Abstract
This paper compares the vibroacoustic behavior of a tapered annular circular plate having different parabolic varying thickness with different combinations of rectangular and concentric stiffener patches keeping the mass of the plate and the patch constant for a clamped-free boundary condition. Both numerical and analytical methods are used to solve the plate. The finite element method (FEM) is used to determine the vibration characteristic and both Rayleigh integral and FEM is used to determine the acoustic behavior of the plate. It is observed that a Case II plate with parabolic decreasing–increasing thickness variation for a plate with different stiffener patches shows reduction in frequency parameter in comparison to other cases. For acoustic response, the variation of peak sound power level for different combinations of stiffener patches is investigated with different taper ratios. It is investigated that Case II plate with parabolic decreasing–increasing thickness variation for an unloaded tapered plate as well as case II plate with 2 rectangular and 4 concentric stiffeners patches shows the maximum sound power level among all variations. However, it is shown that the Case III plate with parabolically increasing–decreasing thickness variation with different combinations of rectangular and concentric stiffeners patches is least prone to acoustic radiation. Furthermore, it is shown that at low forcing frequency, average radiation efficiency with different combinations of stiffeners patches remains the same, but at higher forcing frequency a higher taper ratio causes higher radiation efficiency, and the radiation peak shifts towards the lower frequency and alters its stiffness as the taper ratio increases. Finally, the design options for peak sound power actuation and reduction for different combinations of stiffener patches with different taper ratios are suggested.
Highlights
Tapered annular circular plates with different combinations of rectangular and concentric patches has many engineering applications
The plate is made tapered with different taper ratios of 0.25, 0.50 and the plate plus rectangular or concentric patches are kept constant for this analysis
When the excitation frequency increases beyond 2000 HZ and up to the first peak, the sound power level is higher for only higher taper ratios for a Case I plate with both 1 rectangular stiffener and 1 concentric stiffener patch, and variation of sound power level due to variation of peaks for different taper ratios is observed for a plate with both 2 rectangular stiffener and 2 concentric stiffener patches and for 4 rectangular stiffener and 4 concentric stiffener patch combinations
Summary
Tapered annular circular plates with different combinations of rectangular and concentric patches has many engineering applications. Lee and Singh [10] used the thin and thick plate theories to determine the sound radiation from out-of-plane modes of a uniform thickness annular circular plate. Bipin et al [20] analyzed an isotropic plate with attached discrete patches and point masses with different thickness variation with different taper ratios to determine its vibro acoustic response. This comes to a discussion at a common point that has inspired the present paper based on a comparison of vibroacoustic behavior of a parabolic tapered annular circular plate with attached rectangular and concentric patches at different positions. Mathematical Modeling and Analysis ratios under time-varying harmonic excitations
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