Martin G. Manley

Linear stability of stagnation flow

The linear stability of a steady stagnation flow over a cylindrical body is examined. Special consideration is given to the influence oscillatory modulation of the steady flow has on the bifurcation of three‐dimensional vortical disturbances from stability. It is shown that such modulations result in a fixed bifurcation point according to linear stability theory. The sensitivity of the bifurcation point to the time‐harmonic modulation and steady flow speed is considered in the analysis. It is shown that stagnation flow exhibits instability if unsteadiness is introduced into the basic state of the flow. Analytical results are compared to experimental data.

Sensitivity of a spherically focused transducer to focal length and aperture

A method is presented to calculate the impulse respone of a spherically focused transducer which generates a signal and then receives the reflection of the signal from a rigid surface. Results of calculations are shown in order to illustrate the effects of varying the focal length and the aperture. These results suggest a method for empirical determination of effective values of the governing parameters of the transducer impulse response.

The ultrasonic reflection from a flat‐bottom hole

The reference for calibration of ultrasonic measuring equipment used to detect flaws in metal is the reflection from a set of flat‐bottom holes in metal blocks. Early experimental observation as well as an early analysis using a far‐field assumption suggested that the response should vary linearly with the area of the hole. Recently, the validity of this linear result has been called into question by new analyses as well as experiment. This paper presents a new analysis of the reflected signal and evaluates the block set which is used for ASTM recommended practice E‐127 in light of this analysis.

Selection of a shell model for a cylindrical shell immersed in fluid

There are many thin shell models available to the investigator studying the vibrations of thin‐walled, circular, cylindrical shells. A rational method for selecting a model for any given problem is needed. An asymptotically exact dispersion relation for waves on fluid‐loaded, elastic, hollow cylinders derived from the exact equations of elasticity previously [M. Manley, J. Acoust. Soc. Am. 93, 2335(A) (1993)] is applied to determine dominant terms for dispersion of axial waves. This is compared with dispersion relations obtained from shell models. The simplest shell model retaining the dominant terms in the dispersion relation is recommended. Some examples are presented. [The author acknowledges the advice of A. D. Pierce.]

Influence of finite impedance walls on the sound field in an enclosure

A numerical technique is presented for computing the pressure distribution in the interior of a rectangular enclosure. The analysis models the effect of a nonuniform distribution of wall impedance. The normal modes for this problem are evaluated by solving Green’s integral equation. The wall admittance function is represented as the sum of a mean value superimposed by spatially varying fluctuations. An asymptotic series solution for the pressure about the mean value of the wall admittance is not guaranteed convergence for functions that exhibit large perturbations from the mean. The convergence of the series is shown to be improved by transforming the pressure to a rational functional representation. The superposition of normal modes determined by this technique serves as Green’s function that allows the acoustics of the enclosure to be modeled for a variety of sources. The effect of the wall impedance on the transient response and the reverberation time of the room is presented. [Work supported in part b...

Dispersion predictions for waves along a cylindrical shell immersed in fluid

The behavior of guided flexural waves of an infinite, elastic, circular cylinder immersed in fluid was considered previously [M. Manley, J. Acoust. Soc. Am. 92, 2387 (1992)]. The fluid is of lower density than the solid. The asymptotically exact dispersion relation derived previously is applied to determine dominant terms for dispersion of axial waves in the vicinity of the ring frequency. The effect of fluid loading on the cutoff frequency for the longitudinal mode is examined. [Supported by the PSU Applied Research Laboratory Exploratory and Foundational Research Program.]

Elastohydrodynamic waves associated with a thick elastic cylinder immersed in fluid

The behavior of guided flexural waves of an infinite, elastic, thick‐walled circular cylinder immersed in fluid is considered in the low‐frequency limit. The fluid is of lower density than the solid. The dependence of field quantities on φ, t, and x is of the form einφe−iωteikx, where n is the circumferential wave number, ω is the frequency of vibration, k is the wave number in the axial direction, φ is the circumferential coordinate, t is time, and x is the coordinate in the direction of the cylinder axis. Solutions for the exact dispersion relation based on the full elastodynamic equations will be presented. Appropriate approximations will be shown for a simplified representation of the dispersion relation of the lowest‐order flexural wave. It will be shown that standard shell theory results correspond to different limits of the exact result. [Work supported by the PSU Applied Research Laboratory Exploratory and Foundational Research Program. The author acknowledges the advice of A. D. Pierce.]

Higher‐order theory for fluid‐loaded thin elastic plates.

An elastic, infinite plate of finite thickness with fluid loading on one side and vacuum on the other is considered. Appropriate approximations to the dispersion relation based on the full elastodynamic equations will be presented for the range 0<kh<2, where k is the wave number and h is the thickness. [Supported by the PSU Applied Research Laboratory Exploratory and Foundational Research Program. The author acknowledges the advice of A.D. Pierce.]

Waves on fluid‐loaded thin elastic plates near the coincidence frequency.

An elastic, infinite plate of finite thickness with fluid loading on one side and vacuum on the other is considered. Thin plate models are generally adequate for this problem, but fail near the coincidence frequency. Predictions based on the full elastodynamic equations will be presented for waves near the coincidence frequency. [Work supported by the PSU Applied Research Laboratory Exploratory and Foundational Research Program. The author acknowledges the advice of A. D. Pierce.]

Waves on fluid‐loaded cylindrical shells: Systematic expansions based on full elastodynamic equations

Further work is reported for the canonical model of an elastic coaxial cylinder, with inner radius R − 12 h and outer radius R + 12 h immersed in a compressible fluid, with the full set of elastodynamic equations, rather than a simplified shell model, used as a starting point for analysis. This dynamical system admits wave solutions of constant angular frequency ω, in which all of the appropriate field variables vary with azimuthal angle φ and axial coordinate x through a common factor eikxxeinφ with n = kyR not necessarily being an integer. One seeks simplified expressions for the dispersion relation F(ω,kx,ky) = 0 and for the polarization relations that determine the ratio of the complex amplitudes of displacements and stresses on the middle surface of the shell, and on the outer and inner surfaces. Systematic exact analytical (not numerical) expansions of the dispersion relations and the polarization relations in powers of parameters (such as h/R) are derived by a procedure that involves use of a compu...