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In this paper, we examine a method on how to model and produce Chladni Figures. We walk through how a thin metal plate, when vibrating at certain frequencies, can create various interest patterns. First we discuss the equation for the vertical force exerted on the plate, then we derive a PDE to solve for the nodal lines (lines that remain fixed, while the rest of the plate is oscillating). And, discuss how to create and model these figures, through a finite difference method. There have been several experiments on Chladni Figures, using some sort of vibrating membrane or plate and then either through the use of a speaker or a violin bow, produce frequencies in order to resonate with the membrane. These eigenvalue solutions can been physically observed by putting sand on the plate and vibrating it. We will approximate theses figures, calculate the convergence of the approximation, and relate the generated figures to figures produced in experiments.

The high performance of bone implants depends on the positive response of osteoblasts to the surface of the materials manufactured for the implant. Cell response in turn strongly depends on the nature of the initial interaction of macromolecules involved in cell adhesion and proliferation with the atomic structure of the surface of the material used for the implant. The initial interaction between bone specific extracellular matrix proteins and the solid substrate influences cell response at the cell-implant interface. This interaction is crucial for implant stability, long-term durability, and osseointegration. Despite extensive research undertaken to develop high-quality material for implants in order to improve the cell-substrate interaction, little is known about the significance of the atomic structure of the substrate and the role of molecular machinery involved in cell-substrate interaction. Using a combined approach involving material sciences and cell and molecular biology, the objectives of this research are to evaluate the response of pre-osteoblast and fibroblast cell lines to novel bulk polycrystalline and single crystal titanium based material and assess the role of crystal size and orientation. / Novel bulk nano-structured titanium substrates were produced by the process of high-pressure torsion (HPT). These materials have a significant advantage compared to conventional titanium-based materials by having higher surface wettablity, mechanical properties as well as a distinct surface oxide layer and atomic structure. A co-culture system was adapted to investigate the differential response of pre-osteoblast and fibroblast cell lines to titanium and titanium dioxide single-crystal substrates. / The results of this study provide clear evidence that crystal size and specific crystallographic orientation can be used to improve cell adhesion and proliferation. The nanostructured titanium substrates show strong interaction with pre-osteoblast cells as evident by the higher expression of fibronectin and the formation of extensive focal adhesion. Differential cell behaviour of pre-osteoblasts and fibroblasts are observed in cultures grown on the substrates with specific crystallographic orientations. The degree of cell attachment of the pre-osteoblasts is considerably higher on Ti-(1120) crystal face compared with the fibroblasts. These findings have profound implications for the improved osseointegration and inhibition of fibrosis leading to long-term implant consolidation and stability.

This PhD thesis presents research aims to improving the dynamic modelling of coupled plate structures across a wide frequency range by using analytical, statistical and experimental methods. The analytical waveguide method is used to model the flexural displacement of coupled plate structures which are simply supported along two parallel edges. A method of quickly predicting the average energy level in a plate from details of the waveguide model is described, and used for comparison with SEA models. The Poynting and Impedance methods of predicting the energy flow in coupled plate structures are investigated. Transmission coefficients for coupled plate structures are evaluated using the analytical waveguide method for both semi-infinite and finite coupled plate structures. Finite transmission coefficients have traditionally been more difficult to evaluate due to the presence of a reverberant field, but in this work a novel method of separating the reverberant field using a scattering matrix method is presented. The transmission coefficients for semi-infinite and finite structures are then compared for L-shaped plates. A modal transmission coefficient is also defined and for the cases considered, and is used to develop an alternative method of deriving the transmission coefficient in a finite structure. Frequency averaged transmission coefficients are also considered, and the transmission coefficients derived for finite and semi-infinite structures are found to be very similar after frequency averaging. Statistical Energy Analysis models of coupled plates are evaluated using transmission coefficients derived from waveguide models. The results of the SEA models are compared to those predicted by the analytical waveguide method. A modal transmission coefficient based SEA model is also investigated. In an attempt to validate the numerical work presented in this thesis, experiments have been conducted. Using a wave extraction technique, both the wave amplitudes and plate properties have been evaluated from experimental data, and are subsequently used to experimentally measure the transmission coefficient for two plates coupled at different angles.

Typescript (photocopy) / iv, 160 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Civil Engineering, 1979

The relationship between distinctive characteristic fluid-flow regimes and the sound radiation generated by them has been investigated, over a range of Reynolds numbers, for various single plates and two-plate arrays in nominally two-dimensional flows. In preliminary experiments, the characteristics of flow over single plates with rectangular cross-section and faired leading edges and over tandem arrays of an upstream plate with rectangular cross-section and faired leading edges and a downstream plate of rectangular cross-section were investigated, together with the sound radiation produced. However, the main investigation has been concentrated on single plates of rectangular cross-section with various chord-to-thickness ratios C and on arrays of two plates of rectangular cross-section in tandem having various chord-to-thickness ratios C₁ and C₂ and a range of gaps (with gap-to-thickness ratios G) between them. The range of Reynolds number based on plate thickness t and free-stream velocity U, Re[subscript]t = Ut/ν (where ν is the kinematic viscosity of fluid) covered in the measurements is 3.2 x 10[superscript]3 ≤ Re[subscript]t 53 x 10[superscript]3. Spectra of velocity fluctuations in the flow and radiated sound have been measured and their characteristic frequencies related. An attempt has been made to measure force fluctuations on surfaces of the plates in order to relate them to flow characteristics and radiated sound power. Mean and fluctuating pressures associated with the force fluctuations on the plates have also been obtained. The lengths of separation bubbles on long rectangular plates have also been determined. In most cases, the measurements have been complemented by flow-visualisation in a water tunnel to provide additional detailed insight into the flow patterns. Three flow regimes have been identified for single plates of rectangular cross-section. In the first regime (1 ≤ C ≤ 3.13), shear layers separated from the leading edges form a vortex street downstream of the plate without reattachment to it. Associated force fluctuations on the plate are the main source of acoustic radiation. In the second regime (3.05 ≤ C ≤ 9.65), the separated shear layers reattach intermittently to the streamwise plate surfaces. Vortex formation in the shear layer is the dominant cause of sound radiation but the effect becomes weaker as C increases. In the third regime (6.52 ≤ C ≤ 68), the separated shear layers form closed leading-edge separation bubbles. Weak vortex shedding, with only a small contribution to the sound radiation, occurs only at the trailing edges of the plate. Bistable behaviour of the flow over a plate, with random switching between the regimes, occurs for C ≈ 3 and 6.52 ≤ C ≤ 9.65. A proposed classification of possible flow regimes for the flow around two plates of rectangular cross-section in tandem has been confirmed experimentally. For small G, the flow in the gap between the plates is isolated from the external flow. When the gap G between the plates is increased to or beyond a critical value (between 2 and 3.5), the shear layers separated from the upstream plate form a von Karman vortex street in the gap before interacting with the downstream plate. Flow and acoustic measurements indicate that this transition is associated with dramatic changes in the flow character. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1320474 / Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 2008

Thesis (M.S.)--Ohio University, November, 1999. / Title from PDF t.p.

Thesis (M.S.)--Ohio University, June, 2004. / Title from PDF t.p. Includes bibliographical references (leaves 78-80).

Thesis (Ph.D.)--University of Adelaide, Dept. of Civil and Environmental Engineering, 2002. / "June 2002" Includes bibliographical references (leaves 349-374).