<i>Acoustical Engineering</i>

Olson, Harry F.; Beyer, Robert T.

doi:10.1063/1.3060138

Cited by 74 publications

(42 citation statements)

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“…(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) lead to an interesting restriction on the shape of the boundary. It is well known that the reflection of a shear wave at a free boundary is in general accompanied by a partial (or in some cases, total) conversion of the incident energy to longitudinal wave motion.…”

Section: Derivation From Hamilton's Principlementioning

confidence: 99%

“…In cylindrical coordinates, we can express this requirement through the three equations* rr cos(n,r) + r rz cos(n,z) + Tr cos(n,p) = T r 0 0 T cos(n,r) + Tr cos(n,z) + Tr cos(n,cp) = T = 0 , (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) rz zz zcp z r cos(n,r) + r cos(n,z) + T" cos(n,qp) = T = 0 rcp zcp cq C where T, Tz, and T are the three components of the traction, and (n,r), (n,z), and (n,cp) represent the angles between the outward-directed normal to the surface and the r-, z-, and 9-directions, respectively.…”

Section: Derivation From Hamilton's Principlementioning

confidence: 99%

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Solid Torsional Horns

Pyle¹

1963

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The propagation of torsional waves in tapered solid elastic rods has been studied both theoretically and experimentally from the viewpoint of acoustic horn theory.Such tapered rods in torsional vibration have been dubbed "torsional horns," Two differential equations are derived which describe the propagation of torsional waves.One of these is an "exact" wave equation which can be readily solved only when the horn boundaries fit a separable coordinate system.The other is an approximate wave equation based on the assumption that the wavefronts are plane cross sections of the horn.This equation is very similar to Webster's plane-wave equation for compressional waves in an acoustic horn, For purposes of analysis, torsional horns are divided into three categories: those having smooth contours fitting separable coordinates, those having smooth contours not fitting separable coordinates, and those having piecewise-smooth contours.Experimental apparatus was devised and built for the measurement of the standing-wave patterns and ,resonance frequencies of experimental torsional horns made of brass or mild steel. The experimental data are compared with the solutions of the two wave equations for selected horn contours from each category. A quantitative estimate of the error introduced by the plane-wave approximation is obtained for the exponential horn. The boundary condition that the normal derivative of the angular displacement wust vanish at a free surface is also derived in Chapter II.In Chapter III is a description of the techniques and apparatus developed for the experimental investigation of the properties of torsional horns. The goals of the experimental program were the measurement of the resonance frequencies and standing-wave patterns at resonance of finite solid horns, To measure a standing-wave pattern, the specimen horn is excited at the corresponding resonance frequency and the amplitude of vibration at a movable measurement point is comparedwith the amplitude at a fixed reference point. Conventional phonograph pickups are used as the vibration-sensing elements. Torque is exerted on the specimen horn by an eddy-current driver developed for the purpose.This driver has no mechanical connection to the specimen horn. It exerts torque on the specimen horn at two frequencies which are the sum and difference of the frequencies of the currents in its two field wind-ings. An approximate analysis of the driver operation indicates that Os approximately twice as much torque is exerted on ferrous tkimr on nonferrous specimen horns.This was verified experimentally. The'fact that the torque is induced at frequencies other than the driving-current frequencies permits isolation of desired signal from interference coupled xi magnetically directly from driver to phonograph pickup, The horn under study is used as the frequency-determining element in a self-excited oscillator to insure that the drive is applied to the specimen horn at the resonance frequency.The, 0 ftof a resonance of a specimen horn can be calculated f...

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Section: Derivation From Hamilton's Principlementioning

confidence: 99%

Section: Derivation From Hamilton's Principlementioning

confidence: 99%

Solid Torsional Horns

Pyle¹

1963

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show abstract

“…In the preceding discussions, the use of a known gas has been assumed In practice care must be taken by repeated bakeout and evacuation to remove all foreign volatile materials Transducer Transducer theory is discussed in a number of specialized books [12][13][14] ACOR REACTOR GRADE GRAPHITE …”

Section: Acoustical Transmission Linementioning

confidence: 99%

“…As stated previously, 1/4 in. ID ^vas chosen as the maximum diameter for the transmission line that would not be unduly expensive or difficult to install Equation (13) predicts an attenuation at 2 kHz of 0. 42 db ft-1…”

Section: Ratio Of Molecular Volume To Gas Volume and Van Der Waals Fomentioning

confidence: 99%