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In practical multibody systems, various factors such as friction, joint clearances, and external events play a significant role and can greatly influence the optimal design of the system and its controller. This research focuses on the use of gradient-based optimization methods for multibody dynamic systems with the incorporation of joint friction. The dynamic formulation has been derived in using two distinct techniques: Index-1 DAE and the tangent-space formulation in minimal coordinates. It employs a two different approaches for gradient computation: direct sensitivity approach and the adjoint sensitivity approach. After a comprehensive review of different friction models developed over time, the Brown McPhee model is selected as the most suitable due to its accuracy in dynamic simulations and its compatibility with sensitivity analysis. The proposed methodology supports the simultaneous optimization of both the system and its controller. Moreover, the sensitivities obtained using these formulations have been thoroughly validated for numerical accuracy and benchmarked against other friction models that are based on dynamic events for stiction to friction transition. The approach presented is particularly valuable in applications like robotics and servo-mechanical systems where the design and actuation are closely interconnected. To obtain numerical results, a new implementation of the MBSVT (Multi-Body Systems at Virginia Tech) software package, known as MBSVT 2.0, is reprogrammed in Julia and MATLAB to ensure ease of implementation while maintaining high computational efficiency. The research includes multiple case studies that illustrate the advantages of the concurrent optimization of design and control for specific applications. Efficient techniques for control signal parameterization are presented using linear basis functions. A special focus has been made on the computational efficiency of the formulation and various techniques like sparse-matrix algebra and Jacobian-free products have been employed in the implementation. The dissertation concludes with a summary of key results and contributions and the future scope for this research. / Doctor of Philosophy / In simpler terms, this research focuses on improving the design and control of complex mechanical systems, like robots and automotive systems, by considering factors such as friction in the joints. Friction in a system can greatly affect how it performs for the desired task. The research uses a method called gradient-based optimization, which essentially means finding the most optimal parameters of the system and its controller such that they achieve a desired goal in the most optimal way. Before a model for such a system can be developed, various techniques need to be researched for incorporation of friction mathematically. A model known as Brown McPhee friction is one such model suitable for such an analysis. When optimizing any system on a computer, an iterative process needs to be performed which may prove to be very expensive in terms of computational resources required and the time taken to achieve a solution. Hence, proper mathematical and computational techniques need to be employed to ensure that the resources of a computer are utilized in the most efficient way to get the solution is the quickest way possible. Among the various novelties of this research, it is worth noting that this method that allows for simultaneous design and control optimization, which is particularly useful for applications such as robotics and servo-mechanical systems. Considering the design and control together, leads to more efficient and effective systems. The approach is tested using a software package called MBSVT 2.0, which was specifically developed as part of this research. The software is available in 3 languages: Julia, MATLAB and Fortran for universal access to people from various communities. The results from various case studies are presented that demonstrate this simultaneous design and control approach and highlights its effectiveness making the systems more robust and better performing.

In this paper we present an exponential stability result for a diffusion equation arising from dumbbell models for polymer flow. Using the methods of semigroup theory, we show that the semigroup U(t) associated with the diffusion equation is well defined and that all solutions converge exponentially to an equilibrium solution. Both finitely and infinitely extensible dumbbell models are considered. The main tool in establishing stability is the proof of compactness of the semigroup. / Ph. D.

Linear vibration absorbers are a valuable tool used to suppress vibrations due to harmonic excitation in structural systems. Limited evaluation of the performance of nonlinear vibration absorbers for nonlinear structures exists in the current literature. The state of the art is extended in this work to vibration absorbers in their three major physical implementations: the mechanical vibration absorber, the inductive-resistive shunted piezoelectric vibration absorber, and the electronic vibration absorber (also denoted a positive position feedback controller). A single, consistent, physically similar model capable of examining the response of all three devices is developed. The performance of vibration absorbers attached to single-degree-of-freedom structures is next examined for performance, robustness, and stability. Perturbation techniques and numerical analysis combine to yield insight into the tuning of nonlinear vibration absorbers for both linear and nonlinear structures. The results both clarify and validate the existing literature on mechanical vibration absorbers. Several new results, including an analytical expression for the suppression region's location and bandwidth and requirements for its robust performance, are derived. Nonlinear multiple-degree-of-freedom structures are next evaluated. The theory of Nonlinear Normal Modes is extended to include consideration of modal damping, excitation, and small linear coupling, allowing estimation of vibration absorber performance. The dynamics of the N+1-degree-of-freedom system reduce to those of a two-degree-of-freedom system on a four-dimensional nonlinear modal manifold, thereby simplifying the analysis. Quantitative agreement is shown to require a higher order model which is recommended for future investigation. Finally, experimental investigation on both single and multi-degree-of-freedom systems is performed since few experiments on this topic are reported in the literature. The experimental results qualitatively verify the analytical models derived in this work. The dissertation concludes with a discussion of future work which remains to allow nonlinear vibration absorbers, in all three physical implementations, to enter the engineer's toolbox. / Ph. D.

The purpose of this study is to investigate spatial wood structures, trace their response on equilibrium paths, identify failure modes, and predict the ultimate load. The finite element models of this study are based on the Crafts Pavilion dome (Triax) in Raleigh, North Carolina, and the Church of the Nazarene dome (Varax) in Corvallis, Oregon. Modeling considerations include 3-d beam finite elements, transverse isotropy, torsional warping, beam-decking connectors, beam-beam connectors, geometric and material nonlinearities, and the discretization of pressure loads. The primary objective of this study is to test the hypothesis that the beam-decking connectors (B-D connectors) form the weakest link of the dome. The beam-decking connectors are represented by nonlinear springs which model the load slip behavior of nails between the beam and the decking. The secondary objective of this study is to develop models that are sufficiently simple to use in engineering practice. / Ph. D.

This dissertation covers three levels of issues and solutions dealing with unbalanced and/or nonlinear situations in power electronic systems, namely power converter level, power converter system level, and large-scale power electronics system level. At power converter level, after review of traditional PWM methods, especially two-dimensional space vector modulation schemes, three-dimensional space vector modulation schemes are proposed for four-legged voltage source converters, including inverters and rectifiers. The four-legged power converters with three-dimensional space vector modulation schemes have a better DC link voltage utilization and result in a low distortion. It is an effective solution to provide the neutral point for a three-phase four-wire system and to handle the neutral current due to unbalanced load or source and nonlinear loads. Comprehensive design guidelines for a four-legged inverter are presented. The four-legged rectifier is also presented which allows not only fault tolerant operation, but also provides the flexibility of equal resistance, equal current, or equal power operation under unbalanced source. Average large-signal models of four-legged power converters in both the a-b-c and d-q-o coordinates are derived. Small signal models are obtained in the d-q-o rotating coordinates. Voltage control loops are designed in the d-q-o coordinates for a high power utility power supply. Performance is studied under various load conditions. At the power converter system level, the load conditioner concept is proposed for high power applications. A power converter system structure is proposed which consists of a high-power low-switching frequency main inverter and a low-power high-switching frequency load conditioner. The load conditioner performs multiple functions, such as active filtering, active damping, and active decoupling with a high current control bandwidth. This hybrid approach allows the overall system to achieve high performance with high power and highly nonlinear loads. At the large-scale power electronics system level, the nonlinear loading effect of load converters is analyzed for a DC distribution system. Two solutions to the nonlinear loading effect are presented. One is to confine the nonlinear load effect with the sub-converter system, the other is to use a DC bus conditioner. The DC bus conditioner is the extension of the load conditioner concept. / Ph. D.

A two part study is performed to investigate the application of reliability-based design optimization (RBDO) approach to design elastic-plastic stiffener beams with Tsection. The objectives of this study are to evaluate the benefits of reliability-based optimization over deterministic optimization, and to illustrate through a practical design example some of the difficulties that a design engineer may encounter while performing reliability-based optimization. Other objectives are to search for a computationally economic RBDO method and to utilize that method to perform RBDO to design an elastic-plastic T-stiffener under combined loads and with flexural-torsional buckling and local buckling failure modes. First, a nonlinear elastic-plastic T-beam was modeled using a simple 6 degree-of-freedom non-linear beam element. To address the problems of RBDO, such as the high non-linearity and derivative discontinuity of the reliability function, and to illustrate a situation where RBDO fails to produce a significant improvement over the deterministic optimization, a graphical method was developed. The method started by obtaining a deterministic optimum design that has the lowest possible weight for a prescribed safety factor (SF), and based on that design, the method obtains an improved optimum design that has either a higher reliability or a lower weight or cost for the same level of reliability as the deterministic design. Three failure modes were considered for an elastic-plastic beam of T cross-section under combined axial and bending loads. The failure modes are based on the total plastic failure in a beam section, buckling, and maximum allowable deflection. The results of the first part show that it is possible to get improved optimum designs (more reliable or lighter weight) using reliability-based optimization as compared to the design given by deterministic optimization. Also, the results show that the reliability function can be highly non-linear with respect to the design variables and with discontinuous derivatives. Subsequently, a more elaborate 14-degrees-of-freedom beam element was developed and used to model the global failure modes, which include the flexural-torsional and the out-of-plane buckling modes, in addition to local buckling modes. For this subsequent study, four failure modes were specified for an elasticplastic beam of T-cross-section under combined axial, bending, torsional and shear loads. These failure modes were based on the maximum allowable in-plane, out-ofplane and axial rotational deflections, in addition, to the web-tripping local buckling. Finally, the beam was optimized using the sequential optimization with reliabilitybased factors of safety (SORFS) RBDO technique, which was computationally very economic as compared to the widely used nested optimization loop techniques. At the same time, the SOPSF was successful in obtaining superior designs than the deterministic optimum designs (either up to12% weight savings for the same level of safety, or up to six digits improvement in the reliability for the same weight for a design with Safety Factor 2.50). / Ph. D.

These papers analyze two issues in resource economics that are currently debated in academic and policy arenas: global warming and overcompliant behavior amongst regulated sources of water pollution. The first paper examines the evidence for global warming in particular, the published estimates of the rate of global warming. The paper reproduces published results using the same data, provides evidence that the statistical model used to obtain these estimates is misspecified for the data, and re-specifies the model in order to obtain a statistically adequate model. The re-specified model indicates that trends in the surface temperature anomalies are highly nonlinear rather than linear and that currently published estimates of the degree of global warming are based on a misspecified model. It argues for caution in interpreting linear trend estimates and illustrates the importance of model misspecification testing and re-specification when modeling climate change using statistical models. The second paper examines recent evidence for overcompliant behavior amongst wastewater treatment plants whose pollutant discharges are regulated under the Clean Water Act. The historical evidence suggests that many regulated facilities do not comply with permit regulations. This behavior has been attributed to inadequate monitoring and enforcement by the regulatory agencies as well as to an institutional structure that penalizes noncompliance but that does not reward overcompliance. Against this backdrop, the evidence for significant and widespread overcompliance appears puzzling. The paper examines overcompliance with a widely- regulated pollutant, biochemical oxygen demand (BOD). The testable hypotheses are: whether jointness in pollution control between nitrogen and BOD can explain overcompliance and whether variation in BOD output can explain BOD overcompliance. These hypotheses are examined by developing a conceptual model of BOD overcompliance and estimating a model of BOD control. The results indicate that jointness in pollution control plays a significant role in explaining BOD overcompliance. Variation in BOD output is not a significant factor in explaining BOD overcompliance. The paper explores plausible reasons for this result and proposes significant modifications to the traditional marginal analysis of BOD overcompliance/compliance decisions. / Ph. D.

Curved panels constructed of laminated graphite-epoxy composite material are of potential interest in airframe fuselage applications. An understanding of structural response at elevated temperatures is required for anticipated future high speed aircraft applications. This study concentrates on the response of unstiffened, curved composite panels subjected to combinations of thermal and mechanical loading conditions. Mechanical loading is due to compressive end-shortening and thermal loading is due to a uniform temperature increase. Thermal stresses, which are induced by mechanical restraints against thermal expansions or contractions, cause buckling and postbuckling panel responses. Panels with three different lamination sequences are considered, including a quasi-isotropic laminate, an axially soft laminate, and an axially stiff laminate. These panels were chosen because they exhibit a range of stiffnesses and a wide variation in laminate coefficients of thermal expansion. The panels have dimensions of 10 in. by 10 in. with a base radius of 60 in. The base boundary conditions are clamped along the curved ends, and simply supported along the straight edges. Three methods are employed to study the panel response, including a geometrically nonlinear Rayleigh-Ritz solution, a finite element solution using the commercially available code STAGS, and an experimental program. The effects of inplane boundary conditions and radius of curvature are studied analytically, along with consideration of order of application in combined loading. A substantial difference is noted in the nonlinear load vs. axial strain responses of panels loaded in end-shortening and panels loaded with uniform temperature change, depending on the specific lamination sequence, boundary conditions, and radius of curvature. Experiments are conducted and results are presented for both room temperature end-shortening tests and elevated temperature tests with accompanying end-shortening. The base finite element model is modified to include measured panel thicknesses, boundary conditions representative of the experimental apparatus, measured initial geometric imperfections, and measured temperature gradients. With these modifications, and including an inherent end displacement of the panel present during thermal loading, good correlation is obtained between the experimental and numerically predicted load vs. axial strain responses from initial loading through postbuckling. / Ph. D.

The use of piezoelectric ceramic materials for structural actuation is a fairly well developed practice that has found use in a wide variety of applications. However, actuators with piezoceramic fibers and interdigitated electrodes have risen to the forefront of the intelligent structures community due to their increased actuation capability. However, their fiber-reinforced construction causes them to exhibit anisotropic piezomechanical properties, and the required larger driving voltages make the inherent piezoelectric nonlinearities more prevalent. In order to effectively utilize their increased performance, the more complicated behavior of these actuators must be sufficiently characterized. The current work is intended to provide a detailed nonlinear characterization of the mechanical and piezoelectric behavior of the Macro Fiber Composite actuator, which was developed at the NASA Langley Research Center. The mechanical behavior of this planar actuation device, which is both flexible and robust, is investigated by first developing a classical lamination model to predict its short-circuit linear-elastic properties, which are then verified experimentally. The sensitivity of this model to variations in constituent material properties is also studied. Phenomenological models are then used to represent the measured nonlinear short-circuit stress-strain response to various in-plane mechanical loads. Piezoelectric characterization begins with a nonlinear actuation model whose material parameters are determined experimentally for monotonically increasing electric fields. Next, the response of the actuator to a sinusoidal electric field input is measured under various constant mechanical loads and field amplitudes. From this procedure, the common linear piezoelectric strain coefficients are presented as a function of electric field amplitude and applied stress. In addition, a Preisach model is developed that uses the collected data sets to predict the hysteretic piezoelectric behavior of the MFC. Lastly, other related topics, such as manufacturing, cure kinetics modeling and linear thermoelasticity of the Macro Fiber Composite, are covered in the appendices. / Ph. D.