NON-LINEAR VIBRATIONS OF SHELL-TYPE STRUCTURES: A REVIEW WITH BIBLIOGRAPHY

The aim of this paper is to provide a contemporarily relevant survey of studies on non-linear vibrations of shell-type structures. The effects of geometrical non-linearity, and specific difficulties encountered in non-linear dynamic analysis of shell-type structures are presented and discussed. Studies on non-linear vibrations of shells are categorized by different shell configurations (shapes) in a chronological order. Also, the most commonly used methods of modelling and solution are reviewed and commented. Published reviews on non-linear vibrations of shell-type structures including complicating effects of anisotropy, initial stress, added mass, elastic foundation, stiffeners, open geometry (singly and doubly curved), transverse shear deformations, torsion, and interaction with fluid are also surveyed. Comments on the previous non-linear works are presented and some orientations for future research are suggested. Another purpose of this paper is to provide engineers, scientists and researchers with a list of 175 references, which should be very useful for locating relevant existing literature quickly.