Slender structures like plates and shells -- for which at least one dimension is much smaller than the others -- are lightweight, flexible, and offer considerable strength with little material. As such, these structures are abundant in nature (e.g. flower petals, eggshells, and blood vessels) and design (e.g. bridge decks, fuel tanks, and soda cans). However, with slenderness comes suceptibility to large and often sudden deformations, which can be wildly nonlinear, as bending is energetically preferable to stretching. Though once considered categorically undesirable, these instabilities are often coveted nowadays in the engineering community. They provide mechanical explanations for observations in nature like the wrinkled structure of the brain or the snapping mechanism of the Venus fly trap, and when precisely controlled, enable the design of functional devices like artificial muscles or self-propelling microswimmers. As a prerequisite, these achievements require a thorough understanding of how thin structures "shape-shift" in response to stimuli and confinement. Advancing this fundamental knowledge is the goal of this thesis. In the first two chapters, we consider the shape-selection of shells and plates that are confined by their environment. The shells are made by residual swelling of silicone elastomers, a process that mimics differential growth, and causes initially flat structures to irreversibly morph into curved shapes. Flattening the central region forces further reconfiguration, and the confined shells display multi-lobed buckling patterns. These experiments, finite element (FE) simulations, and a scaling argument reveal that a single geometric confinement parameter predicts the general features of this shape-selection. Next, in experiments and molecular dynamics (MD) simulations, we constrain intrinsically flat sheets in the same manner, so that their center remains flat when we quasi-statically force them through a ring. In the absence of planar confinement, these sheets form a well-studied conical shape (the developable cone or d-cone). Our annular d-cone buckles circumferentially into patterns that are qualitatively similar to the confined shells, despite the distinct curvatures and loading methods. This is explained by the dominant role of confinement geometry in directing deformation, which we uncover via a scaling argument based on the elastic energy. There are also marked differences between the way plates and shells change shape, which we highlight when we investigate the rich dynamics of reconfiguration. In the final two chapters, we demonstrate how mechanics, geometry, and materials can inform the design of structures that use instabilities to function. We observe in experiments that dynamic loading causes a spherical elastomer shell to buckle at ostensibly subcritical pressures, following a substantial time delay. To explain this, we show that viscoelastic creep deformation lowers the critical load in the same predictable, quantifiable way that a growing defect would in an elastic shell. This work offers a pathway to introduce tunable, time-controlled actuation to existing mechanical actuators, e.g. pneumatic grippers. The final chapter aims at reducing the energy input required for bistable actuators, wherein snap-through instability is typically induced by a stimulus applied to the entire shell. To do so, we combine theory with 1D finite element simulations of spherical caps with a non-homogeneous distribution of stimuli--responsive material. We demonstrate that restricting the active area to the shell boundary allows for a large reduction in its size, while preserving snap-through behavior. These results are stimulus-agnostic, which we demonstrate with two sets of experiments, using residual swelling of bilayer silicone elastomers as well as a magneto-active elastomer. Our findings elucidate the underlying mechanics, offering an intuitive route to optimal design for efficient snap-through. / 2022-05-06T00:00:00Z

No description available.

Discrete optical systems are a subgroup of periodic structures in which the evolution of a continuous electromagnetic field can be described by a discrete model. In this model, the total field is the sum of localized, discrete modes. Weakly coupled arrays of single mode channel waveguides have been known to fall into this class of systems since the late 1960's. Nonlinear discrete optics has received a considerable amount of interest in the last few years, triggered by the experimental realization of discrete solitons in a Kerr nonlinear AlGaAs waveguide array by H. Eisenberg and coworkers in 1998. In this work a detailed experimental investigation of discrete nonlinear wave propagation and the interactions between beams, including discrete solitons, in discrete systems is reported for the case of a strong Kerr nonlinearity. The possibility to completely overcome "discrete" diffraction and create highly localized solitons, in a scalar or vector geometry, as well as the limiting factors in the formation of such nonlinear waves is discussed. The reversal of the sign of diffraction over a range of propagation angles leads to the stability of plane waves in a material with positive nonlinearity. This behavior can not be found in continuous self-focusing materials where plane waves are unstable against perturbations. The stability of plane waves in the anomalous diffraction region, even at highest powers, has been experimentally verified. The interaction of high power beams and discrete solitons in arrays has been studied in detail. Of particular interest is the experimental verification of a theoretically predicted unique, all optical switching scheme, based on the interaction of a so called "blocker" soliton with a second beam. This switching method has been experimentally realized for both the coherent and incoherent case. Limitations of such schemes due to nonlinear losses at the required high powers are shown.

This work is divided into two main parts. In the first part (chapters 2-7) we consider the nonlinear response of nano-particle colloidal systems. Starting from the Nernst-Planck and Smoluchowski equations, we demonstrate that in these arrangements the underlying nonlinearities as well as the nonlinear Rayleigh losses depend exponentially on optical intensity. Two different nonlinear regimes are identified depending on the refractive index contrast of the nanoparticles involved and the interesting prospect of self-induced transparency is demonstrated. Soliton stability is systematically analyzed for both 1D and 2D configurations and their propagation dynamics in the presence of Rayleigh losses is examined. We also investigate the modulation instability of plane waves and the transverse instabilities of soliton stripe beams propagating in nonlinear nano-suspensions. We show that in these systems, the process of modulational instability depends on the boundary conditions. On the other hand, the transverse instability of soliton stripes can exhibit new features as a result of 1D collapse caused by the exponential nonlinearity. Many-body effects on the systems' nonlinear response are also examined. Mayer cluster expansions are used in order to investigate particle-particle interactions. We show that the optical nonlinearity of these nano-suspensions can range anywhere from exponential to polynomial depending on the initial concentration and the chemistry of the electrolyte solution. The consequence of these inter-particle interactions on the soliton dynamics and their stability properties are also studied. The second part deals with linear and nonlinear properties of optical nano-wires and the coupled mode formalism of parity-time (PT) symmetric waveguides. Dispersion properties of AlGaAs nano-wires are studied and it is shown that the group velocity dispersion in such waveguides can be negative, thus enabling temporal solitons. We have also studied power flow in nano-waveguides and we have shown that under certain conditions, optical pulses propagating in such structures will exhibit power circulations. Finally PT symmetric waveguides were investigated and a suitable coupled mode theory to describe these systems was developed.

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.

No description available.

In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes Generalized Mass Ac- tion kinetics and Michaelis-Menten kinetics, we show that certain submatrices of the stoichiometric matrix, so-called unstable cores, are sufficient for a reaction network to admit instability and potentially give rise to such complex dynami- cal behavior. The determinant of the submatrix distinguishes unstable-positive feedbacks, with a single real-positive eigenvalue, and unstable-negative feedbacks without real-positive eigenvalues. Autocatalytic cores turn out to be exactly the unstable-positive feedbacks that are Metzler matrices. Thus there are sources of dynamical instability in chemical networks that are unrelated to autocatalysis. We use such intuition to design non-autocatalytic biochemical networks with su- perlinear growth and oscillations.

Based on a refined analytical anisotropic thin-walled beam model, aeroelastic instability, dynamic aeroelastic response, active/passive aeroelastic control of advanced aircraft wings modeled as thin-walled beams are systematically addressed. The refined thin-walled beam model is based on an existing framework of the thin-walled beam model and a couple of non-classical effects that are usually also important are incorporated and the model herein developed is validated against the available experimental, Finite Element Anaylsis (FEA), Dynamic Finite Element (DFE), and other analytical predictions. The concept of indicial functions is used to develop unsteady aerodynamic model, which broadly encompasses the cases of incompressible, compressible subsonic, compressible supersonic and hypersonic flows. State-space conversion of the indicial function based unsteady aerodynamic model is also developed. Based on the piezoelectric material technology, a worst case control strategy based on the minimax theory towards the control of aeroelastic systems is further developed. Shunt damping within the aeroelastic tailoring environment is also investigated. The major part of this dissertation is organized in the form of self-contained chapters, each of which corresponds to a paper that has been or will be submitted to a journal for publication. In order to fullfil the requirement of having a continuous presentation of the topics, each chapter starts with the purely structural models and is gradually integrated with the involved interactive field disciplines. / Ph. D.

The utilization of lean premixed combustors has become attractive to designers of industrial gas turbines as a means of meeting strict emissions standards without compromising efficiency.  Mixing the fuel and air prior to combustion allows for lower temperature flame zones, creating the potential for drastically reduced nitrous oxide emissions.  While effective, these systems are commonly plagued by combustion driven instabilities.  These instabilities produce large pressure and heat release rate fluctuations due to a resonant interaction between the combustor acoustics and the flame.  A primary feedback mechanism responsible for driving these systems is the propagation of Fuel/Air Ratio (FAR) fluctuations into the flame zone.  These fluctuations are formed inside of the premixing chamber when fuel is injected into and mixed with an oscillating air flow. The research presented here aimed to develop new technology for premixer designs, along with an application strategy, to avoid resonant thermo-acoustic events driven by FAR fluctuations.  A passive fuel control technique was selected for investigation and implementation. The selected technique utilized fuel injections at multiple, strategically placed axial locations to target and inhibit FAR fluctuations at the dominant resonant mode of the combustor.  The goal of this research was to provide an understanding of the mixing response inside a realistic premixer geometry and investigate the effectiveness of the proposed suppression technique. The mixing response was investigated under non-reacting flow conditions using a unique modular premixer.  The premixer incorporated variable axial fuel injection locations, as well as interchangeable mixing chamber geometries.  Two different chamber designs were tested: a simple annular chamber and one incorporating an axial swirler.  The mixing response of the simple annular geometry was well characterized, and it was found that multiple injections could be effectively configured to suppress the onset of an unstable event at very lean conditions. Energy dense flame zones produced at higher equivalence ratios, however, were found to be uncontrollable using this technique. Additionally, the mixing response of the swirl geometry was difficult to predict. This was found to be the result of large spatial gradients formed in the dynamic velocity field as acoustic waves passed through the swirl vanes. / Ph. D.

The predictive design of fuel injection hardware used for active combustion control is not well established in the gas turbine industry. The primary reason for this is that the underlying mechanisms governing the flow rate authority downstream of the nozzle are not well understood. A detailed investigation of two liquid fuel flow modulation configurations is performed in this thesis: a piston and a throttle-valve configuration. The two systems were successfully built with piezoelectric actuation to drive the prime movers proportionally up to 800 Hz. Discussed in this thesis are the important constituents of the fuel injection system that affect heat release authority: the method of fuel modulation, uncoupled dynamics of several components, and the compressibility of air trapped in the fuel line. Additionally, a novel technique to model these systems by way of one-dimensional, linear transmission line acoustic models was developed to successfully characterize the principle of operation of the two systems. Through these models, insight was gained on the modes through which modulation authority was dissipated and on methods through which successful amplitude scaling would be possible. At high amplitudes, it was found that the models were able to successfully predict the actual performance reasonably well for the piston device. A proportional phase shifting controller was used to test the authority on a 40-kW rig with natural longitudinal modes. Results show that, under limited operating conditions, the sound pressure level at the limit cycle frequency was reduced by about 26 dB and the broadband energy was reduced by 23 dB. Attenuation of the fuel pulse at several combustor settings was due to fluctuating vorticity and temporal droplet distribution effects. / Master of Science