Wave based method for vibration analysis of double-walled cylindrical shells

Abstract

Wave based method (WBM) is presented for vibration analysis of double-walled cylindrical shells coupled by annular plates. To establish the governing equation, the double-walled shell is divided into several cylindrical shell segments and annular plates according to junctions of discontinuities, and they can be easily synthesized through continuity conditions at the junctions. Flügge shell theory and thin plate theory are utilized to describe motions of cylindrical segments and annular plates, displacements of which are expanded as wave functions. In addition, artificial springs are employed to restrain displacements at boundaries to uniformly consider elastic and classic boundary conditions. To test the validity of WBM, free and forced vibration results of WBM are compared with those of literature and finite element method, which demonstrates high accuracy of present method. Some mode shapes are also given for visual understanding. Furthermore, effects of elastic boundary conditions and annular plates on free and forced vibrations are investigated. Results show that axial and circumferential displacements are of great effect on fundamental and beam mode frequencies, and effects of the number of annular plates are obviously greater than the thickness of annular plates. The results of present paper can be used as benchmarks for further researches.