Abstract
Previously, a coupled, two-dimensional structural-acoustic ring model was constructed to simulate the dynamic and acoustical behavior of pneumatic tires. Analytical forced solutions were obtained and were experimentally verified through laser velocimeter measurement made using automobile tires. However, the two-dimensional ring model is incapable of representing higher order, in-plane modal motion in either the circumferential or axial directions. Therefore, in this paper, a three-dimensional pressurized circular shell model is proposed to study the in-plane shearing motion and the effect of different forcing conditions. Closed form analytical solutions were obtained for both free and forced vibrations of the shell under simply supported boundary conditions. Dispersion relations were calculated and different wave types were identified by their different speeds. Shell surface mobility results under various input distributions were also studied and compared. Spatial Fourier series decompositions were also performed on the spatial mobility results to give the forced dispersion relations, which illustrate clearly the influence of input force spatial distribution. Such a model has practical application in identifying the sources of noise and vibration problems in automotive tires.
Highlights
Tire vibration problems can be modeled as ring/shell structure vibration problems
Axial shearing motion in tires is experimentally found to be important in high frequency range
Discrete input forces are applied over an area to represent road surface input
Summary
Tire vibration problems can be modeled as ring/shell structure vibration problems. "Effects of coriolis acceleration on the free and forced in-plane vibrations of rotating rings on elastic foundation.“ Journal of Sound and Vibration 115.2 (1987): 253-274. Experimental dispersion results of a tire with fibrous material filled air cavity. A ring structure tire model can well capture the lower frequency wave types, but incapable of expressing the highlighted wave type in tire structures. Axial shearing motion in tires is experimentally found to be important in high frequency range. Not a good model for wide shell structures such as wide treadbands.
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