Browsing by Author "Thompson, Charles"

Now showing 1 - 9 of 9
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    Acoustic scattering by discontinuities in waveguides
    Sen, Rahul (Virginia Polytechnic Institute and State University, 1988)
    The scattering of acoustic waves by boundary discontinuities in waveguides is analyzed using the Method of Matched Asymptotic Expansions (MAE). Existing theories are accurate only for very low frequencies. In contrast, the theory developed in this thesis is valid over the entire range of frequencies up to the first cutoff frequency. The key to this improvement lies in recognizing the important physical role of the cutoff cross-modes of the waveguide, which are usually overlooked. Although these modes are evanescent, they contain information about the interaction between the local field near the discontinuity and the far-field. This interaction has a profound effect on the far-field amplitudes and becomes increasingly important with frequency. The cutoff modes also present novel mathematical problems in that current asymptotic techniques do not offer a rational means of incorporating them into a mathematical description. This difficulty arises from the non-Poincare form of the cross-modes, and its resolution constitutes the second new result of this thesis. We develop a matching scheme based on block matching intermediate expansions in a transform domain. The new technique permits the matching of expansions of a more general nature than previously possible, and may well have useful applications in other physical situations where evanescent terms are important. We show that the resulting theory leads to significant improvements with just a few cross-mode terms included, and also that there is an intimate connection with classical integral methods. Finally, the theory is extended to waveguides with slowly varying shape. We show that the usual regular perturbation analysis of the wave regions must be completely abandoned. This is due to the evanescent nature of the cross-modes, which must be described by a WKB approximation. The pressure field we so obtain includes older results. The new terms account for the cutoff cross-modes of the variable waveguide, which play a central role in extending the dynamic range of the theory.
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    Acoustic streaming in a waveguide with slowly varying height
    Thompson, Charles (Acoustical Society of America, 1984-01-01)
    An analysis of acoustic streaming in a two-dimensional waveguide having slowly varying height is presented. Special attention is paid to waveguides with cross sections that are small compared to the acoustic and/or wall wavelengths. It is shown that the dynamic behavior of the enclosed fluid can be parameterized by the values of three small parameters, ɛ, 1/S, and 1/R, where ɛ is the ratio of the typical duct height H₀ to the wall wavelength L₀, 1/S is the ratio of the typical oscillatory particle displacement U₀ to the typical duct height H₀ and 1/R is the ratio of the oscillatory boundary layer thickness lᵥ to the typical duct height H 0. An analytical solution describing the streaming flow in the duct is given in terms of a regular perturbation sequence in ɛ. It is shown that the oscillatory pressure must satisfy the lossy Webster horn equation to O(ɛ²) if the no slip boundary condition is to be satisfied. Outside the boundary layer it is shown that the time averaged slip velocity is the sum of two terms. The first term is proportional to the product of the incident and reflected wave amplitudes. The second term is proportional to the difference between the incident and reflected acoustic intensity of the wave. For small values of 1/S, 1/R, and ɛ the streaming solution given is shown to be valid until R/S 2 becomes of O(1).
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    Acoustic wave propagation in a circular cosh duct carrying a mean flow
    Thompson, Charles; Sen, Rahul (Acoustical Society of America, 1987-09-01)
    An analysis of acoustic wave propagation in a waveguide carrying an incompressible mean flow is presented. The radius of the waveguide is taken to vary slowly as a function of axial location. It is shown that the dynamic behavior of the enclosed fluid can be parametrized by the small parameter where is the ratio of the typical duct radius R 0 and the wall wavelength L 0. An analytical solution for the pressure field in the duct is given in terms of a regular perturbation expansion in The method of matched asymptotic expansions is used to evaluate the refractive effect of a thin mean-flow boundary layer on the acoustic pressure field. It is shown that in the case where the duct geometry conforms to that of a circular cosh duct the effect of higher-order turning points in the wave equation can be effectively handled by a closed-form solution that approximately solves the governing equations. The results of analysis are compared to those obtained using numerical methods. 1987 Acoustical Society of America
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    Linear inviscid wave propagation in a waveguide having a single boundary discontinuity: Part I: Theory
    Thompson, Charles (Acoustical Society of America, 1984-02-01)
    An examination of wave propagation in waveguides of rectangular cross section having a single boundary discontinuity is presented. Special attention is paid to waveguides with heights that are small compared to an acoustic wavelength. It is shown that the dynamic behavior of the enclosed fluid can be parametrized by the value of a single small parameter ɛ, where ɛ is the ratio of the typical duct height H₀ to the wall wavelength L₀. The influence of planar discontinuities of zero and small but finite thickness on wave propagation is determined using the method of matched asymptotic expansions. Junction conditions, impedance across the junction, and uniformly valid composite expansions for the pressure in the duct are presented.
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    Linear inviscid wave propagation in a waveguide having a single boundary discontinuity: Part II: Application
    Thompson, Charles (Acoustical Society of America, 1984-02-01)
    The method of match asymptotic expansions MMAE, is used to analyze wave propagation in two problem geometries. The acoustic pressure is evaluated for a waveguide having a single discontinuity in wall slope and a waveguide having a right-angle bend. A two-port representation of the fluid motion across the discontinuity for each problem is tabulated. A uniformly valid expression for the pressure for each problem is given.
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    On the acoustics of a coupled space
    Thompson, Charles (Acoustical Society of America, 1984-03-01)
    An examination of acoustic wave propagation in a coupled space is presented. The analysis presented is limited to the first two longitudinal modes of the cavity. It is shown that the spacial behavior of the modes of vibration in the cavity is affected by the coupling discontinuity. The degree with which the discontinuity influences the pressure variation is parametrized by a single small parameter ɛ, where ɛ is the ratio of the typical cavity height, H₀ to the cavity length L 0. An approximate solution for the pressure in the space is obtained using the method of matched asymptotic expansions. Experimental results are also presented as verification of the theoretical results.
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    The response of multidegree-of-freedom systems with quadratic and cubic nonlinearities subjected to parametric and external excitations
    HaQuang, Ninh (Virginia Polytechnic Institute and State University, 1986)
    A weakly nonlinear system under simultaneous sinusoidal external and parametric excitations is investigated. Quadratic and cubic nonlinearities are present in the governing equations. A general perturbation analysis, the Method of Multiple Scales (MMS), is performed for numerous resonance frequencies. Emphasis is initially placed on the response of the system under parametric excitation alone. The nonresonant external and parametric excitations are then considered. Finally, responses involving both parametric and external excitations are considered. The excitation frequencies are assumed to be from the same source. . When the frequency of the_parametric and external excitations are different (λ≠Ω), many of the different resonances investigated have solvability conditions similar to those found in two preliminary works performed by Mook, Plaut and HaQuang. When the frequencies are nearly equal, numerous steady-state response curves are shown. Unlike the linear analysis, the frequency-response curves show many multi-valued responses. In some instances, as many as five amplitudes exist for a given frequency. Three are stable and two are unstable. In addition, multi-modal responses were found to exist under a single-mode excitation. This result is unique since no internal resonance was considered. For certain values of the coefficient of the nonlinear restoring forces, stable bimodal steady states were observed. In order to verify some of the theoretical results obtained by MMS, a sixth-order Runge Kutta procedure was performed on the original governing equation. The numerically integrated results and the approximate solution of MMS show excellent agreement when the parameter ε is sufficiently small. However, when ε is sufficiently large, the MMS approximate solution breaks down. Interesting phenomena, such as periodic doubling and chaos, are observed.
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    Response to 'Comment on Linear inviscid wave propagation in a waveguide having a single boundary discontinuity: Part II: Application [J. Acoust. Soc. Am. 75, 356-362 (1984)]'
    Thompson, Charles (Acoustical Society of America, 1986-10-01)
    This paper addresses the comments of Dr. Bruggeman and Dr. van de Wetering. The source of the error present in the paper entitled "Linear inviscid wave propagation in a waveguide having a single boundary discontinuity: Part II: Application is addressed. A rational fraction approximation for the transmission coefficient is presented.
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    Scattering of acoustic waves in a waveguide
    Sen, Rahul; Thompson, Charles (Acoustical Society of America, 1987)
    The problem of scattering from boundary discontinuity in a waveguide is discussed. The relationship between the static and dynamic representations of the scattered pressure field will be investigated for those frequencies falling below the first cross mode of the duct. Special attention is paid to the influence of cutoff cross modes to the solution of the pressure field. It is shown that the method of matched asymptotic expansions can be successfully used to determine globally valid pressure field junction conditions near a boundary discontinuity. The matching of exponentially decaying terms of the inner solution is shown to, in turn, contribute to the junction impedance and extend the frequency range of the solution's validity.