京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第18991号 / 工博第4033号 / 新制||工||1621(附属図書館) / 31942 / 京都大学大学院工学研究科電気工学専攻 / (主査)教授 引原 隆士, 教授 土居 伸二, 教授 小林 哲生 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

In this dissertation, the mechanical models of 2-DOF and 4-DOF nonlinear journal bearing rotor systems are established. A more accurate model of oil film forces is derived from Reynolds equations. The periodic motions in such nonlinear journal bearing systems are obtained through discrete mapping method. Such a semi-analytical method constructs an implicit discrete mapping structure for periodic motions by discretization of the continuous journal bearing rotor differential equations. Stable and unstable periodic solutions of periodic motions are obtained with prescribed accuracy. The bifurcation tree of periodic motions in rotor system without oil film forces is demonstrated through the route from period-1 motion to period-8 motion. Stable period-2 and unstable period-1 motion are presented for 2 DOF journal bearing rotor system. Possibly infinite periodic solutions are found in 4 DOF journal bearing rotor system. For the rotor systems, the stability and bifurcations of periodic motions are analyzed through eigenvalue analysis of the corresponding Jacobian matrix of the discretized nonlinear systems. The frequency amplitude characteristics of periodic motions in 2 DOF journal bearing system are presented for a good understanding of the nonlinear dynamics of journal bearing rotor system in frequency domain . The rich dynamics of the journal bearing systems are discovered. The numerical illustrations of stable periodic motions are brought out with the initial conditions from analytical prediction.

In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions of both models here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves for each model, we find a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. For the microstructure equation, the new family of solutions occur in regions of parameter space distinct from the known solitary wave solutions and are thus entirely new. Directions for future work, including the dynamics of each family of solitary waves using exponential asymptotics techniques, are also mentioned.

By nature discrete solitons represent self-trapped wavepackets in nonlinear periodic structures and result from the interplay between lattice diffraction (or dispersion) and material nonlinearity. In optics, this class of self-localized states has been successfully observed in both one-and two-dimensional nonlinear waveguide arrays. In recent years such lattice structures have been implemented or induced in a variety of material systems including those with cubic (Kerr), quadratic, photorefractive, and liquid-crystal nonlinearities. In all cases the underlying periodicity or discreteness leads to new families of optical solitons that have no counterpart whatsoever in continuous systems. In the first part of this dissertation, a theoretical investigation of linear and nonlinear optical wave propagation in semi-infinite waveguide arrays is presented. In particular, the properties and the stability of surface solitons at the edge of Kerr (AlGaAs) and quadratic (LiNbO3) lattices are examined. Hetero-structures of two dissimilar semi-infinite arrays are also considered. The existence of hybrid solitons in these latter types of structures is demonstrated. Rabi-type optical transitions in z-modulated waveguide arrays are theoretically demonstrated. The corresponding coupled mode equations, that govern the energy oscillations between two different transmission bands, are derived. The results are compared with direct beam propagation simulations and are found to be in excellent agreement with coupled mode theory formulations. In the second part of this thesis, the concept of parity-time-symmetry is introduced in the context of optics. More specifically, periodic potentials associated with PT-symmetric Hamiltonians are numerically explored. These new optical structures are found to exhibit surprising characteristics. These include the possibility of abrupt phase transitions, band merging, non-orthogonality, non-reciprocity, double refraction, secondary emissions, as well as power oscillations. Even though gain/loss is present in this class of periodic potentials, the propagation eigenvalues are entirely real. This is a direct outcome of the PT-symmetry. Finally, discrete solitons in PT-symmetric optical lattices are examined in detail.

The nonlinear static and dynamic response of circular and annular plates under electrostatic, thermal, and combined loading is investigated. The main motivation for the study of these phenomena is providing fundamental insights into the mechanics of micro-electro-mechanical-systems (MEMS). MEMS devices are usually miniaturization of the corresponding macro-scale devices. The basic mechanics of the components of many MEMS devices can be modeled using conventional structural theories. Some of the most used and actively researched MEMS devices- namely pressure sensors and micropumps- use circular or annular diaphragms as principle components. The actuation and sensing principles of these devices are usually electrostatic in nature. Most MEMS devices are required to operate under wide environmental conditions, thus, a study of thermal effects on the performance of these devices is a major design consideration. There exists a wide arsenal of analytic, semi-analytic, and numerical tools for nonlinear analysis of continuous systems. The present work uses different tools for the analysis of different types of problems. The selection of the analysis tools is guided by two principles. The first consideration is that the analysis should reveal the fundamental mechanics and dynamics of the problem rather than simply generating numerical data. The second consideration is numerical efficiency. Guided by the same principles, the basic structural model adopted in this work is the von-Karman plate model. This model captures the basic nonlinear phenomena in the plate with minimal complexity in the equations of motion, thus providing a balance between simplicity and accuracy. We address a wide array of problems for a variety of loading and boundary conditions. We start by analyzing annular plates under static electrostatic loading including the variation of the plate natural frequencies with the applied voltage. We also analyze parametric resonances in plates subjected to sinusoidally varying thermal loads. We investigate the prebuckling and postbuckling static thermal response and the corresponding variation of the natural frequencies. Finally, we close by investigating the problem of a circular plate under a combination of thermal and electrostatic loading. The results of this investigation demonstrate the importance of including nonlinear phenomena in the modeling of MEMS devices both for correct quantitative predictions and for qualitative description of operations. / Ph. D.

Yes / Fractional-order chaotic systems have more complex dynamics than integer-order chaotic systems. Thus, investigating fractional chaotic systems for the creation of image cryptosystems has been popular recently. In this article, a fractional-order memristor has been developed, tested, numerically analyzed, electronically realized, and digitally implemented. Consequently, a novel simple three-dimensional (3D) fractional-order memristive chaotic system with a single unstable equilibrium point is proposed based on this memristor. This fractional-order memristor is connected in parallel with a parallel capacitor and inductor for constructing the novel fractional-order memristive chaotic system. The system’s nonlinear dynamic characteristics have been studied both analytically and numerically. To demonstrate the chaos behavior in this new system, various methods such as equilibrium points, phase portraits of chaotic attractor, bifurcation diagrams, and Lyapunov exponent are investigated. Furthermore, the proposed fractional-order memristive chaotic system was implemented using a microcontroller (Arduino Due) to demonstrate its digital applicability in real-world applications. Then, in the application field of these systems, based on the chaotic behavior of the memristive model, an encryption approach is applied for grayscale original image encryption. To increase the encryption algorithm pirate anti-attack robustness, every pixel value is included in the secret key. The state variable’s initial conditions, the parameters, and the fractional-order derivative values of the memristive chaotic system are used for contracting the keyspace of that applied cryptosystem. In order to prove the security strength of the employed encryption approach, the cryptanalysis metric tests are shown in detail through histogram analysis, keyspace analysis, key sensitivity, correlation coefficients, entropy analysis, time efficiency analysis, and comparisons with the same fieldwork. Finally, images with different sizes have been encrypted and decrypted, in order to verify the capability of the employed encryption approach for encrypting different sizes of images. The common cryptanalysis metrics values are obtained as keyspace = 2648, NPCR = 0.99866, UACI = 0.49963, H(s) = 7.9993, and time efficiency = 0.3 s. The obtained numerical simulation results and the security metrics investigations demonstrate the accuracy, high-level security, and time efficiency of the used cryptosystem which exhibits high robustness against different types of pirate attacks.

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Although instabilities and large oscillations are traditionally considered as conditions to be avoided in structures, a new design philosophy based on their exploitation towards the achievement of innovative mechanical features has been initiated in the last decade. In this spirit, instabilities are exploited towards the development of systems that can yield designed responses in the post-critical state. Further, the presence of oscillating constraints may allow for a stabilization of the dynamic response. These subjects entail a rich number of phenomena due to the non-linearity, so that the study of such mechanical systems becomes particularly complex, from both points of view of the mechanical modeling and of the computational tools. Two elastic structures are studied. The first consists of a flexible and extensible rod that is clamped at one end and constrained to slide along a given profile at the other. This feature allows one to study the effect of the axial stiffness of the rod on the tensile buckling of the system and on the compressive restabilization. A very interesting effect is that in a region of parameters double restabilization is found to occur, involving four critical compressive loads. Also, the mechanical system is shown to work as a novel force limiter that does not depend on sacrificial mechanical elements. Further, it is shown that the system can be designed to be multi-stable and suitable for integration in metamaterials. The second analyzed structure is a flexible but inextensible rod that is partially inserted into a movable rigid sliding sleeve which is kept vertical in a gravitational field. The system is analytically solved and numerically and experimentally investigated, when a horizontal sinusoidal input is prescribed at the sliding sleeve. In order to model the system, novel computational tools are developed, implementing the fully nonlinear inextensibility and kinematic constraints. It is shown that the mathematical model of the system agrees with the experimental data. Further, a study of the inclusion of dissipative terms is developed, to show that a steady motion of the rod can be accomplished by tuning the amplitude or the frequency of the sliding sleeve motion, in contrast with the situation in which a complete injection of the rod inside the sleeve occurs. A special discovery is that by slowly decreasing the frequency of the sleeve motion, the length of the rod outside the sleeve can be increased significantly, paving the way to control the rod’s end trajectory through frequency modulation.

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No description available.