The Rayleigh-Ritz method is a convenient tool for the analysis of deflections in structures subjected to external forces. Bending moment relations can be developed and reliable values obtained for bending moments. In this thesis the Rayleigh-Ritz method is used for the analysis of a single-span, pin-connected circular arch subjected to uniform load along the arch. The method is explained, equations for deflections and moments are developed and the results of an illustrated problem are tabulated. The illustrated problem is also solved by a conventional method using the dummy load and virtual work techniques. Results are compared and found to be good. In both methods, account is taken of bending and axial forces; shear distortion is neglected. For the Rayleigh-Ritz method where undetermined coefficients are evaluated, a tabulation of the rate of convergence is presented. Computer programs for both methods are included. / Master of Science

This research focuses on estimating the shear wave velocity (Vs) profile based on the dispersion curve obtained from SASW field test data (i.e., inversion of SASW data). It is common for the person performing the inversion to assume the prior information required to constrain the problem based on his/her own judgment. Additionally, the Vs profile is usually shown as unique without giving a range of possible solutions. For these reasons, this work focuses on: (i) studying the non-uniqueness of the solution to the inverse problem; (ii) implementing an inversion procedure that presents the estimated model parameters in a way that reflects their uncertainties; and (iii) evaluating tools that help choose the appropriate prior information. One global and one local search procedures were chosen to accomplish these purposes: a pure Monte Carlo method and the maximum likelihood method, respectively. The pure Monte Carlo method was chosen to study the non-uniqueness by looking at the range of acceptable solutions (i.e., Vs profiles) obtained with as few constraints as possible. The maximum likelihood method was chosen because it is a statistical approach, which enables us to estimate the uncertainties of the resulting model parameters and to apply tools such as the Bayesian criterion to help select the prior information objectively. The above inversion methods were implemented for synthetic data, which was produced with the same forward algorithm used during inversion. This implies that all uncertainties were caused by the nature of the SASW inversion problem (i.e., there were no uncertainties added by experimental errors in data collection, analysis of the data to create the dispersion curve, layered model to represent a real 3-D soil stratification, or wave propagation theory). At the end of the research, the maximum likelihood method of inversion and the tools for the selection of prior information were successfully used with real experimental data obtained in Memphis, Tennessee.

An effective way to describe changes in the microstructure of a material or to assess fatigue damage at an early stage in fatigue life is by measuring the acoustic nonlinearity parameter beta. The nonlinearity parameter is defined for harmonic longitudinal plane waves and it depends on the ratio of the amplitudes of the first harmonic of the exciting signal and the second harmonic. A reliable measurement of the amplitudes of these harmonics is crucial since their amplitude of the second (higher) harmonic is much smaller than the amplitude of the first harmonic. This research investigates the influence of the apparent nonlinearity that can occur due to the signal processing and shows how this influence can be quantified and minimized to enable a more accurate evaluation of the acoustic nonlinearity parameter. Furthermore the concept of the nonlinear parameter is extended to Rayleigh surface waves by developing a connection between the harmonic amplitudes and the third order elastic constants, using the approximate model by Zabolotskaya. Finally the problem of modeling the influence of fatigue damage on the nonlinear parameter and the elastic constants is discussed. The reduction of the processing nonlinearity combined with Rayleigh surface waves - Rayleigh surface waves are more efficient in the detection of fatigue damage initiated and concentrated at the surface - helps improve the prediction of fatigue damage and the remaining life of a sample.

This thesis describes the beach field-testing of a 2-degree-of-freedom (2-DOF) transverse line Rayleigh wave source for use in a seismo-acoustic SONAR for buried mine detection. The source is composed of six identical modules, each composed of two radial and two vertical inertial mass shakers, all mounted to a common base plate. The vertical and horizontal excitation of each module is independent. Electrically, the six modules are organized into three independent sets of two. The length of the source is 46 inches (1.17m), the width 6 inches (0.15m) and the weight 126 pounds (562N). Field tests were conducted using a 5-cycle, (smooth-)amplitude-modulated transient excitation signal. Based on past and present experience that the Rayleigh wave speed at the beach test site is approximately 90 m/s, a carrier frequency of 100 Hz was employed, producing a Rayleigh wavelength and surface penetration depth of approximately 1 m (approximately equal to the source aperture length), which is appropriate for the intended application. The source radiation directional characteristics were investigated for various relative amplitudes and phases of vertical and horizontal shaker excitation. A null result was obtained, that is, no unambiguous evidence of directivity was observed in any of the experiments conducted using this source. These included measurements wherein the source modules were removed from the common base plate and emplaced on the sand. The reason for this result is unknown, but it is suspected that a good possibility is that the beach sand medium just below its surface, whereupon the present source and receivers were deployed, is not homogeneous enough to support coherent spatial beamforming. Based upon the past success of a 4-element end-fire line array in producing directional Rayleigh wave radiation (10-15 dB front-to-back rejection), it is suggested that, if such a source can be made mobile, it may well be the best source candidate for a seismo-acoustic SONAR for buried mine detection.

This research investigates the effects of beam diffraction from a source of finite width on nonlinear Rayleigh wave propagation in an elastic half space. Previous work has shown that nonlinear ultrasonic Rayleigh waves can be used to evaluate material damage due to plastic deformation and fatigue. In this measurement, a relatively small wedge transducer is employed to launch Rayleigh surface waves in the specimen and the first and second harmonic amplitudes are measured in the far field as a function of propagation distance. In order to obtain a reliable set of measurement data, one needs to make numerous points in a wide range of distance, which can be impractical in many cases. This research investigates model is employed and the computation results are compared with experiment ones. This research will make measurements on 7075-T651 aluminum as a specimen, compensate the diffraction effects and then, will compare the feasibility of the method proposed in this research in the results of normalized second harmonic amplitude vs propagation distance.

This thesis describes a method developed to quickly measure the Rayleigh wave Q for a test material using a minimally invasive laser probe. The probe was donated to our lab by Dr. Alex Maznev at Phillips AMS in Natick, Ma. The machine was originally used to measure ultra thin film metal thicknesses; however we have utilized it to suit our needs. The optics head relies on a technique known as the transient grating method to generate a dispersion curve. This dispersion curve is then operated on by a local approximation for the Kramers-Kronig relations. The Kramers-Kronig relations for acoustic waves relate the real and imaginary parts of the dynamic compressibility to one another. The real part of the compressibility relates to the phase velocity of the wave and the imaginary part relates to the attenuation. Once the attenuation for the corresponding range of frequencies is determined the last step is to apply both the dispersion data and the attenuation data to the material Q equation to find Q over a range of frequencies. This thesis discusses the design of the machine, the theory behind the Kramers-Kronig relations and surface acoustic waves, the experimental procedure, and lastly results generated by the technique.

Στην εργασία αυτή θα πραγματευθούμε προβλήματα με βάση τη γενικευμένη θεωρία των Lord και Shulman και αυτή των Green και Lindsay. / --

No description available.

The application of laser generated ultrasonics was first demonstrated in the mid-seventies and has shown good potential when applied to isotropic materials. However, its use with composite materials is still in the early stages of development. This study explores the potential for application of laser generated Rayleigh and Lamb waves in graphite/epoxy composites. Numerical results are obtained by the solution of the wave equations using assumed solutions, and enforcing the boundary conditions. Experimentally, Rayleigh and Lamb waves were generated by a Q-switched ruby laser in the ablation regime and detected by piezoelectric pinducers which permitted accurate phase velocity measurements. The Rayleigh wave velocity was measured at various directions relative to the fiber direction and results were found to agree closely with numerical predictions. The increase of surface wave velocity using thin plates could be useful for the application of delamination detection in thick composites and an increase of Rayleigh wave attenuation could indicate damages caused by impact. Also, surface waves can reflect from small surface cracks. Therefore, laser generated surface waves, particularly along the fiber direction, have high potential for application in non-destructive testing. Lamb wave experiments were conducted in aluminum plates and gave distinctive signals, but there were some difficulties in detecting the precise arrival of each Lamb wave mode for the graphite/epoxy composite plates. / Graduation date: 1992

Thesis (M. Eng.)--Carleton University, 1993. / Also available in electronic format on the Internet.