Courtney B. Burroughs

An introduction to statistical energy analysis

The basic concepts and underlying assumptions of Statistical Energy Analysis (SEA) are reviewed. Using coupled simple oscillators as models for resonant modes, power balance equations are derived. Equipartition of energy among modes within a subsystem, and strong versus weak coupling between subsystems are discussed. Input requirements for exercising SEA power balance equations are defined and methods of obtaining the required input are outlined. Examples of the applications of SEA are presented and discussed.

Acoustic radiation from fluid‐loaded infinite circular cylinders with doubly periodic ring supports

Analytic expressions are derived for the farfield acoustic radiation from a point‐driven, fluid‐loaded circular cylindrical shell reinforced with doubly periodic ring supports. The ring supports interact with the cylindrical shell only through normal forces. The model includes the effects of fluid loading and interactions between supports. Predictions are compared to measured farfield acoustic radiation data taken on a finite circular cylindrical shell with doubly periodic ring supports. Characteristics of the acoustic radiation are examined by example and some physical interpretation of significant features are offered.

Acoustic radiation from bowed violins

Near-field acoustic holography (NAH) is applied to visualize the acoustic radiation from bowed violins across a frequency range from 294 Hz to 3 kHz. These visualizations are employed to localize regions of acoustic radiation from surfaces of violins. Three violins were tested: a common student instrument by Scherl and Roth; Hutchins violin SUS295, which has been the subject of many previous investigations; and a Hutchins mezzo violin from the Violin Octet set of instruments, which is longer, broader, and thinner than a standard instrument. The violins were bowed continuously with an open-frame mechanical bowing machine, while NAH measurements were made on four planes surrounding the instrument. Mappings of the acoustic intensity are presented that show locations of maximum radiation at low and high frequencies with a spatial resolution smaller than the acoustic wavelength. Comparisons are made of the radiation patterns between the two conventional instruments and the mezzo violin. Radiation patterns from...

CAVITY FLOW TONES IN WATER

Measurements of tones generated by flow over cavities were conducted in the ARL Penn State small water tunnel. The frequency dependence of cavity tones on the flow velocity and the size of the cavity opening in the streamwise direction are presented and discussed. Measured cavity wall vibration levels, unsteady pressure levels inside the cavity, and flow visualization are used to analyze generating mechanisms for cavity tones and Helmholtz resonances.

Power flow in coupled bending and longitudinal waves in beams

In complex structures, curvature and impedance discontinuities (e.g., junctions) couple bending and longitudinal waves. Propagation losses for longitudinal waves are often much less than losses for bending waves, and damping treatments often less effective on longitudinal waves. When the dissipation in longitudinal waves is less than that on bending waves, longitudinal waves can provide an efficient means of power flow between bending waves generated at one location and bending waves that are a source of acoustic radiation at another location. In order to design and locate effective treatments, knowledge of the power flow in longitudinal as well as bending waves is required. The measurement of power in both bending and longitudinal waves when both waves are present is demonstrated. Measurements conducted on a straight beam and a T-beam are compared to predictions obtained using finite element methods. The effect of coupling between waves at the junction in a T-beam is illustrated using results from measurements of power flow.

An analytic model for the free in‐plane vibration of beams of variable curvature and depth

In this study a flexible and powerful model is presented for the in‐plane vibration of a beam whose curvature and depth are arbitrary, constrained only to such smoothness as can be accommodated by a quartic polynomial in the centerline arc length. The model includes the effects of shear deformation, rotary inertia, and centerline extensibility. The equations of motion are solved by an extension of the classic Galerkin method wherein the effect of boundary residuals is included. Timoshenko models are compared to other theoretical models and to experimental results; the comparisons are done for a variety of support schemes. A detailed study of a cantilever beam of variable curvature and depth is done and, finally, the utility and flexibility of the model is demonstrated for an arch whose shape is given only by a scale drawing, devoid of any other information except material properties.

Acoustic radiation from fluid‐loaded, ribbed cylindrical shells excited by different types of concentrated mechanical drives

Analytic expressions are derived for the far‐field acoustic radiation from a fluid‐loaded circular cylindrical shell reinforced with two sets of parallel periodic ribs and excited by seven types of mechanical point drives: single radial, in‐ and out‐of‐phase double radial, axial moment, circumferential moment, and in‐ and out‐of‐phase in‐plane double circumferential. The ribs interact with the cylindrical shell only through normal forces. The model includes the effects of fluid loading, internal damping, and interactions between ribs. Measurements of the acoustic radiation from a ribbed cylindrical shell excited by different types of drives are presented. Comparisons between measured and predicted results are made. Predictions of the acoustic radiation from the unsupported and supported shell with different types of drives are compared. The effects of properties of the shell and types of drives on the acoustic radiation are examined by example and some physical interpretation of significant features are o...

Forced Harmonic and Random Vibrations of Concentric Cylindrical Shells Immersed in Acoustic Fluids

The forced harmonic and random vibrations of an elastic cylindrical shell surrounded by an inviscid fluid and concentrically contained by another thin elastic shell which itself is immersed in another inviscid fluid of infinite extent is considered. The motion of the shells and fluids is assumed independent of the axial coordinate. The motion of the shells is described by a theory which accounts for transverse shear and rotatory inertia. The motion of the fluids is described by the classical wave equation. Expressions for the acoustic pressure at the outer surface of the inner shell and the inner and outer surfaces of the outer shell are obtained along with the displacements (velocity) at these surfaces. Numerical results for the near‐ and farfield acoustic pressure are given for the case wherein the interior of the cylinder is subjected to diametrically opposed point forces which vary either harmonically or randomly with time. The random excitation is assumed to be spatially uncorrelated, broad‐band whit...

Identification of sources of tire/pavement interaction noise

Although most highway noise is due to radiation from rolling tires, the dominant sources of tire/pavement interaction noise remain largely unknown. In this study, near‐field acoustical holography (NAH) is used to visualize the acoustic field of a rolling tire on outdoor pavement surfaces. Since NAH measurements are conducted in the near field, areas of maximum radiation from the tire may be localized with a much finer resolution than with conventional measurements. Planar NAH is used to scan planes along the side, front, and rear planes of the tire. A scanning mechanism will be attached to an automobile trailer for measurements of tire noise under realistic conditions and procedure as developed in earlier results [R. J. Ruhala and C. B. Burroughs, SAE 972047 (1997)]. Several types of tires are evaluated, including blank tire, tire with even spaced transverse grooves, tire with only circumferential grooves, and a production passenger car tire. The tires are tested on both smooth and rough pavements, and at several speeds. The results will provide further insight into the sources and mechanisms of tire/pavement interaction noise. [Work supported by Goodyear, DOT, and GM.]

Frequencies of resonance of axisymmetric modes of open prolate spheroidal shells

Governing differential equations are derived for the axisymmetric motion of an open prolate spheroidal shell with inner and outer surfaces defined by prolate spheroidal coordinate surfaces. Transverse shear and rotary inertia terms are included in the shell equations. The open end of the shell, defined by a circumferential coordinate line, is assumed clamped. Approximate solutions for the axisymmetric frequencies of resonance of the in‐vacuo and fluid‐loaded shell are derived using the Galerkin method. For the in‐vacuo shell, good agreement with published results for the exact frequencies of resonance of a spherical shell is obtained. Results are presented for the frequencies of resonance of open prolate spheroidal shells as a function of shell eccentricity, mode number, shell thickness, and opening angle, with and without fluid loading.