Free vibrations of freely supported oval cylinders

Abstract

A study was made of the free vibration frequencies and mode shapes for freely supported oval cylindrical shells. Cross section curvatures were expressed in terms of a single eccentricity parameter that allowed a wide range of doubly symmetric ovals to be studied. Kinematic equations employing both the Love and the Donnell assumptions from thin shell theory were used in this study and results of the two formulations were compared. Little difference was observed between the results obtained from the two theories for a wide range of shell configurations. Comparisons were also made between the results obtained from this study and those from two previous approximate analyses. It was found that one of the approximate analyses (a Rayleigh-Ritz technique) was quite accurate for all ranges of eccentricities studied. The other approximate analysis (a perturbation technique) was found to be reliable for ovals with eccentricities in the range ( — 0.5 < € < 0.5). A study was also made to determine the effects of eccentricity of oval cross sections. The frequencies and mode shapes were found to vary significantly with increasing eccentricities. Irregularities in the frequency vs wave-number curves and a localized cupping in the region near the minimum frequency were observed. In-plane inertias were retained yielding the expected three frequencies for each combination of longitudinal and circumferential wave numbers. However, unlike the unstiffened circular cylinder, more than one set of three natural frequencies and associated mode shapes were found for some combinations of longitudinal and circumferential wave numbers. However, although the wave numbers (i.e., number of crossings) were the same in these cases, the wave shapes were obviously different.