee Member: Min Zhou; Committee Member: Mo Li.

Thesis (Ph. D.)--University of Alabama at Birmingham, 2009. / Title from PDF title page (viewed Sept. 2, 2009). Additional advisors: Alexander Blokh, Lex G. Oversteegen, Purushotham Bangalore, Vo Thanh Liem, Kyle Siegrist. Degree earned with the cooperation of additional faculty from the University of Alabama and the University of Alabama in Huntsville. Includes bibliographical references.

Thesis (Ph..D.), Memorial University of Newfoundland, 1998. / Restricted until June 1999. Bibliography: leaves 179-187.

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2007. / Committee Chair: Itzhak Green; Committee Member; Jeffrey Streator; Committee Member: Richard Neu. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1971. / Typescript. Vita. Description based on print version record. Includes bibliographical references.