| Summary: | 碩士 === 國立臺灣大學 === 造船及海洋工程學研究所 === 89 === This study is mainly intended to the determination on the wall vibration of duct, which is produced by the acoustic wave propagation through it. Therefore, the sound pressure in a steel duct is measured first. And then regarding the result as the required excited force to the other ducts else. Furthermore, some thin-shell ducts with materials iron, aluminum and plastics are selected to be the elastic ducts for this study. In the mean time, the resulting vibration for each elastic duct is calculated when excited by the same acoustic field as that obtained from the case for steel duct.
From the viewpoint of energy conservation, the energy loss of an actual duct while in vibration due to its internal damping must equal the difference of acoustic power output at entrance from that at exit. Two acoustic power outputs can be measured by sound intensity method.
The result as obtained clearly shows the predicted vibrations of elastic ducts are quite agreeable with that of measurement. Thereafter, the empirical formula developed from energy loss viewpoint can be used in some acceptable accuracy to predict the vibration of duct when acoustic waves propagate through it at low frequency.
Upon the assumption as above, the law of energy conservation tells that the acoustic energy difference of the acoustic power of source from that at the exit of duct must equal the damping power efflux produced by the duct vibration. Therefore in mathematical expression, if we let the damping force of duct wall be equal to , the related damping power efflux will be , where U is the velocity amplitude,
and . So forth the conservation of acoustic energy shows:
where are, respectively, the acoustic intensities at source and exit. r, L are the radius and length of duct respectively. Since for single frequency sound, the amplitude A of wall vibration can be obtained as:
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