Thesis (Ph.D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains ix, 176 p.; also includes graphics. Includes bibliographical references (p. 172-176). Available online via OhioLINK's ETD Center

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Bibliography: leaves 222-223. / by John Lambros Tassoulas. / Ph.D.

A modified source and dipole panel method to calculate the flow properties around an oscillating arbitrary body in the presence of a free surface is proposed. To demonstrate the feasibility of the method the problem of a pulsating line source submerged under a free surface is treated. The technique chosen is based on Green's identity whereby the boundary-value problem is expressed as a boundary integral equation which is solved numerically. The near field of the water surface is represented by singularity panels with constant strength. The work was motivated by the reported large computing times for existing programs using Green's functions satisfying the free surface boundary condition. The present approach uses free-space Green's function. The free surface boundary condition is applied to surface singularity panels using Green's theorem. Thus free surface effects are included in the solution while panel integrations are simplified considerably by the use of simpler Green's function. The matrix equations resulting from Green's identity were solved by using IMSL routines for Gaussian Elimination, and the behavior of the influence coefficient matrix was tested by using LINPACK routines. The depth of the submerged-source and wave number was kept constant while the length of near field and the number of panels per wavelength was varied systematically. A minimum of 10 panels per wavelength and paneled water surface length of 2 wavelengths gives good agreement with the known exact solution. Computing times were low, indicating the feasibility of the technique for application to unsteady ship problems. / Ph. D.

The vibration of and wave propagation in periodic cellular structures are analyzed. Cellular structures exhibit a number of desirable multifunctional properties, which make them attractive in a variety of engineering applications. These include ultra-light structures, thermal and acoustic insulators, and impact amelioration systems, among others. Cellular structures with deterministic architecture can be considered as example of periodic structures. Periodic structures feature unique wave propagation characteristics, whereby elastic waves propagate only in specific frequency bands, known as "pass band", while they are attenuated in all other frequency bands, known as "stop bands". Such dynamic properties are here exploited to provide cellular structures with the capability of behaving as directional, pass-band mechanical filters, thus complementing their well documented multifunctional characteristics. This work presents a methodology for the analysis of the dynamic behavior of periodic cellular structures, which allows the evaluation of location and spectral width of propagation and attenuation regions. The filtering characteristics are tested and demonstrated for structures of various geometry and topology, including cylindrical grid-like structures, Kagom and eacute; and tetrhedral truss core lattices. Experimental investigations is done on a 2-D lattice manufactured out of aluminum. The complete wave field of the specimen at various frequencies is measured using a Scanning Laser Doppler Vibrometer (SLDV). Experimental results show good agreement with the methodology and computational tools developed in this work. The results demonstrate how wave propagation characteristics are defined by cell geometry and configuration. Numerical and experimental results show the potential of periodic cellular structures as mechanical filters and/or isolators of vibrations.

Surface wave methods have been used to determine dynamic properties of near-surface soils in geotechnical engineering for the past 50 years. Although the capabilities of engineering surface wave methods have improved in recent years due to several advances, several issues including (1) near-field effects, (2) combined active and passive measurements, and (3) accurate measurements of surface wave attenuation still require study to further improve the capabilities of modern surface wave methods. Near-field effects have been studied for traditional surface wave methods with two receivers and several filtering criteria to mitigate the effects have been recommended. However, these filtering criteria are not applicable to surface wave methods with multiple receivers. Moreover, the criteria are not quantitatively based and do not account for different types of soil profiles, which strongly influence near-field effects. A new study of near-field effects on surface wave methods with multiple receivers was conducted with numerical and experimental methods. Two normalized parameters were developed to capture near-field effects. Quantitatively based near-field effect criteria for an ideal homogeneous half-space and three typical soil profiles are presented. Combining active and passive surface wave measurements allows developing a shear wave velocity profile to greater depth without sacrificing the near-surface resolution offered by active measurements. Generally, active and passive measurements overlap in the frequency range from approximately 4 to 10 Hz, and there are often systematic differences between the two measurements. The systematic errors in active and passive surface wave methods were explored to explain and resolve the differences, allowing for a more accurate composite dispersion curve. The accuracy of measured surface wave attenuation is improved by properly accounting for (1) geometric spreading, (2) near-field effects, and (3) ambient noise. In this study, a traditional estimation method and a frequency-wavenumber method utilizing sub-arrays were investigated using displacement data from numerical simulations, focusing on near-field and ambient noise effects. Detailed procedures for the frequency-wavenumber estimation method are developed based on a study of the primary factors affecting attenuation estimates. The two methods are also evaluated using experimental displacement data obtained from surface wave field measurements with three different arrays.

This study investigates wave propagation in an elastic half-space with quadratic nonlinearity due to a line load on the surface. The consideration of this problem is one of the well known Lamb problems. Even since Lamb's original solution, numerous investigators have obtained solutions to many different variants of the Lamb problem. However, most of the solutions existing in the current literature are limited to wave propagation in a linear elastic half-space. In this work, the Lamb problem in an elastic half-space with quadratic nonlinearity is considered. For this, the problem is first formulated as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. The accuracy of the numerical method is first studied by comparing the numerical solution with the analytical solution for a half-space with linear response (the original Lamb's problem). The numerical results for the half-space with quadratic nonlinearity are than studied using signal-processing tools such as the fast Fourier transform (FFT) in order to analyze and interpret any nonlinear effects. This in particular gives the possibility to evaluate the excitation of higher order harmonics whose amplitude is used to infer material properties. To quantify and compare the nonlinearity of different materials, two parameters are introduced; these parameters are similar to the acoustical nonlinearity parameter for plane waves.

Rotating convection in the Earth's core produces columnar vortices of radius ~10 km or less near the inner core boundary. Small-scale motions in the core can travel as Alfvén waves in the face of Ohmic diffusion, provided the ratio of the magnetic diffusion time th to the Alfvén wave travel time tA (measured by the Lundquist number S0) is much greater than unity. These motions transfer angular momentum from the core to the mantle, a process that can help explain variations in length of day. Vortices subject to the combined influence of a magnetic field and background rotation give rise to fast and slow Magneto-Coriolis (MC) waves whose damping is not well understood. This thesis investigates the long-time evolution of magneto hydrodynamic (MHD) waves generated by an isolated, small-scale motion in an otherwise quiescent, electrically conducting fluid. The first part of the study focuses on the damping of small-scale Alfvén waves, which is independent of rotation. For a plausible magnetic field strength in the Earth's core, it is shown that flows of lengthscale ~ 5 km or larger can propagate across the core as damped Alfvén waves on sub-decadal timescales. The second part of the study looks at MC waves generated from an isolated blob under rotation and a uniform axial magnetic field. The decay laws for these waves are obtained by considering the decay of fast and slow waves individually. While the fast waves are subject to strongly anisotropic magnetic diffusion, the slow waves diffuse isotopically. New timescales are derived for the onset of damping and the transition from the wave-dominated to the diffusion-dominated (quasi-static) phase of decay. This study shows for the first time that MC waves originating from small-scale vortices of magnetic Reynolds number Rm ~ 1 can be long-lived. The results of this study are extendible to small-scale MHD turbulence under rotation, whose damped wave phase has not been adequately addressed in the literature. Furthermore, it is thought that this study would help place a lower bound on the poloidal magnetic field strength in the Earth’s core.

In 1966 Mark Kac posed an interesting question regarding vibrating membranes and the sounds they make. His article entitled "Can One Hear the Shape of a Drum?", which appeared in The American Mathematical Monthly, generated much interest and scholarly debate. The evolution of Kac's intriguing question will be the subject of this project.

A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. The current research focuses on wave propagation in nonlinear periodic structures to explore tunability in filtering properties such as bandgaps, cut-off frequencies and response directionality. The first part of the research documents amplitude-dependent dispersion properties of weakly nonlinear periodic media through a general perturbation approach. The perturbation approach allows closed-form estimation of the effects of weak nonlinearities on wave propagation. Variation in bandstructure and bandgaps lead to tunable filtering and directional behavior. The latter is due to anisotropy in nonlinear interaction that generates low response regions, or "dead zones," within the structure.The general perturbation approach developed has also been applied to evaluate dispersion in a complex nonlinear periodic structure which is discretized using Finite Elements. The second part of the research focuses on wave dispersion in strongly nonlinear periodic structures which includes pre-compressed granular media as an example. Plane wave dispersion is studied through the harmonic balance method and it is shown that the cut-off frequencies and bandgaps vary significantly with wave amplitude. Acoustic wave beaming phenomenon is also observed in pre-compressed two-dimensional hexagonally packed granular media. Numerical simulations of wave propagation in finite lattices also demonstrated amplitude-dependent bandstructures and directional behavior so far observed.

This research investigates wave propagation in an elastic half-space with a quadratic nonlinearity in its stress-strain relationship. Different boundary conditions on the surface are considered that result in both one- and two-dimensional wave propagation problems. The goal of the research is to examine the generation of second-order frequency effects and static effects which may be used to determine the nonlinearity present in the material. This is accomplished by extracting the amplitudes of those effects in the frequency domain and analyzing their dependency on the third-order elastic constants (TOEC). For the one-dimensional problems, both analytical approximate solutions as well as numerical simulations are presented. For the two-dimensional problems, numerical solutions are presented whose dependency on the material's nonlinearity is compared to the one-dimensional problems. The numerical solutions are obtained by first formulating the problem as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. In the one-dimensional cases, it is shown that the analytical and numerical solutions are in good agreement with each other, as well as how different boundary conditions may be used to measure the TOEC. In the two-dimensional cases, it is shown that there exist comparable dependencies of the second-order frequency effects and static effects on the TOEC. Finally, it is analytically and numerically investigated how multiple reflections in a plate can be used to simplify measurements of the material nonlinearity in an experiment.