The free vibrations of cylindrical shells with various end closures

Abstract

The natural frequencies of vibration of cylindrical shells clamped at one end and closed at the other by different types of shells of revolution (cones, hemispheres, ellipsoids, etc.) were determined using programs written for the digital computer. The principal numerical methods investigated were variational finite-differences and finite elements. However, some results obtained by numerical integration of the differential equations of motion, together with some obtained from series solutions, are also given for purposes of comparison. For L D = 0.5 , h D = 0.01 the lowest four natural frequencies for all the cylinder/end closures investigated were concentrated in a band such that ω 4 ω 1 ⋍ 1.7 . Thus, changing the head shape does not cause radical changes in the natural frequencies for these geometric ratios. Results for other values of the geometric parameters are also given in the paper. Again for L D = 0.5 , h D = 0.01 , the effect of not equating to zero the in-plane circumferential displacement at the base of the cylinder caused a marked reduction in the n = 1 natural frequencies. In many of the cases studied, the n = 1 frequency was either the fundamental one or was close to it. Insofar as dynamic analyses are concerned, designers ought to be aware of the influence that the in-plane boundary conditions at the cylinder base can have on the natural frequencies. With regard to the main two numerical methods studied, the authors found both of them to be very effective for the natural frequency and mode shape predictions. For pointed shells (e.g. cones) it appears that for n = 0 and n = 1, the conditions employed at the apex in some of the programs need re-examination.