Free and forced vibration analysis of non-uniformly supported cylindrical shells through wave based method

Abstract

This paper presents a unified analytic method, wave based method (WBM), to investigate free and forced vibrations of non-uniformly supported cylindrical shells. WBM is involved in decomposing the cylindrical shell to several shell segments according to locations of interior supports and excitations. Flügge shell theory is adopted to describe motions of segments. Displacement functions are expanded as wave functions, rather than general trigonometric functions or polynomials, and they can accurately satisfy both motion equations and boundary conditions. Two kinds of non-uniform supports, point and line ones, are consistently considered through discrete artificial springs. Boundary and continuity conditions modified by supports and excitations are assembled to the governing equation. To examine accuracy of WBM, vibration results of cylindrical shells subjected to different supports are firstly compared with the ones in literature and calculated by finite element method, which demonstrates high accuracy and wide application of WBM. Some mode shapes are also presented to visually illustrate coupling effects of different modes. Furthermore, influences of stiffness constants of springs, point supports and structural damping are discussed. They reveal that fundamental frequencies can be maximumly increased as point supports equally spaced in circumferential direction.