Most engineering structures include nonlinearity to some degree. Depending on the dynamic conditions and level of external forcing, sometimes a linear structure assumption may be justified. However, design requirements of sophisticated structures such as satellites, stabilized weapon systems and radars may require nonlinear behavior to be considered for better performance. Therefore, it is very important to successfully detect, localize and parametrically identify nonlinearity in such cases. In engineering applications, the location of nonlinearity and its type may not be always known in advance. Furthermore, as the structure will be excited from only a few coordinates, the frequency response function matrices will not be complete. In order to parametrically identify more than one type of nonlinearity which may co-exist at the same location with the above mentioned limitations, a method is proposed where restoring force surface plots are used which are evaluated by describing function inversion. Then, by reformulating this method, a second method is proposed which can directly evaluate the total describing function of more than one type of nonlinearity which may co-exist at the same location without using any linear frequency response function matrix. It is also aimed in this study to use the nonlinearity localization formulations for damage localization purposes. The validation of the methods developed in this study is demonstrated with case studies based on simulated experiments, as well as real experiments with nonlinear structures and it is concluded that the methods are very promising to be used in engineering structures.

In this paper we examine the stabilization of LTI discrete-time systems with control input constraints in the form of saturation nonlinearities. This kind of constraint is usually introduced to simulate the effect of actuator limitations. Since global controllability can not be assumed in the presence of constrained control, the controllable regions and their characterizations are analyzed first. We present an efficient algorithm for finding controllable regions in terms of their boundary hyperplanes (inequality constraints). A previously open question about the exact number of irredundant boundary hyperplanes is also resolved here. The main result of this research is a time-optimal nonlinear controller which stabilizes the system on its controllable region. We give analgorithm for on-line computation of control which is also implementable for high-order systems. Simulation results show superior response even in the presence of disturbances.

In this paper we examine the stabilization of LTI discrete-time systems with control input constraints in the form of saturation nonlinearities. This kind of constraint is usually introduced to simulate the effect of actuator limitations. Since global controllability can not be assumed in the presence of constrained control, the controllable regions and their characterizations are analyzed first. We present an efficient algorithm for finding controllable regions in terms of their boundary hyperplanes (inequality constraints). A previously open question about the exact number of irredundant boundary hyperplanes is also resolved here. The main result of this research is a time-optimal nonlinear controller which stabilizes the system on its controllable region. We give analgorithm for on-line computation of control which is also implementable for high-order systems. Simulation results show superior response even in the presence of disturbances.

Group of piles are widely used deep foundation systems to resist lateral and vertical loads. Seismic and static performance of pile groups mostly depend on soil type, pile spacing and pier rigidity. Not many pile lateral load tests have been performed due to high costs. Advanced and complex analytical methods were developed over the years to assess nonlinear lateral pile response. This research is conducted aiming at developing a practical analysis method to verify the lateral performance of pile groups and its effect on overall response of bridge utilizing the available pile lateral load test data. Empirical constants derived from evaluation of lateral load tests are used in a simple formulation to define the nonlinear behavior of the pile-soil system. An analysis guideline is established to model the nonlinear soil-bridge interaction by the help of a general purpose structural analysis program comprising recommendations for various cases. Results of the proposed method is compared to the results of industry accepted advanced methods using response spectrum and nonlinear time history analyses to assess the suitability of this new application. According to the analysis results, proposed simple method can be used as an effective analysis tool for the determination of response of the superstructure.

We introduce a steepest-descent-like search algorithm for the design of Boolean functions, yielding multiple desirable cryptographic properties in their Walsh and autocorrelation spectra together. The algorithm finds some Boolean functions on 9, 10, 11, 13 variables with very good cryptographic properties unattained in the literature. More specifically, we have discovered 9-variable rotation symmetric Boolean functions (RSBFs) having nonlinearity of 241, which exceeds the bent concatenation bound and has remained as an open question in the literature for almost three decades. We have then shown that there is no RSBF having nonlinearity greater than 241, and that there are 8x189 many RSBFs having nonlinearity of 241, such that, among them there are only two that are different up to the affine equivalence. We also propose a generalization to RSBFs and dihedral symmetric Boolean functions (DSBFs), which improves the nonlinearity result of 9-variable Boolean functions to 242. Further, we classify all possible permutations (362, 880) on the input variables of 9-variable Boolean functions and find that there are only 30 classes, which are different with respect to the linear equivalence of invariant Boolean functions under some permutations. Some of these classes and their subsets yield new 9-variable Boolean functions having the nonlinearity of 242 with different autocorrelation spectra from those of the Boolean functions found in generalized RSBF and DSBF classes. Moreover, we have attained 13-variable balanced Boolean functions having nonlinearity of 4036 which is greater than the bent concatenation bound of 4032, and improves the recent result of 4034.

Chatter is unwanted since it causes deteriorating effects on the milling process. Stability lobe diagrams are developed in order to determine the stable cutting conditions at which chatter-free machining can be made. The need of cutting away more chips to make milling operations quicker has brought the concept of high-speed milling. This increased the importance of estimating stability lobe diagrams of the milling process more accurately. The state-of-art chatter and spindle-toolholder-tool models predict the stability lobe diagram for milling process quite effectively. However, sometimes chatter might occur even at cutting conditions selected using theoretically obtained stability lobe diagrams. One of the reasons for that may be nonlinearities in the system. This being the motivation, in this work, nonlinearities at the bearings of spindle-toolholder-tool system are investigated. In this thesis, cubic nonlinearity is assumed to represent stiffness of a bearing in a spindle-toolholder-tool system. Effects of nonlinearity on stability lobe diagram of a milling process are studied by using the mathematical model developed for such a system. Frequency response function of spindle-toolholder-tool system without bearings is obtained using Timoshenko beam model. Then, bearings are modeled by using describing function theory and coupled to the dynamics of spindle-toolholder-tool modeled. Solution of the equations of motion of the system in frequency domain is obtained via Newton&#039 / s method with ALC. It is an effective frequency domain method in which turning points on frequency response function are traced. This is important for the system studied, as bearing nonlinearity may introduce turn backs in the response of the system. Case studies are carried out to study the effects of bearing nonlinearity on stability lobe diagram. The effects of the following factors are studied: Magnitude of cutting force, degree of nonlinearity and number of teeth on cutter. Displacement amplitude dependent stiffness of bearings affects the dynamic response due to rigid body modes of the system. It is observed that an increase in cutting force magnitude or in coefficient of bearing nonlinearity results in increase of natural frequencies, thus showing hardening behavior. Shifting of frequencies in the response curve shifts stability lobes related to the affected modes, to the right. For increased number of flutes on cutter, effect of nonlinearity at bearings on stability of the milling process becomes lower. Experimental studies to determine the changes in dynamics of a system during cutting are also carried out in this thesis. Inverse chatter analysis is conducted to obtain modal parameters of a single-degree-of-freedom system using the experiment data. Decrease in natural frequency is observed at high cutting speeds for the particular spindle used. This shift may be due to speed-dependent bearing dynamics and real time adjustment of preload on bearings.

Asphalt mixtures are complex composites that comprise aggregate, asphalt binder, and air. Several research studies have shown that the mechanical behavior of the asphalt mixture is strongly influenced by the matrix, i.e. the asphalt binder. Therefore, accurate constitutive models for the asphalt binders are critical to ensure accurate performance predictions at a material and structural level. However, researchers who use computational methods to model the micromechanics of asphalt mixtures typically assume that (i) asphalt binders behave linearly in shear, and (ii) either bulk modulus or Poisson’s ratio of asphalt binders is not time dependent. This research develops an approach to measure and model the shear and bulk behavior of asphalt binders at intermediate temperatures. First, this research presents the findings from a systematic investigation into the nature of the linear and nonlinear response of asphalt binders subjected to shear using a Dynamic Shear Rheometer (DSR). The DSR test results showed that under certain conditions a compressive normal force was generated in an axially constrained specimen subjected to cyclic torque histories. This normal force could not be solely attributed to the Poynting effect and was also related to the tendency of the asphalt binder to dilate when subjected to shear loads. The generated normal force changed the state of stress and interacted with the shear behavior of asphalt binder. This effect was considered to be an “interaction nonlinearity” or “three dimensional effect”. A constitutive model was identified to accommodate this effect. The model was successfully validated for several different loading histories. Finally, this study investigated the time-dependence of the bulk modulus of asphalt binders. To this end, poker-chip geometries with high aspect ratios were used. The boundary value problem for the poker-chip geometry under step displacement loading was solved to determine the bulk modulus and Poisson’s ratio of asphalt binders as a function of time. The findings from this research not only improve the understanding of asphaltic materials behavior, but also provide tools required to accurately predict pavement performance. / text

In this thesis, two finalists of the AES (Advanced Encryption Standard) contest, RC6 developed by Rivest et al, Twofish proposed by Schneier et al, and preceding algorithm of RC6 cipher, RC5, are studied. The strength of ciphers to cryptanalytic attacks is measured according to different criteria. The studied evaluation criteria are the avalanche criterion and its derivations. After theimplementation of the algorithms and the test procedures, they are compared with each other. Different test criteria, including avalanche criterion, avalanche weight distribution (AWD) for randomness of RC5, RC6 and Twofish algorithms are applied / and the S-boxes of the Twofish algorithm are analyzed according to nonlinearity criterion. The avalanche criteria results of RC6 and Twofish are compared with NIST (National Institute of Standards and Technology) Statistical Test Suite results.

In this study two dimensional steel frames, reinforced with un-stiffened thin steel panels, are investigated. In the first part of the study, the strip model, a method for analyzing un-stiffened thin steel plate shear walls, was investigated. Sensitivity studies to investigate the influence of the number of strip members to be used to in the strip model and their angle of inclination were conducted. In the second part, responses of various un-stiffened steel plate shear wall systems to lateral loads were investigated. The influences of three major parameters were studied. These are the beam-to-column connection type, the boundary frame stiffness and the plate slenderness ratio (the ratio of the centerline column spacing to the thickness of the plate). In both parts nonlinear pushover analysis were performed with SAP2000 structural analysis program. In this study, the history of development, theory and advantages of un-stiffened thin steel plate shear walls and recommendations for this lateral load resisting system are presented.

The recent empirical literature has shown that the dynamic generating mechanism of macroeconomic variables can be asymmetric. Inspiring from these empirical results, this thesis uses a class of nonlinear models called smooth transition autoregressive models to investigate possible asymmetric dynamics in inflation and nominal exchange rate series of Turkey. Estimation results imply that variables under consideration contain strong nonlinearities and these can be modeled by STAR models.