Variations in vehicle noise, vibration and harshness (NVH) response from one vehicle to the next can have significant impact on an automotive company’s profile and profitability. The warranty claims due to excessive NVH response end up costing the manufacturers a large sum of money each year. In addition, the OEM will suffer a larger financial loss due to the poor perception of quality and customer dissatisfaction with their products due to the unacceptable NVH response. Therefore, measures must be taken to ensure less warranty claims and higher levels of customer satisfaction. This research focuses on aspects of design variations that are costly or difficult to be avoided in the design process such as variations with rubber parts and variations due to rotating components. Vibrations induced at the tire/wheel assembly due to variations in the radial and tangential forces and radial runout are responsible for the driverelt vibrations that can lead to a large number of warranty claims. The purpose of this research is to improve the process of determining and analyzing vibration sources in the tire/wheel assembly in order to benefit the automotive manufacturer during the development and manufacturing phases. This research identifies the relationship between non-uniformity forces of the tire/wheel assemblies and the driverelt vibrations during typical highway driving speeds. The contribution from each assembly location is analyzed and sensitivities are determined. A Monte Carlo process is used to predict numerous non-uniformity properties that are statistically representative of the assembly properties that can be expected at the manufacturing plant. The Monte Carlo produced non-uniformity properties are combined with the sensitivities to predict driverelt vibrations that can be expected from vehicles leaving the manufacturing plant. This process provides the tools to determine an acceptable level of non-uniformities based on targets for interior vibration levels or determine if the vehicle sensitivities to non-uniformities need to be improved.

To provide fundamental information for the second generation of cross laminated timber manufacturing, wood sections that glued by different orientations were constructed and tested. To reveal adhesive differences, phenol resorcinol formaldehyde (PRF) and polyurethane (PU) adhesive were used and the gluelines were evaluated in accordance with different conditions for shear strength, wood failure, dimensional stability and delamination. A non-destructive testing method was applied to measure the dynamic modulus of elasticity (dMOE) change. The results showed that the radical wood section of lumber produced with the starsawn process had much less deformation and was more suitable for glueline. PRF had better performance than PU in terms of shear strength, dimensional stability, and delamination. Confocal microscopic pictures revealed that the tangential to tangential (TT) glueline showed the tendency of collapse, indicating a poor bond strength and therefore a poor glueline durability of TT glueline, especially when it was subject to wet conditions.

<p> One of the major industrial metalworking processes is extrusion and it is of technological importance to be able to estimate the loads and material flow characteristics within the deforming metal. Hot metals and superplastic materials are particularly sensitive to the speed of the operation al though it is difficult to col".sider this in an analysis of the problem. </p> <p> This thesis reviews the analytical techniques available to the engineer to determine the loads in bulk forming processes and examines the way in which rate effects have been accommodated. The upper bound method, which is an approximate analytical technique, is reviewed in detail. The concept of a tangential shear zone of constant shear strain rate is introduced and used to enable strain rate effects to be considered within the upper bound technique. The work rate across each discontinuity is shown to be a function of the material strain rate sensitivity, the shear zone width and the tangential veloc i ty change. </p> A number of tangential velocity fields are proposed for the side extrusion process. These are examined and compared by minimizing the work rate using a computer optimization technique. The optimum solution for a simple tangential velocity discontinuity field is shown to give load estimates which are within 10% of those given by the more exact slip-line field method. </p> <p> Experiments, performed by the author on the side extrusion of two materials, which have very different strain rate sensitivities, are reported in detail. A characteristic difference in the extrudate geometry for the two materials is identified and shown to be a result of the difference in the materials strain rate sensitivity index. The experimental extrusion pressures for the two materials at different ram velocities are compared with theoretical values derived using the theory developed earlier in the thesis; the correlation is good. </p> <p> The shape of the tangential discontinuity between a uniform translational and uniform rotational field is examined and shown to be a circular arc. A number of new tangential velocity discontinuity fields are presented for a variety of common metalworking processes. These fields comprise straight and circular discontinuities and represent a new type of "mixed" field which predicts the rotation of the extrudate. </p> / Thesis / Doctor of Philosophy (PhD)

Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematic areas. Despite they have been studied for decades, several aspects of their geometry are still mysterious, among which identifiability and singularity of their points. In this thesis we study the secant varieties of lines of Grassmannians and of Spinor varieties. As first result, we completely determine their posets of orbits under the action of the groups SL and Spin, respectively. Then we solve the problems of identifiability and tangential-identifiability of points in the secant varieties of lines: as a consequence, we also determine the second Terracini locus to a Grassmannian and to a Spinor variety. Our main result concerns the singular locus of the secant variety of lines: we completely determine it for Grassmannians, and we give lower and upper bounds for Spinor varieties. Finally, we partially describe the poset of orbits in the secant variety of lines of any cominuscule variety.

No description available.

No description available.

In this dissertation, we solve multivariable Nevanlinna-Pick type interpolation problems. Particularly, we consider the left tangential interpolation problems on the commutative or noncommutative unit ball. For the commutative setting, we discuss left-tangential operator-argument interpolation problems for Schur-class multipliers on the Drury-Arveson space and for the noncommutative setting, we discuss interpolation problems for Schur-class multipliers on Fock space. We apply the Krein-space geometry approach (also known as the Grassmannian Approach). To implement this approach J-versions of Beurling-Lax representers for shift-invariant subspaces are required. Here we obtain these J-Beurling-Lax theorems by the state-space method for both settings. We see that the Krein-space geometry method is particularly simple in solving the interpolation problems when the Beurling-Lax representer is bounded. The Potapov approach applies equally well whether the representer is bounded or not. / Ph. D.

This thesis deals with different computational techniques related to some classes of nonlinear response regimes of engineering interest. The work is mainly divided into two parts. In the first part different numeric-analytic integration techniques for nonlinear oscillators are developed. In the second part, procedures for handling arbitrarily large rotations are addressed and a few novel developments are reported in the process. To begin the first part, we have proposed an explicit numeric-analytic technique, based on the Adomian decomposition method, for integrating strongly nonlinear oscillators. Numerical experiments suggest that this method, like most other numerical techniques, is versatile and can accurately solve strongly nonlinear and chaotic systems with relatively larger step-sizes. It is then demonstrated that the procedure may also be effectively employed for solving two-point boundary value problems with the help of a shooting algorithm. This has been followed up with the derivation and numerical exploration of variants of a recently developed numeric-analytic technique, the multi-step transversal linearization (MTrL), in the context of nonlinear oscillators of relevance in engineering dynamics. A considerable generalization and improvement over the original form of a MTrL strategy is achieved in this study. Finally, we have used the concept of MTrL method on the nonlinear variational (rate) equation corresponding to a nonlinear oscillator and thus derive another family of numeric-analytic techniques, presently referred to as the multi-step tangential linearization (MTnL). A comparison of relative errors through the MTrL and MTnL techniques consistently indicate a superior quality of approximation via the MTrL route. In the second part of the thesis, a scheme for numerical integration of rigid body rotation is proposed using only rudimentary tensor analysis. The equations of motion are rewritten in terms of rotation vectors lying in same tangent spaces, thereby facilitating vector space operations consistent with the underlying geometric structure of rotation. One of the most important findings of this part of the dissertation is that the existing constant-preserving algorithms are not necessarily accurate enough and may not be ideally applicable to cases wherein numerical accuracy is of primary importance. In contrast, the proposed rotation-algorithms, the higher order ones in particular, are significantly more accurate for conservative rotational systems for reasonably long time. Similar accuracy is expected for dissipative rotational systems as well. The operators relating rotation variables corresponding to different tangent spaces are also investigated and this should provide further insight into the understanding of rotation vector parametrization. A rotation update is next proposed in terms of rotation vectors. This update, employed along with interpolation of relative rotations, gives a strain-objective and path independent finite element implementation of a geometrically exact beam. The method has the computational advantage of requiring considerably less nodal variables due to the use of rotation vector parametrization. We have proposed a new isoparametric interpolation of nodal quaternions for computing the rotation field within an element. This should be a computationally efficient alternative to the interpolation of local rotations. It has been proved that the proposed interpolation of rotation leads to the objectivity of strain measures. Several numerical experiments are conducted to demonstrate the frame invariance, path-independence and other superior aspects of the present approach vis-`a-vis the existing methods based on the rotation vector parametrization. It is emphasized that, in order to develop an objective finite element formulation, the use of relative rotation is not mandatory and an interpolation of total rotation variables conforming with the rotation manifold should suffice.

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The superficial tangential zone (STZ) plays a significant role in normal articular cartilage’s ability to support loads and retain fluids. To date, tissue engineering efforts have not replicated normal STZ function in cartilage repairs. Finite element models were developed to examine the STZ’s role in normal and repaired articular surfaces under different contact conditions. Models were developed by incrementally adding improvements which culminated in contact loading of curved models by permeable and impermeable rigid surfaces and a normal cartilage layer. In the normal STZ, permeability was strain-dependent on volumetric strain; tension-compression nonlinearity modeled collagen behavior. Nonlinear geometry accounted for finite deformation. Results showed that STZ properties of sufficient quality maybe critical for the survival of transplanted constructs in vivo. As compared to rigid surfaces, loading via normal cartilage provided more physiologic results. These models can provide guidance in identifying critical features for the design of tissue engineered articular cartilage constructs.