Generalized modal identification of linear and nonlinear dynamic systems

This dissertation is concerned with the problem of determining the dynamic characteristics of complicated engineering systems and structures from the measurements made during dynamic tests or natural excitations. Particular attention is given to the identification and modeling of the behavior of structural dynamic systems in the nonlinear hysteretic response regime. Once a model for the system has been identified, it is intended to use this model to assess the condition of the system and to predict the response to future excitations.

A new identification methodology based upon a generalization of the method of modal identification for multi-degree-of-freedom dynaimcal systems subjected to base motion is developed. The situation considered herein is that in which only the base input and the response of a small number of degrees-of-freedom of the system are measured. In this method, called the generalized modal identification method, the response is separated into "modes" which are analogous to those of a linear system. Both parametric and nonparametric models can be employed to extract the unknown nature, hysteretic or nonhysteretic, of the generalized restoring force for each mode.

In this study, a simple four-term nonparametric model is used first to provide a nonhysteretic estimate of the nonlinear stiffness and energy dissipation behavior. To extract the hysteretic nature of nonlinear systems, a two-parameter distributed element model is then employed. This model exploits the results of the nonparametric identification as an initial estimate for the model parameters. This approach greatly improves the convergence of the subsequent optimization process.

The capability of the new method is verified using simulated response data from a three-degree-of-freedom system. The new method is also applied to the analysis of response data obtained from the U.S.-Japan cooperative pseudo-dynamic test of a full-scale six-story steel-frame structure.

The new system identification method described has been found to be both accurate and computationally efficient. It is believed that it will provide a useful tool for the analysis of structural response data.

Earthquake response of steel braces and braced steel frames

This thesis consists of three parts. Chapter 2 deals with the dynamic buckling behavior of steel braces under cyclic axial end displacement. Braces under such a loading condition belong to a class of "acceleration magnifying" structural components, in which a small motion at the loading points can cause large internal acceleration and inertia. This member-level inertia is frequently ignored in current studies of braces and braced structures. This chapter shows that, under certain conditions, the inclusion of the member-level inertia can lead to brace behavior fundamentally different from that predicted by the quasi-static method. This result is to have significance in the correct use of the quasi-static, pseudo-dynamic and static condensation methods in the simulation of braces or braced structures under dynamic loading. The strain magnitude and distribution in the braces are also studied in this chapter.

Chapter 3 examines the effect of column uplift on the earthquake response of braced steel frames and explores the feasibility of flexible column-base anchoring. It is found that fully anchored braced-bay columns can induce extremely large internal forces in the braced-bay members and their connections, thus increasing the risk of failures observed in recent earthquakes. Flexible braced-bay column anchoring can significantly reduce the braced bay member force, but at the same time also introduces large story drift and column uplift. The pounding of an uplifting column with its support can result in very high compressive axial force.

Chapter 4 conducts a comparative study on the effectiveness of a proposed non-buckling bracing system and several conventional bracing systems. The non-buckling bracing system eliminates buckling and thus can be composed of small individual braces distributed widely in a structure to reduce bracing force concentration and increase redundancy. The elimination of buckling results in a significantly more effective bracing system compared with the conventional bracing systems. Among the conventional bracing systems, bracing configurations and end conditions for the bracing members affect the effectiveness.

The studies in Chapter 3 and Chapter 4 also indicate that code-designed conventionally braced steel frames can experience unacceptably severe response under the strong ground motions recorded during the recent Northridge and Kobe earthquakes.

Frictional properties of faults : from observation on the Longitudinal Valley Fault, Taiwan, to dynamic simulations

Faults can slip either aseismically or through episodic seismic ruptures, but we still do not understand the factors which determine the partitioning between these two modes of slip. This challenge can now be addressed thanks to the dense set of geodetic and seismological networks that have been deployed in various areas with active tectonics. The data from such networks, as well as modern remote sensing techniques, indeed allow documenting of the spatial and temporal variability of slip mode and give some insight. This is the approach taken in this study, which is focused on the Longitudinal Valley Fault (LVF) in Eastern Taiwan. This fault is particularly appropriate since the very fast slip rate (about 5 cm/yr) is accommodated by both seismic and aseismic slip. Deformation of anthropogenic features shows that aseismic creep accounts for a significant fraction of fault slip near the surface, but this fault also released energy seismically, since it has produced five M_w>6.8 earthquakes in 1951 and 2003. Moreover, owing to the thrust component of slip, the fault zone is exhumed which allows investigation of deformation mechanisms. In order to put constraint on the factors that control the mode of slip, we apply a multidisciplinary approach that combines modeling of geodetic observations, structural analysis and numerical simulation of the "seismic cycle". Analyzing a dense set of geodetic and seismological data across the Longitudinal Valley, including campaign-mode GPS, continuous GPS (cGPS), leveling, accelerometric, and InSAR data, we document the partitioning between seismic and aseismic slip on the fault. For the time period 1992 to 2011, we found that about 80-90% of slip on the LVF in the 0-26 km seismogenic depth range is actually aseismic. The clay-rich Lichi M\'elange is identified as the key factor promoting creep at shallow depth. Microstructural investigations show that deformation within the fault zone must have resulted from a combination of frictional sliding at grain boundaries, cataclasis and pressure solution creep. Numerical modeling of earthquake sequences have been performed to investigate the possibility of reproducing the results from the kinematic inversion of geodetic and seismological data on the LVF. We first investigate the different modeling strategy that was developed to explore the role and relative importance of different factors on the manner in which slip accumulates on faults. We compare the results of quasi dynamic simulations and fully dynamic ones, and we conclude that ignoring the transient wave-mediated stress transfers would be inappropriate. We therefore carry on fully dynamic simulations and succeed in qualitatively reproducing the wide range of observations for the southern segment of the LVF. We conclude that the spatio-temporal evolution of fault slip on the Longitudinal Valley Fault over 1997-2011 is consistent to first order with prediction from a simple model in which a velocity-weakening patch is embedded in a velocity-strengthening area.

Discrete Modeling of Granular Media: A NURBS-based Approach

This dissertation is concerned with the development of a new discrete element method (DEM) based on Non-Uniform Rational Basis Splines (NURBS). With NURBS, the new DEM is able to capture sphericity and angularity, the two particle morphological measures used in characterizing real grain geometries. By taking advantage of the parametric nature of NURBS, the Lipschitzian dividing rectangle (DIRECT) global optimization procedure is employed as a solution procedure to the closest-point projection problem, which enables the contact treatment of non-convex particles. A contact dynamics (CD) approach to the NURBS-based discrete method is also formulated. By combining particle shape flexibility, properties of implicit time-integration, and non-penetrating constraints, we target applications in which the classical DEM either performs poorly or simply fails, i.e., in granular systems composed of rigid or highly stiff angular particles and subjected to quasistatic or dynamic flow conditions. The CD implementation is made simple by adopting a variational framework, which enables the resulting discrete problem to be readily solved using off-the-shelf mathematical programming solvers. The capabilities of the NURBS-based DEM are demonstrated through 2D numerical examples that highlight the effects of particle morphology on the macroscopic response of granular assemblies under quasistatic and dynamic flow conditions, and a 3D characterization of material response in the shear band of a real triaxial specimen.

A systems approach to cardiovascular health and disease with a focus on aortic wave dynamics

Cardiovascular diseases (CVDs) have reached an epidemic proportion in the US and worldwide with serious consequences in terms of human suffering and economic impact. More than one third of American adults are suffering from CVDs. The total direct and indirect costs of CVDs are more than $500 billion per year. Therefore, there is an urgent need to develop noninvasive diagnostics methods, to design minimally invasive assist devices, and to develop economical and easy-to-use monitoring systems for cardiovascular diseases. In order to achieve these goals, it is necessary to gain a better understanding of the subsystems that constitute the cardiovascular system. The aorta is one of these subsystems whose role in cardiovascular functioning has been underestimated. Traditionally, the aorta and its branches have been viewed as resistive conduits connected to an active pump (left ventricle of the heart). However, this perception fails to explain many observed physiological results. My goal in this thesis is to demonstrate the subtle but important role of the aorta as a system, with focus on the wave dynamics in the aorta.

The operation of a healthy heart is based on an optimized balance between its pumping characteristics and the hemodynamics of the aorta and vascular branches. The delicate balance between the aorta and heart can be impaired due to aging, smoking, or disease. The heart generates pulsatile flow that produces pressure and flow waves as it enters into the compliant aorta. These aortic waves propagate and reflect from reflection sites (bifurcations and tapering). They can act constructively and assist the blood circulation. However, they may act destructively, promoting diseases or initiating sudden cardiac death. These waves also carry information about the diseases of the heart, vascular disease, and coupling of heart and aorta. In order to elucidate the role of the aorta as a dynamic system, the interplay between the dominant wave dynamic parameters is investigated in this study. These parameters are heart rate, aortic compliance (wave speed), and locations of reflection sites. Both computational and experimental approaches have been used in this research. In some cases, the results are further explained using theoretical models.

The main findings of this study are as follows: (i) developing a physiologically realistic outflow boundary condition for blood flow modeling in a compliant vasculature; (ii) demonstrating that pulse pressure as a single index cannot predict the true level of pulsatile workload on the left ventricle; (iii) proving that there is an optimum heart rate in which the pulsatile workload of the heart is minimized and that the optimum heart rate shifts to a higher value as aortic rigidity increases; (iv) introducing a simple bio-inspired device for correction and optimization of aortic wave reflection that reduces the workload on the heart; (v) deriving a non-dimensional number that can predict the optimum wave dynamic state in a mammalian cardiovascular system; (vi) demonstrating that waves can create a pumping effect in the aorta; (vii) introducing a system parameter and a new medical index, Intrinsic Frequency, that can be used for noninvasive diagnosis of heart and vascular diseases; and (viii) proposing a new medical hypothesis for sudden cardiac death in young athletes.