This thesis considers three problems in the field of elastodynamics. The first concerns small-amplitude elastic disturbances in an infinite cylinder, a problem first investigated by Pochhammer and Chree. Our approach extends the results of Pochhammer and Chree by utilising a method of successive approximation through which the governing equations are solved to produce dispersion relations. The second investigation, recently considered by Eringen and Suhubi, is of the propagation of elastic waves in a prestressed body, with particular reference to the circular cylinder and the half-space. The governing equations are again solved via successive approximation to give new and detailed results describing the wave motion. The final investigation is of a compressible strain-energy function which is an extension of the Ko model. The model is examined in the light of various a priori inequalities, and is then used to obtain solutions to the problem of vibrations in a stressed plate.

Hybrid modelling of blast vibration uses the signal produced from a single hole test shot to simulate the vibration that would be produced by a full-scale production blast. This simulation can be used to determine optimum hole timings to minimise the vibration generated at a point of interest. This thesis studies the assumptions that are made to facilitate the use of hybrid modelling with emphasis placed on near to mid field applications. A highly accurate seismograph is developed and used to monitor a series of test blasts carried out in limestone and chalk. The repeatability of single hole test shots is investigated. It is shown that in the near field single holes are generally highly repeatable even with relatively major differences in design. It is also shown that an inversion of the radial and transverse vibration traces may occur. The factors which affect the vibration magnitude are also explored, showing that the level of confinement can have a large effect on the magnitude of vibration. Two, three and five hole production blasts are examined to determine the signal generated by each hole in the blast. It is shown that in a two hole blast the second hole can produce an inverted signal in the radial and transverse components. The three and five hole are disassembled by using a computer program to test every possible combination of convolved single holes and select the best. It is concluded that the complex interaction of the vibration generated by each blast hole makes it very difficult to model the vibration generated by a production blast in the near field.

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Please read the abstract in the section 00front of this document / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2006. / Mechanical and Aeronautical Engineering / unrestricted

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Aerodynamically bluff elastic structures such as suspension bridges and industrial smokestacks have been observed to vibrate violently in the presence of a low speed wind. Although a number of theories such as Den Hartog's quasi-steady instability criterion and the vortex resonance theory have been proposed to explain the phenomenon, the problem is still not completely solved nor yet fully understood. The purpose of this research was to dynamically test a number of two-dimensional cylinders of simple cross-section and to observe whether or not the results correlated with either of the two theories mentioned above. Necessary aerodynamic coefficients were obtained by the graphical integration of measured surface pressure distributions. Tests were performed on models mounted elastically with six degrees of freedom. Generally only one of two modes of vibration was excited at a given airspeed. Dynamic response curves are presented for several lightly damped cylinders. For cylinders with rectangular cross-section of length/width (b/h/ greater than 0.75, vibration occurred at any airspeed above a certain minimum which depended on the structural damping (galloping). Cylinders with b/h less than 0.683 were found to vibrate over a limited range of airspeeds which always included the critical velocity for resonance with the periodic formation of vortices in the wakes. Using quasi-steady theory, it was found that the D-section and rectangles with b/h less than 0.683 have zero aerodynamic damping to large relative angles of attack, due to the symmetry of the wake pressures at angles of attack greater than zero. Because of this the D-section is subject to galloping only when given a substantial initial amplitude. Vortex resonance was observed for all the cylinders tested with two exceptions; the reversed D-section and the D-section with the flat face initially at an angle of attack greater than 40°, both of which appear to be completely stable. Measurements of the frequency of vortex formation for stationary cylinders gave Strouhal numbers which showed only slight variation over the speed range used in the tests, However, a strong variation with b/h was noted for the rectangles 1.0 < b/h < 3.0. During vibration of any kind, the frequency of vortex formation was controlled at the frequency of vibration which in all cases was a natural frequency of the system being tested. An energy balance based on quasi-steady theory and neglecting structural damping yields velocity-amplitude curves which give good agreement with the experimental data for the galloping D-section and the square section at various initial angles of attack. The test results indicate that the steady state aerodynamic coefficients provide a useful approximation to the dynamic values; they also indicate that any theory which will completely predict the behaviour of such systems must include the effects of both negative aerodynamic damping and vortex resonance. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The investigation is concerned with the vibrational response of a circular cylindrical body when subjected to oscillating lift and drag forces of varying frequency. The cylindrical body was mounted on a long flexible cantilever and the stiffness of the cantilever could be varied to study the effects of resonance, amplitude and induced damping. An explanation of the two-dimensional excitation due to vortex shedding is presented. Both longitudinal and transverse vibrations were induced and the frequency of the excitation in the longitudinal direction was about twice that in the lateral. Therefore, for equal structural natural frequencies in the lateral and longitudinal directions, resonance in the lateral direction will occur at twice the velocity of the longitudinal resonance, assuming the Strouhal Number to be constant in this range. Coefficients of the elastic response forces, in both longitudinal and lateral directions near the lonitudinal resonance, were plotted for comparison. The development of irregularity in the lateral vibrating oscillogram caused by the longitudinal vibration was demonstrated. In the critical Reynolds Number range the effect of a fixed eddy-starter wire was investigated and the excitations in both lateral and longitudinal directions were altered. The resonance of longitudinal vibration occurs at V/V[subscript res] = 0.3 to 0.5. Lateral amplitude in this region is also increased. The peak of the curve: S[subscript y] vs R[subscript e], in the region of longitudinal resonance, approaches tengentially the curve: S[subscript x] vs R[subscript e]. The structural response coefficient of vibrating lift and drag rises at longitudinal resonance to a value of 3.0 to 8.0, but drops quickly after resonance. The damping coefficients of the structure are in the range of 0.25 to 0.60. Since the motion of the vibration may influence the oscillating lift and drag due to the eddy shedding, this study presents an investigation of the longitudinal and lateral resonances in a range of R[subscript e]: 5 × 10³ × 10⁵, and the interaction of the excitation between the oscillating lift and drag with the two-dimensional elastic response forces. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Low-amplitude floor vibrations have become a governing serviceability performance design consideration for floors constructed with low mass-to-stiffness ratio materials such as wood. Studies reported here were conducted at the University of Ottawa to assess vibration serviceability performance of glued-laminated-timber (glulam) beam-and-deck floor systems. Such floors are applicable in non-residential buildings having spans up to about 10 m. The primary goal was to use test and numerical analysis methods to investigate how construction variables (e.g. beam span, beam spacing, addition of nonstructural overlays) affect the vibration responses of such floors. A secondary goal was to assess applicability of vibration serviceability design criteria proposed for other types of floors to glulam beam-and-deck floors. Apart from tests aimed at characterizing responses of laboratory built rectangular plan floors, focus groups were asked to subjective rate acceptability of the performances of those floors. Focus group ratings determined ability of humans to discern alterations in floor motions resulting from construction modifications, based on an opinion survey technique developed by other researchers. This determined that humans can detect and rate performance of floors having different engineering design characteristic, but cast doubts on the consistency of the employed opinion survey technique. Laboratory tests revealed that mid-span displacements of floors are functions of two-way deflected shapes of floors and are reduced by adding nonstructural overlays and extra beams. Adding non-structural overlays reduces fundamental natural frequency demonstrating gain in modal mass was greater than for modal stiffness. There was inconsistency between the result of focus group evaluations and predictions of acceptability of floors made using available suggested vibration serviceability design criteria. Finite Element (FE) models of glulam beam-and-deck floor systems were created and verified using laboratory test data. Based on those models it was concluded that fundamental natural frequencies and mid-span displacements of floors are relatively insensitive to variations in floor width-to-span ratios. However, higher order natural frequencies are strongly affected by floor width-to-span ratios. Increasing thickness of deck elements can decrease natural frequencies and cause them to cluster in ways that amplify surface motions caused by dynamic forces like human footfall impacts. Field vibration tests were conducted to investigate the dynamic behaviour of a large glulam beam-and-deck office floor having a complex plan shape and support conditions. That floor has long beam spans and partial continuity between bays defined by a mixture of column and wall supports. It was tested before non-structural floor toppings were added and after building completion and occupation. FE modeling of the floor was created and predicted modal characteristics (i.e. mode shapes, natural frequencies) compared with experimentally derived ones. Controlled walking tests were conducted to assess the dynamic response under office occupation conditions. It was concluded the vibration serviceability response of the floor was satisfactory based on peak acceleration measurements and lack of office worker dissatisfaction. Importance of this is the floor has low order natural frequencies less than 8Hz, which means existing proposed design practices created for lightweight timber floor would incorrectly classify its performance. The discrepancy is indicative that such design practices fail to capture effects of construction variables and damping characteristics of large floors. In general, vibration characteristics of lightweight floors are highly related to effects of construction details such as plan aspect ratio, boundary conditions and presence of nonstructural elements. Apart from clarifying specifics of how glulam beam-and-deck floors vibrate, this thesis is intended to contribute to Canadian and international efforts to create engineers design methods that robustly predict whether or not specific floors will have adequate vibration serviceability performance under defined floor occupancy conditions.

Time-average and stroboscopic real-time holography have become established as the prominent tools of holographic vibration analysis. Both are able to provide a quantitative determination of the amplitudes of standing waves of a vibrating flat surface, but have to date been limited to qualitative examination of curved surfaces. The purpose of this thesis has been to investigate the problems of extending the holographic technique to the analysis of surfaces of single curvature. The presence of several component motions in curved surface vibration prompted an examination of the fringe behaviour of the individual components of motion. This was performed by studying pure rigid body step displacements using double exposure holography. The experimental work of previous investigators was duplicated and the results tabulated according to the sensitivities of the fringe period density to a change in displacement magnitude. This was then related to the rotations and translations occurring in the motion of a vibrating surface. A fully clamped curved panel was studied using the time-average method with the assumption that all points on the surface were displaced normal to it. Good agreement was obtained between the amplitudes calculated from the fringes and the measured amplitudes, by accounting for the variation in displacement direction across the surface. A fixed-free cylinder was examined simultaneously from two overlapping views using both the time-average and stroboscopic real-time methods. Comparison of the calculated and measured amplitudes of the time-average indicated that the interference fringes were not localized upon or very near the cylinder's surface. The real-time results had reinforced these findings. However, the inherent presence of residual fringes in this method caused difficulties in obtaining an accurate quantitative evaluation of the vibration amplitudes. The real-time fringes were analyzed with attention paid to the effects of the initial residual fringes upon the resultant fringes. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

The infrared spectra of single crystals of naphthalene-d₈, anthracene-h₁₀ and anthracene-d₁₀ are reported with the plane of the incident radiation parallel to all three principal optical directions of the crystals. The polarized measurements extend down to 50 cm⁻¹and all low-energy infrared-active molecular vibrations and many lattice vibrations have been assigned. The laser-excited Raman spectra of single crystals of naphthalene-d₈ and anthracene-d₁₀ also are reported and this data was supplemented by depolarization ratio measurements from solution and from the melt. With the new information available from these studies a re-evaluation of the assignments of the molecular fundamentals of these three molecules has been made. When the list of fundamentals was as complete as possible, attention was directed to the force fields. The out-of-plane field of benzene was reconsidered, and the assumption that interaction constants should be as small as possible was completely supported. Transfer of these force constants to naphthalene was successful; however, it proved to be impossible to fit all the observed non-planar frequencies of anthracene with the force constants developed for benzene. An in-plane modified valence force field designed for benzene was extended to naphthalene and anthracene and refined to fit simultaneously the observed frequencies of all three molecules and their three perdeuterated analogues. The results were compared with the results of a similar calculation carried out by Neto, Scrocco and Califano and presented elsewhere, and certain differences were noted, particularly in the anthracene-h₁₀ and -d₁₀ B₂[subscript u] ring modes. In order to find out how well force fields developed for these molecules would transfer to related but less similar molecules, the vibrations of pyrene and acenaphthene were considered. The infrared spectra of single crystals of pyrene-h₁₀, pyrene-d₁₀ and acenaphthene were measured, with emphasis on the low-frequency regions not previously studied. The data obtained were supplemented by Raman measurements carried out by others in this laboratory and fairly complete assignments of the normal vibrations were possible. The fundamental frequencies of these molecules were calculated with force fields synthesized from the two planar fields mentioned earlier and from the out-of-plane fields of benzene and (for acenaphthene) cyclopentane. Comparison of the observed and calculated frequencies showed that although some fairly large discrepancies did arise, they were few in number and located only in the region of the ring stretching vibrations (above about 1200 cm⁻¹) . The fit to the fundamentals below that energy was most encouraging, and indicated that the transfer of force constants from one molecule to another in order to calculate approximate frequencies was certainly possible. / Science, Faculty of / Chemistry, Department of / Graduate