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Nov 1978

Volume 64, Issue S1, pp. S1-S183

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back to top Session FFF. Shock and Vibration V: (a) Seismics, Shells and Smashes. (b) Plates, Ribs, and Panels
Contributed Papers
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Assessment of acoustical technology for minimizing seismic damage to urban utility system network (A)

Arun G. Jhaveri

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S156-S156 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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The Puget Sound region of Washington State is one of the most seismically active areas in the country, as demonstrated by two major earthquakes, one in 1949 and the other in 1965. The United States Geological Survey (USGS) report, A Study of Earthquake Losses In the Puget Sound, Washington Area (Open File Report 75‐375), concludes that the maximum credible earthquake that can be expected in the Puget Sound area is 7.5 on the Richter Scale of magnitude, and that extensive damage would result, including the deaths of some 2000 people. Earthquakes are a potential threat to the continuous functioning of a city's lifelines (e.g. water and power utilities, communication and transportation networks); however, until recently seismic considerations have not been an integral part of the planning, design, construction, and operational phases of urban lifeline systems. Acoustical technology can play an important role in both the new and retrofitting system design as well as construction of structures, equipment, and facilities associated with such utility components as metropolitan water supply and distribution network. Vibration dampening, shock absorption/isolation techniques, and acoustical instruments for preventive maintainence and potential damage/risk analyses are specific areas of investigation discussed in this paper.
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Analytical solutions for open nonshallow spherical shell vibrations (A)

G. F. Lin

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S156-S156 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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This paper is concerned with axisymmetric as well as nonsymmetric vibrations of open nonshallow thin elastic spherical shells. Without employing the usual auxiliary variables for reduction of shell motion equations introduced by Van der Neut and Berry, independent analytical solutions for middle‐surface displacements are obtained and explicitly expressed in terms of associated Legendre functions. In order to gain physical insights into the free‐vibration characteristics of an open nonshallow shell, theoretical calculations together with asymptotic descriptions are made of natural frequencies and mode shapes of a hemispherical shell with a free edge. The numerical predictions obtained herein compare excellently against the experimental results obtained previously by Hwang and recently in the David W. Taylor Naval Ship R & D Center, Bethesda, Maryland. Essential features of shell dynamics are ultimately displayed by normalized frequency (Ω) and nondimensional shell thickness parameter (β). Five families of natural frequencies, i.e., low Rayleigh bending, mixed bending‐membrane, torsional, bending, and membrane frequencies, are found. The corresponding mode shapes exhibit distinctive displacement patterns. [Work supported by Naval Sea Systems Command.]
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Structure response to free‐field acoustic excitation using the statistical energy analysis method (A)

D. M. Wong

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S156-S156 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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The statistical energy analysis (SEA) method has been used very successfully in the prediction of structural response to reverberant acoustic fields. This paper will extend the method to the free field acoustic excitation. The coupling loss factor (an important parameter in the SEA method) between the plate and the exciting acoustic field was derived. The analytical results compare reasonably well with test data obtained during the Space Shuttle (OV‐101) acoustic test conducted at Dryden Flight Research Center. In that test two F‐104 jets were used as sound sources. Accelerometer readings were obtained both at the cargo bay door and the side wall. Also, the correlation constants of the pressure field were obtained from the test.
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A method to estimate collision point of a rod (A)

Osamu Ikeda, Takuso Sato, Jiro Yamamoto, and Akira Manabe

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S156-S156 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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A method to estimate a collision point on a metal rod is presented, which is based on spectral analyses of the signal detected by a single accelerometer attached to the rod. First, the transfer function from a forcing point to the detector is derived, where space‐variant and dispersive characteristics of the rod are taken into consideration in connection with varying diameter, the change of surrounding condition along the axis, and various transmission and reflection loss characteristics. Then an algorithm to estimate collision point is derived by using the obtained transfer function. The fundamental experimental results obtained by using a 17S aluminum rod of 2003 mm length and 10 mm diameter show that the estimated positions agree with the actual collision positions with a precision of less than 1 cm [O. Ikeda, T. Sato, J. Yamamoto and A. Manabe, J. Acoust. Soc. Am (to be published)].
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Nonlinear random vibration of a beam impacting stops (A)

Huw G. Davies

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S157-S157 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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The random vibration of a beam whose motion is constrained at one point by nonlinear springlike stops separated by a gap is considered. The beam is driven by white noise excitation. The beam's motion is described in terms of the unconstrained vibration modes. An equivalent linearisation method is used to obtain from the Fokker‐Planck equation an approximate expression for the joint probability density function of the modal amplitudes. The equivalent linearisation includes the interactions between the unconstrained modes that are caused by the stops. An approximate expression is obtained for the mean square response of the beam to band limited white noise. An estimate based on the equivalent linear, resonant modes is obtained also for the number of impacts.
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Digital simulation of impacting vibration of a cantilever (A)

K. Kishi

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S157-S157 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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The digital computer simulation method is described for analyzing the vibration of a cantilever impacting against a fixed wall. In this study, the local deformation of the impact parts are taken into account. The mechanical vibration system with which a cantilever is subjected to external forces on its arbitrary points and impacts against a fixed wall at one of these points is represented by an equivalent electrical circuit. The equations of motion of this system can be derived from the equivalent circuit. These equations are simultaneous nonlinear differential equations and can be integrated by Runge‐Kutta‐Gill method. In this numerical integration, the time step is chosen to 100 times the period of the highest mode of the cantilever so as to make the accumulated error minimum. Applying this method to several cases, it was found that there are evident differences between the solutions, taking into account the local deformation and those neglected. This method can easily be extended to the more general problem of impacting vibrations and is useful for the study of chattering phenomenon in a relay apparatus.
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On structural‐acoustic scale modeling (A)

G. SenGupta and C. G. Hodge

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S157-S157 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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Use of scale models to study the dynamic response of a fuselage structure subjected to acoustic excitation has many advantages. Recently, constructing a ring‐stiffened cylinder model of a fuselage for verifying some of the concepts for reducing cabin noise is being considered at Boeing. This has raised questions about the feasibility of using geometrically scaled models for simulating dynamic response of a pressurized fuselage structure. A review of the existing literature shows that it is possible to simulate the dynamic response using geometrically scaled models. The effect of internal pressurization was not considered earlier. It is observed that in order to preserve the scaling laws it is necessary to keep the same pressure differential in the model scale and the full scale structure. Another aspect that was not previously looked into in sufficient details was the effect of scaling down the fuselage stiffeners such as the stringers and frames on their natural frequencies. The importance of stiffener resonances on the low‐frequency vibration of the fuselage has been appreciated only recently [G. SenGupta, AIAA Paper 78‐504, 19th Structural Dynamics Conference (April 1978)]. It is shown that the relationship among the natural frequencies of the various components existing in a full scale structure can be easily preserved in the model scale structure. It is also shown that the structural‐acoustic scaling laws are considerably simplified if a structural Strouhal Number (SSN) is defined in terms of the speed of propagation of the bending waves (VB) in the structure. It is observed that the excitation convection speed in the model scale experiment should be the same as in the full scale, if coincidence excitation of the structure is to be properly simulated.
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Effect of stiffener resonances on the vibration response and sound transmission loss of periodically stiffened structures (A)

G. SenGupta

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S157-S157 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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In analyzing the problem of vibration response and sound transmission through periodically stiffened plates and cylinders, the stiffeners are very often represented by line supports or by springs with equivalent translational and torsional stiffnesses. Sometimes, the effects of the stiffeners are also smeared out. As a result, the vibrational response and the transmission loss at low frequencies are often predicted to be stiffness controlled. Recent studies at Boeing has shown that in the “stiffness controlled” region, the structural response and noise transmission may be governed by the resonances of the stiffeners, depending upon the relationship between the natural frequency of the plate between the stiffeners and that of the stiffener. Therefore, noise transmission in the “stiffness controlled” region may be effectively controlled by applying damping treatment on the stiffeners. This recent understanding has grown out of the “intrinsic structural tuning” concept presented earlier (G. SenGupta and E. F. Small, J. Acoust. Soc. Am. 58, S (A)(1975). The problems under consideration are discussed in terms of (1) stringer‐stiffened plates and (2) frame‐stiffened cylinders. Analytical as well as experimental results are presented. [Work supported by NASA‐Langley Research Center.]
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Acoustic boundary layer and acoustic radiation from a ribbed flat plate (A)

Mauro Pierucci

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S157-S157 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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The acoustic boundary‐layer theory (patterned after the viscous boundary‐layer theory) is derived by noting that for low frequencies, where the structural wavelength is much less than the fluid acoustic wavelength, there is a region about the vibrating structure which behaves as if the fluid was incompressible. The dimension of this region depends upon the particular conditions of the problem. In a paper presented by the author [J. Acoust. Soc. Am. 62, S32(A) (1977)] the theory behind the acoustic boundary layer was developed and applied to simple unit problems. In this paper the near and the far field of a force driven plate is obtained by the use of the acoustic boundary‐layer theory. Two different problems are addressed. In the first instance the structure is assumed to be homogeneous, while in the second problem presented a rib is attached to the flat plate. In both instances the fully coupled fluid structure problem is solved, and comparisons between the exact classical approach and the proposed theory are discussed.
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Measurement of the effects of fluid loading on the dispersion of flexural waves in a plate (A)

James L. Jarvis and O. B. Wilson, Jr.

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S157-S158 (1978); (2 pages)

Online Publication Date: 11 Aug 2005

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Dispersion curves for axially symmetric flexural waves in a circular aluminum plate were determined using both direct phase measurement and measurement of normal mode frequencies. Measurements were conducted with the 8 mm thick plate in air and with one surface loaded by water in an anechoic tank over a frequency range of 20–80 kHz. At frequencies larger than the critical frequency (at which the free plate flexural wave speed is equal to the sound speed in water) the phase speeds with the plate in air and in water are nearly equal and agree well with the Mindlin‐Timoshenko theory. Below critical frequency, water loading causes significantly lower values, about fifteen percent here. The speed in the water‐loaded plate appears to change abruptly at or just above the critical frequency, in reasonable agreement with the theory of Kurtze and Bolt [Acustica 9, 238–242 (1959)]. Significance of these results will be discussed. [Supported by the Naval Undersea Warfare Engineering Station, Keyport, WA.]
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Mechanical impedances of clamped rectangular plates without and with a rib (A)

K. Fujiwara

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S158-S158 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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Mechanical impedances of clamped rectangular plates without and with a rib were investigated. First, the mechanical impedances of a clamped plate without a rib were treated. The driving conditions were the one‐point drive and the four‐point drive with the same amplitudes and phases and the uniformly distributed force over the rectangular area. The analysis was carried out by the method to solve the simultaneous linear equations obtained by applying the series of normalized orthogonal functions to the differential equation governing the bending vibration of a plate. The results were presented by the normalized mechanical impedance as a function of the interval of the driving points. Secondarily, the mechanical impedances of a clamped plate stiffened by a rib with rectangular cross‐section were treated. The driving conditions were the one point drive and the four points drive with the same amplitudes and phases. The analysis was carried out by FEM. The results were also presented by the normalized mechanical impedance and compared with that of a plate without a rib for the one‐point drive and the four‐point drive, and then the effect of the rib on the vibration of a rectangular plate with clamped boundaries was discussed.
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Transmission across, radiation from, and reflection by ribs on a panel (A)

G. Maidanik, D. G. Crighton, and T. Eisler

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S158-S158 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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A formalism of the response of an infinite, plane, and uniform panel is derived in terms of the impulse response function. The modification of the impulse response function caused by attaching parallel line mechanical constraints is considered. It is shown that the impulse response function of the so constrained panel can be cast in the form of two terms. The first is simply the impulse response of the unconstrained panel. The second is a functional of the impulse response function of the unconstrained panel and the impedances of the line mechanical constraints. It is argued that the formalism so cast is particularly suitable for ascertaining the modification to the response introduced by line mechanical constraints (ribs). The argument is exemplified by deriving the expressions for the transmission coefficient across the ribs, the radiation to the farfield generated by the presence of the ribs, and the change in the reflective properties of the panel introduced by the ribs.
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Effects of fluid loading on the transmission of free waves across a rib (A)

D. G. Crighton, G. Maidanik, and T. Eisler

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S158-S158 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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The line drive admittance and the transfer admittance have been evaluated in closed form for a plate or membrane. The evaluation takes into account the influence of fluid loading. Both admittances are necessary for the evaluation of the transmission of free waves across a rib. In this calculation the rib is characterized by an impedance, and the influence of fluid loading can thus be ascertained. Computations illustrating this effect in a number of cases of interest are presented and discussed. In the case of the membrane the phenomenon associated with the critical frequency is introduced by assuming the tension to be frequency dependent.
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Effects of fluid loading on the transmission of free waves across two ribs (A)

T. Eisler, D. G. Crighton, and G. Maidanik

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S158-S158 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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The effects of fluid loading on the transmission of free waves across a single rib has been considered in the preceding paper. In this paper the transmission of free waves across two parallel ribs is considered. If the interaction between the two ribs is or can be ignored, the evaluation of the transmission can be readily deduced from that of the single rib. Of particular interest in the paper are, however, the conditions on the characteristics of the ribs, the panel, and the fluid loading under which the interaction between the ribs is significant. A number of computations illustrating this significance are presented.
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Structure/air noise power ratio spectra of machine casings (A)

Howard A. Thorpe

J. Acoust. Soc. Am. Volume 64, Issue S1, pp. S158-S158 (1978); (1 page)

Online Publication Date: 11 Aug 2005

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A formula for approximating these ratio spectra has been developed as part of Rohr's surface effects ship noise prediction methodology. These spectra are used as multipliers of measured or predicted aerenoise power spectra (Watts) of bare machine casings to predict the corresponding available machine structure‐noise true power spectrum. The latter rarely is available. The formula developed for this ratio, R, is R  =  (1.5/c) (ρs/ρ)t(v + 300) where c and ρ are, respectively, speed of sound in and density of the fluid medium surrounding the casing, ρs is casing material density, t is casing thickness, and v is frequency in hertz. Units consistent with the dimensionless nature of R must be used. Underlying idealized theory and results will be sketched. Also, rationale for moderately adjusting constants of theoretical results on empirical grounds will be sketched. Adjustment of the initial constant is based on results of a relevant Rohr test/analysis program. The second constant is based on a Rohr study of compartment noise prediction validity involving a tested ship. [Work supported by U.S. Navy, NAVSEA, PMS304.]
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