The use of cross correlation as a tool for analyzing propagation of energy in structural systems is investigated. Each energy-transmission path will have a characteristic delay time, and examination of the cross-correlation function of input and response can guide in the determination of the most significant path or paths. Difficulties occur in distributed systems or when the propagation is by a dispersive mechanism. The principles of correlation analysis are examined for both dispersive and nondispersive systems. Experimental evidence is presented that supports the theory and concepts developed. On the basis of these preliminary results, it appears that the technique holds promise and bears further investigation.
The transmission of an acoustic wave through an infinite, homogeneous, isotropic cylinder has been derived to be a strong function of frequency and the angle of incidence between the axis of the cylinder and the incoming wave. From this analysis, two important characteristics are found: the ring frequency, where the wavelength of a longitudinal wave in the material is equal to the circumference, and the coincidence frequency, where the trace wavelength of the incident wave is equal to the bending wavelength in the shell wall. The transmission loss will take on minimum values at these two points. Measurements with 13 oct-band noise excitation of a closed cylindrical shell with l/d - 1.5 show the same gross features to be present and with additional effects of low-frequency resonances, but with very little angular dependence. The presence of stiffening corrugations and irregularities in the shell leads to a random-vibration field and allows methods developed for the transmission of random sound through flat panels to be used successfully for noise-reduction estimates.
The simple pressure source model of the sound radiated by a sonic jet is investigated analytically and experimentally. From the simple source model, the ratio of the frequency spectra of the radiated sound power and the jet pressure is derived for an assumed form of the jet-pressure cross correlation. The spatial variation of the overall jet pressures, the frequency spectra of the jet pressures, the axial and radial cross correlations of the jet pressures, and the cross correlation between jet pressure and farfield sound pressure are measured for a cold jet. Some implications of the simple source model with regard to noise suppression are also discussed.
The transmission of an acoustic wave through an infinite, homogeneous, isotropic cylinder has been derived to be a strong function of frequency and the angle of incidence between the axis of the cylinder and the incoming wave. From this analysis, two important characteristics are found: the ring frequency, where the wavelength of a longitudinal wave in the material is equal to the circumference, and the coincidence frequency, where the trace wavelength of the incident wave is equal to the bending wavelength in the shell wall. The transmission loss will take on minimum values at these two points. Measurements with 13-oct-band noise excitation of a closed cylindrical shell with l/d=1.5 show the same gross features to be present and with additional effects of low-frequency resonances, but with very little angular dependence. The presence of stiffening corrugations and irregularities in the shell leads to a random vibration field and allows methods developed for the transmission of random sound through flat panels to be successfully used for noise-reduction estimates.
The existence of many modes of vibration in a complex system makes a detailed classical analysis almost intractable. However, when excited by broad-band random noise, the detailed response characteristics may be overlooked and statistical properties such as mean-square values and power spectra provide a measure of the vibration. The existence of classes of similarly excited modes allows theories of room acoustics and thermodynamics to be applied successfully. For sound transmission through a rectangular double wall, this technique gives results that agree within experimental error of measured transmission loss, much better than do conventional loss estimates. Both theory and experiment confirm that the product of modal density, average joint acceptance of the first panel, and the ratio of radiation to total resistance of the second panel are the most important characteristics in determining the transmission characteristics of the wall.
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