Linear vibration measurement and analysis techniques have appeared to be sufficient with most vibration problems. This is partially due to the lack of proper identification of physical nonlinear dynamic responses. Therefore, as an example, a vehicle driveshaft exhibits a nonlinear super harmonic jump due to nonconstant velocity, NCV, joint excitation. Previously documented measurements or analytical predictions of vehicle driveshaft systems do not indicate nonlinear jump as a typical vibration mode. The nonlinear jump was both measured on a driveshaft test rig and simulated with a correlated model reproduced the jump. Subsequent development of the applied moments and simplified equations of motion provided the basis for nonlinear analysis. The nonlinear analyses included bifurcation, Poincare, Lyapunov Exponent, and identification of multiple solutions. Previous analytical models of driveshafts incorporating NCV joints are typically simple lumped parameter models. Complexity of models produce significant processing costs to completing significant analysis, and therefore large DOF systems incorporating significant flexibility are not analyzed. Therefore, a generalized method for creating simplified equations of motion while retaining integrity of the base system was developed. This method includes modal coupling, modal modification, and modal truncation techniques applied with nonlinear constraint conditions. Correlation of resonances and simulation results to operating results were accomplished. Previous NCV joint analyses address only the torsional degree of freedom. Limited background on lateral excitations and vibrations exist, and primarily focus on friction in the NCV joint or significant applied load. Therefore, the secondary moment was developed from the NCV joint excitation for application to the driveshaft system. This derivation provides detailed understanding of the vibration harmonic excitations due to NCV joints operating at misalignment angles. The model provides a basis for completing nonlinear analysis studying the system in more detail. Bifurcation analysis identified ranges of misalignment angles and speeds that produced nonlinear responses. Lyapunov Exponent analysis identified that these ranges were chaotic in nature. In addition, these analyses isolated the nonlinear response to the addition of the ITD nonlinear stiffness. In summary, the system and analysis show how an ITD installed to attenuate unwanted vibrations can cause other objectionable nonlinear response characteristics.

When testing for the equality of regression slopes based on ordinary least squares (OLS) estimation, extant research has shown that the standard F performs poorly when the critical assumption of homoscedasticity is violated, resulting in increased Type I error rates and reduced statistical power (Box, 1954; DeShon & Alexander, 1996; Wilcox, 1997). Overton (2001) recommended weighted least squares estimation, demonstrating that it outperformed OLS and performed comparably to various statistical approximations. However, Overton's method was limited to two groups. In this study, a generalization of Overton's method is described. Then, using a Monte Carlo simulation, its performance was compared to three alternative weight estimators and three other methods. The results suggest that the generalization provides power levels comparable to the other methods without sacrificing control of Type I error rates. Moreover, in contrast to the statistical approximations, the generalization (a) is computationally simple, (b) can be conducted in commonly available statistical software, and (c) permits post hoc analyses. Various unique findings are discussed. In addition, implications for theory and practice in psychology and future research directions are discussed.

O propósito deste trabalho é estudar a dinâmica assintótica de problemas parabólicos em domínios tipo dumbbell. Para isto primeiro estudaremos a semi-continuidade superior de atratores para problemas parabólicos com condição de fronteira do tipo Neumann homogênea e depois estudaremos a existência de equilíbrios estáveis não-constantes para problemas de reação-difusão com condições de fronteira tipo Neumann não-lineares. / The aim of this work is to study the asymptotic dynamics of parabolic problems in dumbbell type domains. To that end firstly, we study upper semicontinuity of attractors for parabolic problems with homogeneous Neumann boundary conditions and afterwards we study the existence of stable nonconstant equilibria for reaction-diffusion problems with nonlinear Neumann boundary conditions.

O propósito deste trabalho é estudar a dinâmica assintótica de problemas parabólicos em domínios tipo dumbbell. Para isto primeiro estudaremos a semi-continuidade superior de atratores para problemas parabólicos com condição de fronteira do tipo Neumann homogênea e depois estudaremos a existência de equilíbrios estáveis não-constantes para problemas de reação-difusão com condições de fronteira tipo Neumann não-lineares. / The aim of this work is to study the asymptotic dynamics of parabolic problems in dumbbell type domains. To that end firstly, we study upper semicontinuity of attractors for parabolic problems with homogeneous Neumann boundary conditions and afterwards we study the existence of stable nonconstant equilibria for reaction-diffusion problems with nonlinear Neumann boundary conditions.

In this thesis we study the zeros and asymptotics of sequences that satisfy linear recurrence relations with generally nonconstant coefficients. By the theorem of Skolem-Mahler-Lech, the set of zero terms of a sequence that satisfies a linear recurrence relation with constant coefficients taken from a field of characteristic zero is comprised of the union of finitely many arithmetic progressions together with a finite exceptional set. Further, in the nondegenerate case, we can eliminate the possibility of arithmetic progressions and conclude that there are only finitely many zero terms. For generally nonconstant coefficients, there are generalizations of this theorem due to Bézivin and to Methfessel that imply, under fairly general conditions, that we obtain a finite union of arithmetic progressions together with an exceptional set of density zero. Further, a condition is given under which one can exclude the possibility of arithmetic progressions and obtain a set of zero terms of density zero. In this thesis, it is shown that this condition reduces to the nondegeneracy condition in the case of constant coefficients. This allows for a consistent definition of nondegeneracy valid for generally nonconstant coefficients and a unified result is obtained. The asymptotic theory of sequences that satisfy linear recurrence relations with generally nonconstant coefficients begins with the basic theorems of Poincaré and Perron. There are some generalizations of these theorems that hold in greater generality, but if we restrict the coefficient sequences of our linear recurrences to be polynomials in the index, we obtain full asymptotic expansions of a predictable form for the solution sequences. These expansions can be obtained by applying a transfer method of Flajolet and Sedgewick or, in some cases, by applying a bivariate method of Pemantle and Wilson. In this thesis, these methods are applied to a family of binomial sums and full asymptotic expansions are obtained. The leading terms of the expansions are obtained explicitly in all cases, while in some cases a field containing the asymptotic coefficients is obtained and some divisibility properties for the asymptotic coefficients are obtained using a generalization of a method of Stoll and Haible.

The numerical simulation of a moving heat source from a fixed point observer is often done by discretely adjusting its position over the steps of a thermal transient analysis. The efficiency of these simulations is increased when using a coarse temporal discretization whilst maintaining the quality of results. One systematic error source is the rare update of a nonconstant moving heat source with regard to its magnitude and location. In this work, we present an analysis of the error and propose a correction approach based on conserving the specified heat from a continuous motion in analyses with large time-step sizes. Deficiencies associated with the correction in special motion situations are identified by means of performance studies and the approach is extended accordingly. The advantages of applying the proposed correction are demonstrated through examples.