Over the past few decades there has been significant interest in the design and construction of hypersonic vehicles. Such vehicles exhibit strongly coupled aerodynamics, acoustics, heat transfer, and structural deformations, which can take significant computational efforts to simulate using standard finite element and computational fluid dynamics techniques. This situation has lead to development of various reduced order modelling (ROM) methods which reduce the parameter space of these simulations so they can be run more quickly. The planned hypersonic vehicles will be constructed by assembling a series of sub-structures, such as panels and stiffeners, that will be welded together creating built-up structures.In this light, the focus of the present investigation is on the formulation and validation of nonlinear reduced order models (NLROMs) of built-up structures that include nonlinear geometric effects induced by the large loads/large response. Moreover, it is recognized that gaps between sub-structures could result from the these intense loadings can thus the inclusion of the nonlinearity introduced by contact separation will also be addressed. These efforts, application to built-up structures and inclusion of contact nonlinearity, represent novel developments of existing NLROM strategies. A hat stiffened panel is selected as a representative example of built-up structure and a compact NRLOM is successfully constructed for this structure which exhibited a potential internal resonance. For the investigation of contact nonlinearity, two structural models were used: a cantilevered beam which can contact several stops and an overlapping plate model which can exhibit the opening/closing of a gap. Successful NLROMs were constructed for these structures with the basis for the plate model determined as a two-step process, i.e., considering the plate without gap first and then enriching the corresponding basis to account for opening of the gap. Adaptions were then successfully made to a Newton-Raphson solver to properly account for contact and the associated forces in static predictions by NLROMs.

This investigation focuses on the development of uncertainty modeling methods applicable to both the structural and thermal models of heated structures as part of an effort to enable the design under uncertainty of hypersonic vehicles. The maximum entropy-based nonparametric stochastic modeling approach is used within the context of coupled structural-thermal Reduced Order Models (ROMs). Not only does this strategy allow for a computationally efficient generation of samples of the structural and thermal responses but the maximum entropy approach allows to introduce both aleatoric and some epistemic uncertainty into the system.

While the nonparametric approach has a long history of applications to structural models, the present investigation was the first one to consider it for the heat conduction problem. In this process, it was recognized that the nonparametric approach had to be modified to maintain the localization of the temperature near the heat source, which was successfully achieved.

The introduction of uncertainty in coupled structural-thermal ROMs of heated structures was addressed next. It was first recognized that the structural stiffness coefficients (linear, quadratic, and cubic) and the parameters quantifying the effects of the temperature distribution on the structural response can be regrouped into a matrix that is symmetric and positive definite. The nonparametric approach was then applied to this matrix allowing the assessment of the effects of uncertainty on the resulting temperature distributions and structural response.

The third part of this document focuses on introducing uncertainty using the Maximum Entropy Method at the level of finite element by randomizing elemental matrices, for instance, elemental stiffness, mass and conductance matrices. This approach brings some epistemic uncertainty not present in the parametric approach (e.g., by randomizing the elasticity tensor) while retaining more local character than the operation in ROM level.

The last part of this document focuses on the development of “reduced ROMs” (RROMs) which are reduced order models with small bases constructed in a data-driven process from a “full” ROM with a much larger basis. The development of the RROM methodology is motivated by the desire to optimally reduce the computational cost especially in multi-physics situations where a lack of prior understanding/knowledge of the solution typically leads to the selection of ROM bases that are excessively broad to ensure the necessary accuracy in representing the response. It is additionally emphasized that the ROM reduction process can be carried out adaptively, i.e., differently over different ranges of loading conditions.

In the past decade, real-world applications of Vertical Take-Off and Landing (VTOL) Unmanned Aerial Vehicles (UAV) have increased significantly. There has been growing interest in one of these types of UAVs, called a tail-sitter UAV, due to its VTOL and cruise capabilities. This thesis presents the fabrication of a spherical tail-sitter UAV and derives a nonlinear mathematical model of its dynamics. The singularity in the attitude kinematics of the vehicle is avoided using Modified Rodrigues Parameters (MRP). The model parameters of the fabricated vehicle are calculated using the bifilar pendulum method, a motor stand, and ANSYS simulation software. Then the trim conditions at hover are calculated for the nonlinear model, and the rotational dynamics of the model are linearized around the equilibrium state with the calculated trim conditions. Robust controllers are designed to stabilize the UAV in hover using the H2 control and H-infinity control methodologies. For H2 control design, Linear Quadratic Gaussian (LQG) control is used. For the H infinity control design, Linear Matrix Inequalities (LMI) with frequency-dependent weights are derived and solved using the MATLAB toolbox YALMIP. In addition, a nonlinear controller is designed using the Sum-of-Squares (SOS) method to implement large-angle maneuvers for transitions between horizontal flight and vertical flight. Finally, the linear controllers are implemented in the fabricated spherical tail-sitter UAV for experimental validation. The performance trade-offs and the response of the UAV with the linear and nonlinear controllers are discussed in detail.

This investigation is focused on the consideration of structural uncertainties in nearly-straight pipes conveying fluid and on the effects of these uncertainties on the dynamic response and stability of those pipes. Of interest more specifically are the structural uncertainties which affect directly the fluid flow and its feedback on the structural response, e.g., uncertainties on/variations of the inner cross-section and curvature of the pipe. Owing to the complexity of introducing such uncertainties directly in finite element models, it is desired to proceed directly at the level of modal models by randomizing simultaneously the appropriate mass, stiffness, and damping matrices. The maximum entropy framework is adopted to carry out the stochastic modeling of these matrices with appropriate symmetry constraints guaranteeing that the nature, e.g., divergence or flutter, of the bifurcation is preserved when introducing uncertainty.

To support the formulation of this stochastic ROM, a series of finite element computations are first carried out for pipes with straight centerline but inner radius varying randomly along the pipe. The results of this numerical discovery effort demonstrate that the dominant effects originate from the variations of the exit flow speed, induced by the change in inner cross-section at the pipe end, with the uncertainty on the cross-section at other locations playing a secondary role. Relying on these observations, the stochastic reduced order model is constructed to model separately the uncertainty in inner cross-section at the pipe end and at other locations. Then, the fluid related mass, damping, and stiffness matrices of this stochastic reduced order model (ROM) are all determined from a single random matrix and a random variable. The predictions from this stochastic ROM are found to closely match the corresponding results obtained with the randomized finite element model. It is finally demonstrated that this stochastic ROM can easily be extended to account for the small effects due to uncertainty in pipe curvature.

This investigation develops small-size reduced order models (ROMs) that provide an accurate prediction of the response of only part of a structure, referred to as component-centric ROMs. Four strategies to construct such ROMs are presented, the first two of which are based on the Craig-Bampton Method and start with a set of modes for the component of interest (the β component). The response in the rest of the structure (the α component) induced by these modes is then determined and optimally represented by applying a Proper Orthogonal Decomposition strategy using Singular Value Decomposition. These first two methods are effectively basis reductions techniques of the CB basis. An approach based on the “Global - Local” Method generates the “global” modes by “averaging” the mass property over α and β comp., respectively (to extract a “coarse” model of α and β) and the “local” modes orthogonal to the “global” modes to add back necessary “information” for β. The last approach adopts as basis for the entire structure its linear modes which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component. In this manner, the non-dominant modal contributions are “lumped” onto the dominant ones, to reduce the number of modes for a prescribed accuracy. The four approaches are critically assessed on the structural finite element model of a 9-bay panel with the modal lumping-based method leading to the smallest sized ROMs. Therefore, it is extended to the nonlinear geometric situation and first recast as a rotation of the modal basis to achieve unobservable modes. In the linear case, these modes completely disappear from the formulation owing to orthogonality. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear terms of the observable modes. A closure-type algorithm is then proposed to eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, was demonstrated on a simple beam model and the 9-bay panel model.

The present investigation is part of a long-term effort focused on the development of a methodology for the computationally efficient prediction of the dynamic response of structures with multiple joints. The first part of this thesis reports on the dynamic response of nominally identical beams with a single lap joint (“Brake-Reuss” beam). The observed impact responses at different levels clearly demonstrate the occurrence of both micro- and macro-slip, which are reflected by increased damping and a lowering of natural frequencies. Significant beam-to-beam variability of impact responses is also observed.

Based on these experimental results, a deterministic 4-parameter Iwan model of the joint was developed. These parameters were randomized following a previous investigation. The randomness in the impact response predicted from this uncertain model was assessed in a Monte Carlo format through a series of time integrations of the response and found to be consistent with the experimental results.

The availability of an uncertain computational model for the Brake-Reuss beam provides a starting point to analyze and model the response of multi-joint structures in the presence of uncertainty/variability. To this end, a 4-beam frame was designed that is composed of three identical Brake-Reuss beams and a fourth, stretched one. The response of that structure to impact was computed and several cases were identified.

The presence of uncertainty implies that an exact prediction of the response of a particular frame cannot be achieved. Rather, the response can only be predicted to lie within a band reflecting the level of uncertainty. In this perspective, the computational model adopted for the frame is only required to provide a good estimate of this uncertainty band. Equivalently, a relaxation of the model complexity, i.e., the introduction of epistemic uncertainty, can be performed as long as it does not affect significantly the uncertainty band of the predictions. Such an approach, which holds significant promise for the efficient computational of the response of structures with many uncertain joints, is assessed here by replacing some joints by linear spring elements. It is found that this simplification of the model is often acceptable at lower excitation/response levels.

Gas turbine efficiency has improved over the years due to increases in compressor

pressure ratio and turbine entry temperature (TET) of main combustion gas, made viable

through advancements in material science and cooling techniques. Ingestion of main

combustion gas into the turbine rotor-stator disk cavities can cause major damage to the

gas turbine. To counter this ingestion, rim seals are installed at the periphery of turbine

disks, and purge air extracted from the compressor discharge is supplied to the disk

cavities. Optimum usage of purge air is essential as purge air extraction imparts a penalty on turbine efficiency and specific fuel consumption.

In the present work, experiments were conducted in a newly constructed 1.5-stage

axial flow air turbine featuring vanes and blades to study main gas ingestion. The disk

cavity upstream of the rotor, the 'front cavity', features a double seal with radial clearance

and axial overlap at its rim. The disk cavity downstream of the rotor, the 'aft cavity', features a double seal at its rim but with axial gap. Both cavities contain a labyrinth seal radially inboard; this divides each disk cavity into an 'inner cavity' and a 'rim cavity'.

Time-averaged static pressure at various locations in the main gas path and disk

cavities, and tracer gas (CO2) concentration at different locations in the cavities were

measured. Three sets of experiments were carried out; each set is defined by the main air flow rate and rotor speed. Each of the three sets comprises of four different purge air flow rates, low to high.

The mass flow rate of ingested main gas into the front and aft rim cavities is

reported at the different purge air flow rates, for the three experiment sets. For the present stage configuration, it appears that some ingestion persisted into both the front and aft rim cavities even at high purge air flow rates. On the other hand, the front and aft inner cavity were completely sealed at all purge flows.

Recent studies of the occurrence of post-flutter limit cycle oscillations (LCO) of the F-16 have provided good support to the long-standing hypothesis that this phenomenon involves a nonlinear structural damping. A potential mechanism for the appearance of nonlinearity in the damping are the nonlinear geometric effects that arise when the deformations become large enough to exceed the linear regime. In this light, the focus of this investigation is first on extending nonlinear reduced order modeling (ROM) methods to include viscoelasticity which is introduced here through a linear Kelvin-Voigt model in the undeformed configuration. Proceeding with a Galerkin approach, the ROM governing equations of motion are obtained and are found to be of a generalized van der Pol-Duffing form with parameters depending on the structure and the chosen basis functions. An identification approach of the nonlinear damping parameters is next proposed which is applicable to structures modeled within commercial finite element software.

The effects of this nonlinear damping mechanism on the post-flutter response is next analyzed on the Goland wing through time-marching of the aeroelastic equations comprising a rational fraction approximation of the linear aerodynamic forces. It is indeed found that the nonlinearity in the damping can stabilize the unstable aerodynamics and lead to finite amplitude limit cycle oscillations even when the stiffness related nonlinear geometric effects are neglected. The incorporation of these latter effects in the model is found to further decrease the amplitude of LCO even though the dominant bending motions do not seem to stiffen as the level of displacements is increased in static analyses.

This paper addresses some aspects of the development of fully coupled thermal-structural reduced order modeling of planned hypersonic vehicles. A general framework for the construction of the structural and thermal basis is presented and demonstrated on a representative panel considered in prior investigations. The thermal reduced order model is first developed using basis functions derived from appropriate conduction eigenvalue problems. The modal amplitudes are the solution of the governing equation, which is nonlinear due to the presence of radiation and temperature dependent capacitance and conductance matrices, and the predicted displacement field is validated using published data. A structural reduced order model was developed by first selecting normal modes of the system and then constructing associated dual modes for the capturing of nonlinear inplane displacements. This isothermal model was validated by comparison with full finite element results (Nastran) in static and dynamic loading environments. The coupling of this nonlinear structural reduced order model with the thermal reduced order model is next considered. Displacement-induced thermal modes are constructed in order to account for the effect that structural deflections will have on the thermal problem. This coupling also requires the enrichment of the structural basis to model the elastic deformations that may be produced consistently with the thermal reduced order model. The validation of the combined structural-thermal reduced order model is carried out with pure mechanical loads, pure thermal loads, and combined mechanical-thermal excitations. Such comparisons are performed here on static solutions with temperature increases up to 2200F and pressures up to 3 psi for which the maximum displacements are of the order of 3 thicknesses. The reduced order model predicted results agree well with the full order finite element predictions in all of these various cases. A fully coupled analysis was performed in which the solution of the structural-thermal-aerodynamic reduced order model was carried out for 300 seconds and validated against a full order model. Finally, a reduced order model of a thin, aluminum beam is extended to include linear variations with local temperature of the elasticity tensor and coefficients of thermal expansion.

Civil infrastructures are susceptible to damage under the events of natural or manmade disasters. Over the last two decades, the use of emerging engineering materials, such as the fiber-reinforced plastics (FRPs), in structural retrofitting have gained significant popularity. However, due to their inherent brittleness and lack of energy dissipation, undesirable failure modes of the FRP-retrofitted systems, such as sudden laminate fracture and debonding, have been frequently observed. In this light, a Carbon-fiber reinforced Hybrid-polymeric Matrix Composite (or CHMC) was developed to provide a superior, yet affordable, solution for infrastructure damage mitigation and protection. The microstructural and micromechanical characteristics of the CHMC was investigated using scanning electron microscopy (SEM) and nanoindentation technique. The mechanical performance, such as damping, was identified using free and forced vibration tests. A simplified analytical model based on micromechanics was developed to predict the laminate stiffness using the modulus profile tested by the nanoindentation. The prediction results were verified by the flexural modulus calculated from the vibration tests. The feasibility of using CHMC to retrofit damaged structural systems was investigated via a series of structural component level tests. The effectiveness of using CHMC versus conventional carbon-fiber reinforced epoxy (CF/ epoxy) to retrofit notch damaged steel beams were tested. The comparison of the test results indicated the superior deformation capacity of the CHMC retrofitted beams. The full field strain distributions near the critical notch tip region were experimentally determined by the digital imaging correlation (DIC), and the results matched well with the finite element analysis (FEA) results. In the second series of tests, the application of CHMC was expanded to retrofit the full-scale fatigue-damaged concrete-encased steel (or SRC) girders. Similar to the notched steel beam tests, the CHMC retrofitted SRC girders exhibited substantially better post-peak load ductility than that of CF/ epoxy retrofitted girder. Lastly, a quasi-static push over test on the CHMC retrofitted reinforced concrete shear wall further highlighted the CHMC's capability of enhancing the deformation and energy dissipating potential of the damaged civil infrastructure systems. Analytical and numerical models were developed to assist the retrofitting design using the newly developed CHMC material.