The Electron Energy Corporation (EEC) along with National Aeronautics and Space Administration (NASA) in collaboration with Vibration Control and Electro mechanics Lab (VCEL), Texas A & M University, College Station, TX are researching on high temperature permanent magnet based magnetic bearings. The magnetic bearings are made of high temperature resistant permanent magnets (up to 1000 degrees F). A test rig has been developed to test these magnetic bearings. The test rig mainly consists of two radial bearings, one axial thrust bearing and two catcher bearings. The test rig that the catcher bearing is inserted in is the first ultra-high temperature rig with permanent magnet biased magnetic bearings and motor. The magnetic bearings are permanent magnet based which is a novel concept. The Graphalloy bearings represent a new approach for ultra-high temperature backup bearing applications. One of the main objectives of this research is to insure the mechanical and electrical integrity for all components of the test rig. Some assemblies and accessories required for the whole assembly need to be designed. The assembly methods need to be designed. The preliminary tests for coefficient of friction, Young's modulus and thermal expansion characteristics for catcher bearing material need to be done. A dynamic model needs to be designed for studying and simulating the rotor drop of the shaft onto the catcher bearing using a finite element approach in MATLAB. The assembly of the test rig was completed successfully by developing assembly fixtures and assembly methods. The components of the test rig were tested before assembly. Other necessary systems like Sensor holder system, Graphalloy press fit system were designed, fabricated and tested. The catcher bearing material (Graphalloy) was tested for coefficient of friction and Young's modulus at room and high temperatures. The rotor drop was simulated by deriving a dynamic model, to study the effect of system parameters like clearance, coefficient of friction, negative stiffness, initial spin speed on system behavior. Increasing the friction increases the backward whirl and decreases the rotor stoppage time. Increasing the clearance reduces the stoppage time and increases the peak bearing force. Increasing the initial spin speed increases the rotor stoppage time. The maximum stress encountered for as built conditions is more than allowable limits.

The research presented in this thesis focuses on the modeling, design, and experimentation of systems containing negative stiffness mechanisms for both vibration and shock isolation. The negative stiffness element studied in this research is an axially compressed beam. If a beam is axially compressed past a critical value, it becomes bistable with a region of negative stiffness in the transverse direction. By constraining a buckled beam in its metastable position through attaching a stiff linear spring in mechanical parallel, the resulting system can reach a low level of dynamic stiffness and therefore provide vibration isolation at low frequencies, while also maintaining a high load-carrying capacity. In previous research, a system containing an axially compressed beam was modeled and tested for vibration isolation [7]. In the current research, variations of this model were studied and tested for both vibration and shock isolation. Furthermore, the mathematical model used to represent the compressed beam in [7] was improved and expanded in current research. Specifically, the behavior exhibited by buckled beams of transitioning into higher-mode shapes when placed under transverse displacement was incorporated into the model of the beam. The piecewise, nonlinear transverse behavior exhibited by a first-mode buckled beam with a higher-mode transition provides the ability of a system to mimic an ideal constant-force shock isolator. Prototypes manufactured through Selective Laser Sintering were dynamically tested using a shaker table. Vibration testing confirmed the ability of a system containing a constrained negative stiffness element to provide enhanced vibration isolation results with increasing axial compression on a beam. However, the results were limited by the high sensitivity of buckled beam behavior to geometrical and boundary condition imperfections. Shock testing confirmed the ability of a system containing a buckled beam with a higher-mode transition to mimic the theoretically ideal constant-force shock isolator. / text

This work demonstrates the effectiveness of coextrusion as a method to manufacture negative stiffness inclusions for use in vibrational damping applications. The theory and mechanics of negative stiffness and coextrusion are introduced and the process of creating and extruding a feed rod with negative stiffness architecture explained. Coextrusion is shown to be a viable method to create negative stiffness inclusions / text

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Current seismic design practice promotes inelastic response in order to reduce the design forces. By allowing the structure to yield while increasing the ductility of the structure, the global forces can be kept within the limited bounds dictated by the yield strength. However, during severe earthquakes, the structures undergo significant inelastic deformations leading to stiffness and strength degradation, increased interstory drifts, and damage with residual drift. The research presented in this thesis has three components that seek to address these challenges. To prevent the inelastic effects observed in yielding systems, a new concept “apparent weakening” is proposed and verified through shake table studies in this thesis. “Apparent weakening” is introduced in the structural system using a complementary “adaptive negative stiffness device” (NSD) that mimics "yielding” of the global system thus attracting it away from the main structural system. Unlike the concept of weakening and damping, where the main structural system strength is reduced, the new system does not alter the original structural system, but produces effects compatible with an early yielding. Response reduction using NSD is achieved in a two step sequence. First the NSD, which is capable of exhibiting nonlinear elastic stiffness, is developed based on the properties of the structure. This NSD is added to the structure resulting in reduction of the stiffness of the structure and NSD assembly or “apparent weakening”-thereby resulting in the reduction of the base shear of the assembly. Then a passive damper, designed for the assembly to reduce the displacements that are caused due to the “apparent weakening”, is added to the structure-thereby reducing the base shear, acceleration and displacement in a two step process. The primary focus of this thesis is to analyze and experimentally verify the response reduction attributes of NSD in (a) elastic structural systems (b) yielding systems and (3) multistory structures. Experimental studies on 1:3 scale three-story frame structure have confirmed that consistent reductions in displacements, accelerations and base shear can be achieved in an elastic structure and bilinear inelastic structure by adding the NSD and viscous fluid damper. It has also been demonstrated that the stiffening in NSD will prevent the structure from collapsing. Analogous to the inelastic design, the acceleration and base shear and deformation of the structure and NSD assembly can be reduced by more than 20% for moderate ground motions and the collapse of structure can be prevented for severe ground motions. Simulation studies have been carried on an inelastic multistoried shear building to demonstrate the effectiveness of placing NSDs and dampers at multiple locations along the height of the building; referred to as “distributed isolation”. The results reported in this study have demonstrated that by placing a NSD in a particular story the superstructure above that story can be isolated from the effects of ground motion. Since the NSDs in the bottom floors will undergo large deformations, a generalized scheme to incorporate NSDs with different force deformation behavior in each storey is proposed. The properties of NSD are varied to minimize the localized inter-story deformation and distribute it evenly along the height of the building. Additionally, two semi-active approaches have also been proposed to improve the performance of NSD in yielding structures and also adapt to varying structure properties in real time. The second component of this thesis deals with development of a novel device to control the response of structural system using adaptive length pendulum smart tuned mass damper (ALP-STMD). A mechanism to achieve the variable pendulum length is developed using shape memory alloy wire actuator. ALP-STMD acts as a vibration absorber and since the length is tuned to match the instantaneous frequency, using a STFT algorithm, all the vibrations pertaining to the dominant frequency are absorbed. ALP-STMD is capable of absorbing all the energy pertaining to the tuned-frequency of the system; the performance is experimentally verified for forced vibration (stationary and non-stationary) and free vibration. The third component of this thesis covers the development of an adaptive control algorithm to compensate hysteresis in hysteretic systems. Hysteretic system with variable stiffness hysteresis is represented as a quasi-linear parameter varying (LPV) system and a gain scheduled controller is designed for the quasi-LPV system using linear matrix inequalities approach. Designed controller is scheduled based on two parameters: linear time-varying stiffness (slow varying parameter) and the stiffness of friction hysteresis (fast varying parameter). The effectiveness of the proposed controller is demonstrated through numerical studies by comparing the proposed controller with fixed robust H∞ controller. Superior tracking performance of the LPV-GS over the robust H∞ controller in different displacement ranges and various stiffness switching cases is clearly evident from the results presented in this thesis. The LPV-GS controller is capable of adapting to the parameter changes and is effective over the entire range of parameter variations.

This thesis focuses on the micromechanical modeling of particulate viscoelastic composite materials in the quasi-static frequency domain to approximate macroscopic damping behavior and has two main objectives. The first objective is the development of a robust frequency dependent multiscale model. For this purpose, the self-consistent (SC) mean-field micromechanical model introduced by Cherkaoui et al [J. Eng. Mater. Technol. 116, 274-278 (1994)] is extended to include frequency dependence via the viscoelastic correspondence principal. The quasi-static model is then generalized using dilute strain concentration tensor formulation and validated by comparison with complex bounds from literature, acoustic and static experimental data, and established models. The second objective is SC model implementation as a tool for the design of high loss materials. This objective is met by integrating the SC model into a Compromise Decision Support Protocol (CDSP) to explore the microstructural design space of an automobile windshield. The integrated SC-CDSP design space exploration results definitively indicate that one microstructural variable dominates structure level acoustic isolation and rigidity: negative stiffness. The work concludes with a detailed description of the fundamental mechanisms leading to negative stiffness behavior and proposes two negative stiffness inclusion designs.

Constrained negative stiffness elements in volume concentrations (1% to 2%) embedded within viscoelastic materials have been shown to provide greater energy absorption than conventional materials [Lakes et al., Nature (London) 410, 565–567 (2001)]. This class of composite materials, called meta-materials, could be utilized in a variety of applications including noise reduction, anechoic coatings and transducer backings. The mechanism underlying the meta-material's behavior relies on the ability of the negative stiffness element to locally deform the viscoelastic material, dissipating energy in the process. The work presented here focuses specifically on the design of the negative stiffness elements, which take the form of buckled beams. By constraining the beam in an unstable, S-shaped configuration, the strain energy density of the beam will be at a maximum and the beam will accordingly display negative stiffness. To date, physical realization of these structures has been limited due to geometries that are difficult to construct and refine with conventional manufacturing materials and methods. By utilizing the geometric freedoms allowed by the Selective Laser Sintering (SLS) machines, these structures can be built and tuned for specific dynamic properties. The objective of this research was to investigate the dynamic behavior of SLS-constructed meso-scale negative stiffness elements with the future intention of miniaturizing the elements to create highly absorptive meta-materials. This objective was accomplished first through the development and analysis of a mathematical model of the buckled beam system. A characterization of the Nylon 11 material was performed to obtain the material properties for the parts that were created using SLS. Applying the mathematical model and material properties, a tuned meso-scale negative stiffness structure was fabricated. Transmissibility tests of the meso-scale structure revealed that the constrained negative stiffness system was able to achieve overall higher damping and vibration isolation than an unconstrained system. Quasistatic behavior of the system indicated that these elements would be ideal for implementation within meta-materials. Based on the results of the meso-scale system, a method to test a representative volume element for a negative stiffness meta-material was developed for future completion. / text

A persistent challenge in the design of composite materials is the ability to fabricate materials that simultaneously display high stiffness and high loss factors for the creation of structural elements capable of passively suppressing vibro-acoustic energy. Relevant recent research has shown that it is possible to produce composite materials whose macroscopic mechanical stiffness and loss properties surpass those of conventional composites through the addition of trace amounts of materials displaying negative stiffness (NS) induced by phase transformation [R. S. Lakes, et al., Nature, 410, pp. 565-567, (2001)]. The present work investigates the ability to elicit NS behavior without employing physical phenomena such as inherent nonlinear material behavior (e.g., phase change or plastic deformation) or dynamic effects, but rather the controlled buckling of small-scale structural elements, metamaterials, embedded in a continuous viscoelastic matrix. To illustrate the effect of these buckled elements, a nonlinear hierarchical multiscale material model is derived which estimates the macroscopic stiffness and loss of a composite material containing pre-strained microscale structured inclusions. The nonlinear multiscale model is then utilized in a set-based hierarchical design approach to explore the design space over a wide range of inclusion geometries. Finally, prototype NS inclusions are fabricated using an additive manufacturing technique and tested to determine quasi-static inclusion stiffness which is compared with analytical predictions. / text

: Les travaux présentés dans cette thèse traitent du contrôle de systèmes dynamiques soumis à des excitations harmoniques et transitoires en utilisant des absorbeurs de type Nonlinear Energy Sink (NES). Plusieurs aspects ont été développés : la conception et la réalisation d'un nouveau design pour le NES cubique, l'étude de la location et du transfert irréversible d'énergie sur un NES bistable et le développement d'un critère de conception pour un NES à Vibro-Impact (VI). Dans un premier temps, un critère de conception est proposé pour le NES à raideur cubique. Le design proposé est basé sur des ressorts coniques ou des ressorts à pas variable. Un mécanisme à raideur négative est aussi introduit pour supprimer la partie linéaire et avoir une raideur cubique pure. Dans un deuxième temps, le concept du NES est validé expérimentalement par des essais statiques et des essais dynamiques. Une analyse de sensibilité est aussi menée sur la longueur des ressorts précontraints, elle dénote parfois un état bistable de l'oscillateur. Ensuite, le NES bistable ainsi obtenu est étudié plus en détail. Ce type d'absorbeur s'avère être très robuste pour différents types d’excitation. Des études expérimentales sont aussi menées afin d'explorer le comportement dynamique. Enfin, un critère de conception est proposé pour le NES à Vibro-Impact. Des calculs analytiques détaillés sont proposés pour contrôler les vibrations sous différentes excitations. L'étude expérimentale montre une bonne cohérence avec les résultats théoriques. / The work presented in this thesis deals with the passive control of dynamics systems subjected to harmonic and transient excitations using a Nonlinear Energy Sink (NES). Several research aspects have been developed: design theory and experimental study of a novel NES, efficient Targeted Energy Transfer (TET) of bistable NES and design criteria for optimally tuned Vibro-Impact (VI) NES. Firstly, a design criterion intended to provide optimal nonlinear stiffness is proposed. Then a novel design of NES system yielding cubic stiffness with conical springs or variable pitch springs and negative stiffness mechanism is developed. Secondly, the experimental procedures for static and dynamic test are presented and applied to validate the concept of NES system. Then a sensitivity analysis is performed with respect to the pre-compressed length of springs. Thirdly, the optimal design of the above device with negative stiffness (termed as bistable NES) is studied. This type of NES is proved to work robustly for different types of excitation, and experimental study of semi-active control are explored. Finally, design criteria for optimally tuned VI NES are studied. Detailed analytical calculations of clearance to control the vibration under different excitations are proposed. A good correspondence between theoretical and experimental results is observed.

Metamaterials are typically described as materials with ’unusual’ wave propagation properties. Originally developed for electromagnetic waves, these materials have also spread into the field of acoustic wave guiding and cloaking, with the most relevant of these ’unusual’ properties, being the so called band-gap phenomenon. A band-gap signifies a frequency region where elastic waves cannot propagate through the material, which in principle, could be used to protect buildings from earthquakes. Based on this, two relevant concepts have been proposed in the field of seismic engineering, namely: metabarriers, and metamaterial-based foundations. This thesis deals with the development of the Metafoundation, a metamaterial-based foundation system for the seismic protection of fuel storage tanks against excessive base shear and pipeline rupture. Note that storage tanks have proven to be highly sensitive to earthquakes, can trigger sever economic and environmental consequences in case of failure and were therefore chosen as a superstructure for this study. Furthermore, when tanks are protected with traditional base isolation systems, the resulting horizontal displacements, during seismic action, may become excessively large and subsequently damage connected pipelines. A novel system to protect both, tank and pipeline, could significantly augment the overall safety of industrial plants. With the tank as the primary structure of interest in mind, the Metafoundation was conceived as a locally resonant metamaterial with a band gap encompassing the tanks critical eigenfrequency. The initial design comprised a continuous concrete matrix with embedded resonators and rubber inclusions, which was later reinvented to be a column based structure with steel springs for resonator suspension. After investigating the band-gap phenomenon, a parametric study of the system specifications showed that the horizontal stiffness of the overall foundation is crucial to its functionality, while the superstructure turned out to be non-negligible when tuning the resonators. Furthermore, storage tanks are commonly connected to pipeline system, which can be damaged by the interaction between tank and pipeline during seismic events. Due to the complex and nonlinear response of pipeline systems, the coupled tank-pipeline behaviour becomes increasingly difficult to represent through numerical models, which lead to the experimental study of a foundation-tank-pipeline setup. Under the aid of a hybrid simulation, only the pipeline needed to be represented via a physical substructure, while both tank and Metafoundation were modelled as numerical substrucutres and coupled to the pipeline. The results showed that the foundation can effectively reduce the stresses in the tank and, at the same time, limit the displacements imposed on the pipeline. Leading up on this, an optimization algorithm was developed in the frequency domain, under the consideration of superstructure and ground motion spectrum. The advantages of optimizing in the frequency domain were on the one hand the reduction of computational effort, and on the other hand the consideration of the stochastic nature of the earthquake. Based on this, two different performance indices, investigating interstory drifts and energy dissipation, revealed that neither superstructure nor ground motion can be disregarded when designing a metamaterial-based foundation. Moreover, a 4 m tall optimized foundation, designed to remain elastic when verified with a response spectrum analysis at a return period of 2475 years (according to NTC 2018), reduced the tanks base shear on average by 30%. These results indicated that the foundation was feasible and functional in terms of construction practices and dynamic response, yet unpractical from an economic point of view. In order to tackle the issue of reducing the uneconomic system size, a negative stiffness mechanism was invented and implemented into the foundation as a periodic structure. This mechanism, based on a local instability, amplified the metamaterial like properties and thereby enhanced the overall system performance. Note that due to the considered instability, the device exerted a nonlinear force-displacement relationship, which had the interesting effect of reducing the band-gap instead of increasing it. Furthermore, time history analyses demonstrated that with 50% of the maximum admissible negative stiffness, the foundation could be reduced to 1/3 of its original size, while maintaining its performance. Last but not least, a study on wire ropes as resonator suspension was conducted. Their nonlinear behaviour was approximated with the Bouc Wen model, subsequently linearized by means of stochastic techniques and finally optimized with the algorithm developed earlier. The conclusion was that wire ropes could be used as a more realistic suspension mechanism, while maintaining the high damping values required by the optimized foundation layouts. In sum, a metamaterial-based foundation system is developed and studied herein, with the main findings being: (i) a structure of this type is feasible under common construction practices; (ii) the shear stiffness of the system has a fundamental impact on its functionality; (iii) the superstructure cannot be neglected when studying metamaterial-based foundations; (iv) the complete coupled system can be tuned with an optimization algorithm based on calculations in the frequency domain; (v) an experimental study suggests that the system could be advantageous to connected pipelines; (vi) wire ropes may serve as resonator suspension; and (vii) a novel negative stiffness mechanism can effectively improve the system performance.