On Boussinesq-type models for long longitudinal waves in elastic rods

In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these derivations to include axially symmetric loading on the lateral boundary surface, and longitudinal pre-stretch. We systematically derive two forced Boussinesq-type models from the full equations of motion and non-zero surface boundary conditions, utilising the presence of two small parameters characterising the smallness of the wave amplitude and the long wavelength compared to the radius of the waveguide. We compare the basic dynamical properties of both models (linear dispersion curves and solitary wave solutions). We also briefly describe the laboratory experiments on generation of bulk strain solitary waves in the Ioffe Institute, and suggest that this generation process can be modelled using the derived equations.Comment: 19 pages, 5 figures, submitted to the Special Issue of Wave Motion, "Nonlinear Waves in Solids", in Memory of Professor Alexander M. Samsono

Deterministic dynamics of stimulated Brillouin scattering in optical fibres

Abstract unavailable please refer to PD

The detection of Gravitational Waves

This chapter is concerned with the question: how do gravitational waves (GWs) interact with their detectors? It is intended to be a theory review of the fundamental concepts involved in interferometric and acoustic (Weber bar) GW antennas. In particular, the type of signal the GW deposits in the detector in each case will be assessed, as well as its intensity and deconvolution. Brief reference will also be made to detector sensitivity characterisation, including very summary data on current state of the art GW detectors.Comment: 33 pages, 12 figures, LaTeX2e, Springer style files --included. For Proceedings of the ERE-2001 Conference (Madrid, September 2001

The elastic wave propagation in rectangular waveguide structure determination of dispersion curves and their application in nondestructive techniques

The use of mechanic waves for assessing structural integrity is a well-known non-destructive technique (NDT). The ultrasound applied in the guided wave in particular requires significant effort in order to understand the complexities of the propagation so as to develop new methods in damage detection, in this case, knowing the interaction between the wave propagation and the geometry of the waveguides is mandatory. In the present work, the wave propagation in rectangular steel rod is presented. In this study, the section dimensions were fixed as 5 × 15 [mm], a typical element of the flexible riser structural amour commonly used in the offshore oil industry. The studies here presented were restricted to [0, 100 KHz] frequencies. This frequency interval is in the range of commercial waveguide equipment commonly applied in ducts in NDT applications. The computation of the dispersion curves is performed by using three different methodologies: (i) analytical solutions, (ii) a method that combines analytical approaches with finite element methods (SAFE), and (iii) experimental method that extracted information from the rod using laser vibrometers and piezoelectric actuators. Finally, two applications based on the dispersion curves determined in the rectangular waveguide are presented to illustrate the possibilities of the curve dispersion knowledge related to the specific geometry in the development and application linked to NDT. The first application consists on showing the possibilities of the techniques that use a fiber grating Bragg cell (FGB) to measure the wave displacement and the second application involves the simulation of pre-fissured prismatic waveguide aimed at searching to induce three characteristic acoustic events. The model was built combining the finite element method and a version of the discrete element method

Intrinsic dissipation in high-frequency micromechanical resonators

We report measurements of intrinsic dissipation in micron-sized suspended resonators machined from single crystals of galium arsenide and silicon. In these experiments on high-frequency micromechanical resonators, designed to understand intrinsic mechanisms of dissipation, we explore dependence of dissipation on temperature, magnetic field, frequency, and size. In contrast to most of the previous measurements of acoustic attenuation in crystalline and amorphous structures in this frequency range, ours is a resonant measurement; dissipation is measured at the natural frequencies of structural resonance, or modes of the structure associated with flexural and torsional motion. In all our samples we find a weakly temperature dependent dissipation at low temperatures. We compare and contrast our data to various probable mechanisms, including thermoelasticity, clamping, anharmonic mode-coupling, surface anisotropy and defect motion, both in bulk and on surface. The observed parametric dependencies indicate that the internal defect motion is the dominant mechanism of intrinsic dissipation in our samples

Index to NASA Tech Briefs, 1975

This index contains abstracts and four indexes--subject, personal author, originating Center, and Tech Brief number--for 1975 Tech Briefs

Longitudinally Graded Optical Fibers

Described herein, for the first time to the best of our knowledge, are optical fibers possessing significant compositional gradations along their length due to longitudinal control of the core glass composition. More specifically, MCVD-derived germanosilicate fibers were fabricated that exhibited a gradient of up to about 0.55 weight percent GeO2 per meter. These gradients are about 1900 times greater than previously reported for fibers possessing longitudinal changes in composition. The refractive index difference is shown to change by about 0.001, representing a numerical aperture change of about 10%, over a fiber length of less than 20 m. The lowest attenuation measured from the present longitudinally-graded fiber (LGF) was 82 dB/km at a wavelength of 1550 nm, though this is shown to result from extrinsic process-induced factors and could be reduced with further optimization. The stimulated Brillouin scattering (SBS) spectrum from the LGF exhibited a 4.4 dB increase in the spectral width, and thus reduction in Brillouin gain, relative to a standard commercial single mode fiber, over a fiber length of only 17 m. Fibers with longitudinally uniform (i.e., not gradient) refractive index profiles but differing chemical compositions among various core layers were also fabricated to determine acoustic effects of the core slug method. The refractive index of the resulting preform varies by about ± 0.00013 from the average. Upon core drilling, it was found that the core slugs had been drilled off-center from the parent preform, resulting in semi-circular core cross sections that were unable to guide light. As a result, optical analysis could not be conducted. Chemical composition data was obtained, however, and is described herein. A third fiber produced was actively doped with ytterbium (Yb3+) and fabricated similarly to the previous fibers. The preforms were doped via the solution doping method with a solution of 0.015 M Yb3+ derived from ytterbium chloride hexahydrate and 0.30 M Al3+ derived from aluminum chloride hexahydrate. The doped preform was engineered to have two core layers of differing chemical composition, resulting in both a gradient refractive index profile as well as a gradient acoustic profile. While exhibiting higher loss than the original LGF, the Yb3+-doped fiber showed slightly better SBS suppression with preliminary calculations showing at least 6 dB reduction in Brillouin gain. Lastly, reported here is a straight-forward and flexible method to fabricate silica optical fibers of circular cladding cross-section and rectilinear cores whose aspect ratio and refractive index profile changes with position along the fiber in a deterministic way. Specifically, a modification to the process developed to produce longitudinally-graded optical fibers, was employed. Herein reported are MCVD-derived germanosilicate fibers with rectangular cores where the aspect ratio changes by nearly 200 % and the average refractive index changed by about 5 %. Fiber losses were measured to be about 50 dB/km. Such rectangular core fibers are useful for a variety of telecommunication and biomedical applications and the dimensional and optical chirp provides a deterministic way to control further the modal properties of the fiber. Possible applications of longitudinally graded optical fibers and future improvements are also discussed. The methods employed are very straight-forward and technically simple, providing for a wide variety of longitudinal refractive index and acoustic velocity profiles, as well as core shapes, that could be especially valuable for SBS suppression in high energy laser systems. Next generation analogs, with longitudinally-graded compositional profiles that are very reasonable to fabricate, are shown computationally to be more effective at suppressing SBS than present alternatives, such as externally-applied temperature or strain gradients

Nondestructive Evaluation and Structural Health Monitoring Based on Highly Nonlinear Solitary Waves

Recent decades have witnessed the rapid growth and acceptance of nondestructive evaluation (NDE) techniques in assessment of infrastructures' conditions. Assessing the conditions of infrastructures is important to determine their safety and reliability which have a great impact on today's society. The existing NDE techniques include acoustics, ultrasound, radiology, thermography, electromagnetic method, optical method, and so on. Properly employed NDE techniques can reduce the maintenance and repair cost and improve the reliability of the infrastructures. In the last two decades, the study of the highly nonlinear solitary waves (HNSWs) has received much attention. Most of these studies focused on the propagation of HNSWs in granular systems, but little work on applications of HNSW-based NDE method has been done. HNSWs are mechanical waves that can form and travel in highly nonlinear systems, one-dimensional chain of identical spheres is one of the most common systems that can support the generation and propagation of HNSWs. In the study presented in this dissertation, a new NDE technique based on the generation and propagation of HNSWs was investigated and applied to different structural materials. First, fundamental research on the generation of HNSWs in a chain of stainless steel beads by laser pulses was conducted. The results showed that the laser-based generation of HNSWs produces results that are equivalent to those obtained by means of a mechanical striker. Then, the feasibility of tuning HNSWs by electromagnetically induced precompression was demonstrated experimentally. By changing the precompression on the chain of particles, the properties of the HNSWs could be tuned in a wide range. Then a HNSW-based transducer was designed and built. The transducer was remotely and automatically controlled by National Instruments PXI running Labview. The ability of the new transducer to generate repeatable HNSWs was assessed. Finally, the HNSW transducer was used to monitor cement setting, concrete curing and epoxy curing, to evaluate the bond condition of an aluminum lap-joint, and to detect the impact damages in a composite plate. The results showed that the HNSW-based technique is promising for structural NDE. A pilot numerical study on acoustic lens which is a device can focus the acoustic waves at a focal point was also conducted

Analysis and Comparison of Effects of an Airfoil or a Rod on Supersonic Cavity Flow.

The effects of an airfoil at different angles of attack and a circular cylindrical rod within the edge of the boundary layer flow at the leading edge of a cavity as a device for controlling the large pressure fluctuations (resonance tones) in the cavity were investigated. The airfoil results were compared with the rod in crossflow method positioned at the same leading edge location. The cavity used for testing corresponded to a length to depth ratio, L/D of 11.0/2.25 with a length to width ratio, L/W of 11.0/3.00 at a freestream Mach 1.84 flow. The study included measurements of dynamic pressure transducer output at 40 kHz and Frequency Spectra calculations, using Schlieren techniques for shock wave structures with velocity and vorticity fields obtained from PIV measurements. All airfoil configurations experienced flow separation to varying degrees. The negative 10 degree angle of attack configuration experienced the greatest amount of flow separation. All airfoil configurations provided varying degrees of cavity (resonant) tone suppression. Of the airfoil configurations, the negative 10 degree airfoil provided the best noise suppression with a 5 dB SPL reduction in broadband noise and a 9 dB reduction in peak amplitude for the 3rd resonant mode. Although all the airfoil configurations provided various levels of noise suppression, none of the configurations performed to the level of the rod in crossflow technique which provided an 8 dB SPL reduction in broadband noise and a 22 dB reduction in peak amplitude for the 2nd resonant mode. Indications of shear flow lofting effects could not be studied within any of the configurations tested. Lofting effect testing would have required flow field visualization of the cavity trailing edge region. Dynamic pressure measurements at a location near the cavity trailing edge did not detect the rod vortex shedding frequency, clearly. Because PIV results showed strong indication of vortex shedding, the lack of vortex shedding frequency data was attributed to the dynamic pressure transducer being located a far distance of 44 rod diameters downstream of the rod location. All airfoil test configurations showed evidence of deflections to the cavity leading edge oblique shock wave. The mechanisms of the deflection were the airfoil trailing edge shocks interacting with the cavity leading edge shock