The methods for analysis of a three degree-of-freedom nonlinear optical support system, subject to periodic and random vibration, are presented. The analysis models were taken from those generated for the dynamic problems related to the NASA Space Infrared Telescope Facility (SIRTF). The models treat the one meter, 116 kilogram (258 pound) primary mirror of the SIRTF as a rigid mass, with elastic elements representing the mirror support structure. Both linear and nonlinear elastic supports are evaluated for the SIRTF. Advanced Continuous Simulation Language (ACSL), a commercially available software package for numerical solution of nonlinear, time-dependent differential equations, was used for all models. The methods presented for handling the nonlinear differential equations can be readily adapted for handling other similar dynamics problems.

A fluid layer of binary alloy is cooled from above with solidification occurring at the lower boundary. Some latent heat and light material is released at the freezing boundary. We assume, due to a small cooling rate and a large thermal diffusivity, that the net effect of thermal buoyancy is insignificant and convection is mainly driven by compositional buoyancy associated with the release of light material. The freezing interface advances upward at a slow speed as a result of solidified binary alloy. A stability problem is formulated for the eigenvalue R as a function of Q and S, where R is a ratio of the release rate of light material at the lower boundary to that diffused by pressure gradient, Q is associated with light material diffused by pressure gradient and S is a ratio of the specific volume change upon solidification to that due to compositional change. Before the onset of convective instability, material is diffused by the pressure and compositional gradients. Convective instability is possible provided R > 1. For infinite Schmidt number P(,L), instability sets in stationarily at the marginal state and the mode having the smallest minimum eigenvalue becomes dominant. Three different modes of instabilities, depending on Q and S, are shown: cellular convective modes of both long and short wavelength and morphological mode of short wavelength. Morphological instabilities, associated with the unstable growth of the freezing interface, occur when the conducting layer near the freezing interface is constitutionally supercooled. The results indicate that cellular convective modes require R 1 + S. Nonlinear analysis shows that disturbances just past the marginal state behave like (R-R(,c))(' 1/2), where R(,c) is the critical eigenvalue. Subcritical instabilities are possible for cellular convective modes of long wavelength other than rolls. Taking into / account the effect of the curved interface, the surface tension tends to suppress the unstable growth of the freezing interface. For fixed values of Q and S, morphological modes with surface tension have larger minimum eigenvalues than those without surface tension. / Source: Dissertation Abstracts International, Volume: 43-04, Section: B, page: 1170. / Thesis (Ph.D.)--The Florida State University, 1982.

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In electronic packaging, solder joints in surface mount technology are used for not only electrical connections, but mechanical connections as well. Due to the mismatch of the coefficients of thermal expansion of different components in chip-substrate systems, solder joints under thermal cycles could develop thermal stress inside and therefore experience fatigue failure after a certain number of load cycles. In this work, the disturbed state concept (DSC) model, a unified and hierarchical approach to model a variety of materials such as soils, rocks, ceramics, metals, and alloys, was appropriately modified to characterize a 63Sn-37Pb solder. This includes a modified hardening function that eliminates some inconsistency in the HISS-delta0 model when the bonding stress is nonzero, and a different fully adjusted state that is properly assumed from test data on the 63Sn-37Pb solder. A generalized computer procedure was then developed for 3-D constitutive level back prediction with the DSC model. In addition, a modified computer procedure for parameter determination was proposed and implemented to calculate the relative intact stress-strain curve for simple shear test data automatically. The above procedures for parameter determination and back prediction were used to model simple shear tests of the 63Sn-37Pb solder at different temperatures and strain rates. Based on material properties determined from test data at different combinations of temperature and strain rate, constitutive level back predictions were performed for each test data set using (1) specific material properties and (2) temperature and rate dependent material properties. Further, a 3-D DSC FEA (finite element analysis) program was used to simulate the same stress-strain behaviors of solder joints at different temperatures and strain rates. The results from back prediction and 3-D FEA simulation show that the test data have been better characterized by the modified DSC model. Moreover, 2-D and 3-D DSC FEA programs were employed to study the fatigue failure of a 144-Pin PBGA solder ball under cyclic thermomechanical loading. An accelerated-approximate procedure was incorporated into the 3-D FEA program to reduce the computational effort for fatigue analysis. Results of 3-D FEAs show that the 3-D geometry of a solder joint has significant influences on its fatigue life. The comparison of 2-D and 3-D results with the test results for the 144-pin PBGA solder ball indicates the FEA results are consistent with the initiation of failure observed in laboratory test. In addition, failure criteria based on fractional volume were also proposed for 2-D and 3-D FEAs by calibration of the available test results.

In this research the cylindrically guided wave inspection technique is proposed for detecting the anomalies in a pipe. Efficient inspection of pipelines for internal and external damages is a challenging task in the chemical and power industries where long pipelines are used and the pipes are coated by insulating materials. Under traditional methods insulation coatings are removed at selected places, then the pipe wall thickness at these spots is measured by ultrasonic transducers. This is a time-consuming and expensive operation since the operation requires point-to-point examination. Guided wave ultrasonics, proposed in this research, is a much more efficient technique because by this technique long pipes can be inspected by removing insulation at only limited places. Detecting anomalies inside the pipe wall at a specific depth can be realized by correctly selecting a cylindrical guided wave and propagating that mode through the pipe. A new transducer holder mechanism has been designed and fabricated for pipe inspection by cylindrical guided waves. A number of advanced coupling mechanisms developed recently for large plate and pipe inspection require the presence of a coupling fluid between the ultrasonic transducer and the pipe or plate specimen. These mechanisms can be used for inspecting horizontal pipes and plates. Commercially available ultrasonic transducers have been used to generate compressional ultrasonic waves in the coupling medium. Those waves are converted to cylindrical guided waves in the pipe by the new coupling mechanism. The new coupling mechanism presented in this research uses solid material as the coupler and can be used equally well for inspecting horizontal as well as inclined or vertical pipes. The new coupling mechanism has been designed to generate efficiently different guided wave modes in the pipe. Different kinds of anomalies in pipes have been successfully inspected. The preliminary results show that a number of Lamb modes when generated properly by the new coupling mechanism are very sensitive to pipe defects. These experimental results along with the new design of the coupling mechanism are presented in this dissertation.

Uniformly sampled filter-bank transforms and their inverses are introduced and the conditions to obtain perfect reconstruction upon inversion are explored. It is shown that perfect reconstruction requires both filter addition and multiplication and the necessary and sufficient conditions for these operations are given. Examples indicate how to use the conditions to construct perfect-reconstruction synthesis filters from a given set of analysis filters. Additionally, an iterative scheme is presented that achieves exact inversion to an arbitrary accuracy. The methods to obtain synthesis filters are applied to discretizations of the continuous wavelet transform using both finite and infinite impulse response filters. If exact reconstruction is not a requisite, it is possible to improve imperfect-reconstruction filter banks so that their inverse is closer to the input signal. Two methods to achieve such improvement are described. To better understand the discretizations, one has to look at the continuous case. Therefore the discrete-time filter-bank transforms definitions are extended to continuous-time signal processing. It is shown that the Gabor and continuous wavelet transforms are special cases of the continuous-time extension. The methods introduced in the discrete-time case are used to derive all the linear time-invariant synthesis functions of these two transforms. A straightforward generalization of the Gabor and wavelet transforms generates filter banks whose bandwidths can vary arbitrarily with center frequency. These filters are used to create a cochlear transform, i.e., a "mixed" transform that behaves like a Gabor transform at low center frequencies and like a continuous wavelet transform at high center frequencies. The methodology described in this thesis is implemented in a set of algorithms whose complete documentation are given in chapter 4.

Material characterization is a very important tool needed to describe and enhance material mechanical properties and to develop optimum material chemistries and microstructures. The usual approach of achieving the above using extensive experimental methods has been shown to be expensive and time consuming. This led to the development of the micro mechanical modeling, which can be used to predict the material behavior without the need for the extensive experimental investigation and is based on microstructural characteristics of the material. / In this work, a micro mechanical model is developed to predict the mechanical properties of dual phase steels consisting of martensite in a matrix of ferrite. This micro model is also used to elucidate the mechanics and mechanisms of deformation, which take place in such materials. DP-steels consisting of several volume fractions of martensite (Vm) representing low, intermediate and high Vm are developed and tested mechanically to obtain their mechanical properties. Metallographical examinations are carried out using image analysis to quantify microstructural material properties of each level of Vm considered. As a validation of the current work, comparison between the model predictions, which include all the significant material behavior investigated in this work and the experimental results, is presented. The comparison demonstrates the ability of the model to capture the behavior of DP-steels up to the instability point. / The Gurson-Tvergaard model, which is the most widely known damage model to describe ductile failure, is coupled with the results of the micro mechanical model, presented in this work to form a complete material model of deformation and fracture of DP-steels. A procedure is developed to determine the parameters in the Gurson-Tvergaard model utilizing the micromechanical model. The results are then implemented to simulate the deformation and failure of tensile bars of DP-steels with different Vm, which shows good agreement with the experimental results at failure.

In this thesis, we propose several algorithms for model reduction of second order dynamical systems. These various projection methods are based on singular value decomposition, Krylov projection, and balanced truncation. In many cases models are given in second order form, and the goal is to produce a reduced order system which is in second order form, gives an accurate approximation of the original system, and maintains some important properties such as stability and passivity. Model reduction on first order linear time invariant dynamical systems has been extensively studied, algorithms and theory are well-developed. People usually study and deal with second order system by transforming to first order form which doubles the dimension. This can be inefficient and generally does not respect the second order form. The reduced model is not realizable as a second order system. So far only a very few algorithms have been proposed for second order model reduction. Most of these are not practical for large scale settings, and no error bounds have been provided. In this thesis, a global error bound is given for some of the algorithms based on SVD and balanced truncation, the error bound is bounded by a constant times the summation of the neglected singular (or Hankel singular) values, that means those second order model reduction algorithms provide accurate approximations to the original systems. The structures of controllability and observability Gramians P and Q are discussed. All algorithms developed in this thesis have been implemented and shown to be numerically efficient, and applicable to large scale settings. All algorithms are implemented in Matlab, some of them are implemented in Fortran and C separately for which we use LAPACK. In this thesis, we apply our algorithms to three real models. The performance of our algorithms is compared with some of the previously existing algorithms. It turns out that most of our algorithms are very competitive with existing methods.

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