Impact is a large and complex field. It embraces both structures as simple as a nail, and more complex systems, such as a car collision. A central feature of impact theory is finding the dependence between the velocities before and after impact. The transformation law of the velocities in an impact interaction can be represented in a purely geometric form, and therefore in the simplest cases, in describing the motion of systems with impacts, it is possible to get by with entirely elementary tools. However, in most engineering applications, the mechanical interactions occurring during a collision are complex. Therefore, impact is usually described by highly complicated mathematical models that can easily lead to cumbersome intricacies. Hitherto, the theories that have been developed either involve a fairly heavy amount of calculations or are severely oversimplified, and, therefore, limited in their application. Our purpose is first to describe the dynamics of a planar collision with as simple equations as possible, and secondly to extract information from those equations with the least and simplest computation. We achieve our task by combining a Kane's dynamical analysis, a simplified model of the deformation of the contact area during impact, and a numerical integration of a set of ordinary differential equations. Subsequently, we verify the consistency, accuracy and efficiency of our results by comparison to those from earlier theories. / Graduation date: 1996

Motivated by the motion of a ship in a heavy sea, a mathematical model for the vertical impact of a two-dimensional solid body onto a half-space of quiescent, inviscid, incompressible fluid is formulated. No solutions to the full problem are known, but in the case when the impacting body has small deadrise angle (meaning that the angle between the tangent to the profile and the horizontal is everywhere small) a uniformly valid solution is obtained by using the method of matched asymptotic expansions. The pressure on the body is calculated and is in fair agreement with experimental results. The model is generalised for more complicated impacts and the justifications for the model are discussed. The method is extended to three-dimensional bodies with small deadrise angle and solutions are obtained in some special cases. A variations! formulation of the leading order outer problem is derived, which gives information about the solution and leads to an fixed domain scheme for calculating solutions numerically. A partial linear stability analysis of the outer problem is given which indicates that entry problems are stable but exit problems are unstable to small perturbations. A mathematical model for the effect of a cushioning air layer between the body and the fluid is presented and analysed both numerically and in appropriate asymptotic limits. Finally, the limitations of the models are discussed and directions for future work indicated.

Not available / text

The work presented in this thesis concerns the theoretical analysis of the motion of floating rectangular cross-section bodies in single-frequency harmonic waves. When a conventional laterally symmetric ship is modelled by such a body, the computation of strip-theory coefficients (derived from the solution of Laplace's equation for the fluid surrounding the ship) is simplified. This technique is used here to model a typical barge, with actual cross-sections very close to the assumed rectangular shapes. In particular, slamming motions are investigated using two conventional linear slamming criteria. The rectangular section model is also applied to the investigation of slamming motions by use of 'quasi-harmonic' slamming criteria, which are developed from an updating technique used with conventional strip theory coefficients. Results are presented for an example. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] Ball-impact injuries in baseball, while relatively rare, have the potential to be catastrophic. These injuries are primarily attributed to impact by the ball after it has been hit, pitched or thrown. As the closest infielder to the hitter, the pitcher is at greatest risk of being struck by the batted ball. This thesis investigated the influence of bat and ball design on ball exit velocity (BEV) and the potential for impact injury to pitchers. Finite element analysis (FEA) was used to quantify the dynamics of bat-ball impact for bats of various moment of inertia and baseballs with different mechanical properties. The analysis was conducted using ANSYS/LSDYNA explicit dynamics software. To replicate a typical bat-ball impact in the field, the model required input of bat linear and angular velocity and orientation in three-dimensional (3-D) space, at the instant prior to impact. This data was obtained from 3-D kinematic analysis using two high-speed video cameras operating at 200 Hz. Seventeen high-performance batters used a wood bat and a metal bat of equal length and mass to hit baseballs thrown by a pitcher. Hitters developed significantly higher resultant linear velocity for both the proximal (38.3 ± 1.8 ms-1;) and distal (8.1 ± 1.8 ms-1) ends of the metal bat (compared with 36.4 ± 1.7 ms-1 and 6.9 ± 2.1 ms-1 respectively for the wood bat). They also achieved a significantly more “square” bat position just prior to impact with the ball (264.3 ± 9.1 deg compared with 251.5 ± 10.4 deg). These factors are important in transferring momentum to the batted ball. Mathematical description of the large-deformation material behaviour of the baseball was also required for this analysis. Previous research is limited to compression tests to 10 % of ball diameter, despite conjecture that during impact with the bat, the ball might deform to 50 % of its original diameter. Uniaxial quasi-static compression tests on seven models of baseballs investigated baseball behaviour during deformation to 50 % of ball diameter. The resulting force-displacement relationship was highly non-linear. Hence FEA was used to derive and verify a relationship to describe the time-dependent and elastic behaviour of the ball during the 1 ms period typical of bat-ball impact. The results of the bat-ball impact analysis indicated that for hits made at the point of maximum momentum transfer on the bat, the metal bat produced greater BEV than the wood bat (61.5 ms-1 and 50.9 ms-1 respectively). The higher BEV from the metal bat was attributed to greater pre-impact bat linear velocity, and bat orientation during impact. The more perpendicular horizontal orientation of the metal bat at the instant of impact resulted in a greater proportion of resultant BEV being directed in the global x-direction (toward the pitcher), compared with the wood bat. This indicates increasing bat moment of inertia (the relative mass of the bat barrel) may be a potential control strategy for BEV. BEV was also reduced for impacts using a baseball with values for instantaneous shear and relaxed modulii approximately 33 % less (9.9 % reduction in BEV for metal bat, 9.7 % for the wood bat).