Free and forced vibration of ring-stiffened conical–cylindrical shells with arbitrary boundary conditions

The wave based method (WBM) is used to analyze the free vibration characteristics of functionally graded material (FGM) cylindrical shell with arbitrary boundary conditions. The motion relationship is described by the first-order shear deformation shell theory (FSDST). The displacement components and transverse rotations are expressed as wave function expansions. In accordance with the dynamic relationship, the final governing equation and global matrix are assembled by incorporating the boundary matrices. The natural frequency of the system is obtained by solving the determinant of the global matrix. By comparing the results with those in the literature, the validity of the proposed method is verified. In addition, the influences of power-law exponents and boundary conditions on natural frequencies are analyzed. The effects of geometric parameters including the ratio of thickness to radius and the ratio of length to the radius on natural frequencies are discussed. The purpose of this paper is to demonstrate the ease of application of the WBM for the free vibration of FGM cylindrical shells with arbitrary boundary conditions. Furthermore, the advantage of the WBM are: (1) the global matrix is easy to construct; (2) different boundary conditions can be conveniently adjusted; (3) it is with high computational efficiency and precision.

Wave based method for free vibration characteristics of functionally graded cylindrical shells with arbitrary boundary conditions

Wave based method for vibration analysis of elastically coupled annular plate and cylindrical shell structures

Vibration analysis of circular cylindrical double-shell structures under general coupling and end boundary conditions

Free and Forced Vibration Analysis of Ring-Stiffened Conical-Cylindrical-Spherical Shells Through a Semi-Analytic Method

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm - shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

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Wave based method for free vibration analysis of ring stiffened cylindrical shell with intermediate large frame ribs

Wave based method (WBM) is presented to analysis the free vibration characteristics of cylindrical shells with nonuniform stiffener distributions for arbitrary boundary conditions. The stiffeners are treated as discrete elements. The equations of motion of annular circular plate are used to describe the motion of stiffeners. Instead of expanding the dynamic field variables in terms of polynomial approximation in element based method (finite element method etc), the ring-stiffened cylindrical shell is divided into several substructures and the dynamic field variables in each substructure are expressed as wave function expansions. Boundary conditions and continuity conditions between adjacent substructures are used to form the final matrix to be solved. Natural frequencies of cylindrical shells with uniform rings spacing and eccentricity distributions for shear diaphragm-shear diaphragm boundary conditions have been calculated by WBM model which shows good agreement with the experimental results and the analytical results of other researchers. Natural frequencies of cylindrical shells with other boundary conditions have also been calculated and the results are compared with the finite element method which also shows good agreement. Effects of the nonuniform rings spacing and nonuniform eccentricity and effects of boundary conditions on the fundamental frequencies and the beam mode frequencies have been studied. Different stiffener distributions are needed to increase the fundamental frequencies and beam mode frequencies for different boundary conditions. WBM model presented in this paper can be recognized as a semianalytical and seminumerical method which is quite useful in analyzing the vibration characteristics of cylindrical shells with nonuniform rings spacing and eccentricity distributions.

Guoxiang Hou

Papers

Wave based method for free vibration analysis of ring stiffened cylindrical shell with intermediate large frame ribs

Wave Based Method for Free Vibration Analysis of Cylindrical Shells With Nonuniform Stiffener Distribution