A comparative study of axisymmetric finite elements for the vibration of thin cylindrical shells conveying fluid

A comparative study of the relative performance of several di erent axisymmetric nite elements, when applied to the dynamic problem of thin cylindrical shells conveying uid, is presented. The methods used are based on (1) the Sanders’ theory of thin shells and the potential ow theory, and (2) the theory of elasticity and the Euler equations. The elements studied are: linear, paralinear, parabolic and cubilinear. Extensive comparison with experiment is carried out for the free vibration of cylindrical shells in the absence of, and containing, quiescent and owing uid. The analysis of the relative competence of these elements is presented for shell length-to-radius ratios 1:956L=R632, shell radius-to-thickness ratios 106R=h6375 and boundary conditions: clamped–clamped, clamped–free and simply supported. We show that natural frequencies of thin cylindrical shells in the absence of, and containing, quiescent and owing uid can be assessed accurately when using two- and eight-noded elements, and the latter are also applicable to the dynamic problem of thick cylindrical shells