Solving the vibration problem of inhomogeneous orthotropic cylindrical shells with hoop-corrugated oval cross section

Abstract

Based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method, this paper investigates how corrugation parameters and material homogeneity affect the vibration behavior of isotropic and orthotropic oval cylindrical shells with sine-shaped hoop. Assume that the Young's moduli, shear moduli and density of the orthotropic material are continuous functions of the coordinate in the circumferential direction. The governing equations of non-homogeneous, orthotropic oval cylindrical shells with variable homogeneity along its circumference are derived and put in a matrix differential equation as a boundary-value problem. The trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction, and also to reduce the two-dimensional problem to a one-dimensional one. Using the transfer matrix approach, the equations can be written in a matrix differential equation of the first order and solved numerically as an initial-value problem. The proposed model is applied to get the vibration frequencies and mode shapes of the symmetric and antisymmetric vibration modes. The sensitivity of the vibration behavior to the corrugation parameters, homogeneity variation, ovality, and orthotropy of the shell is studied for different type modes of vibration.

Geometrically Nonlinear Transversal Vibrations of Corrugated Cylindrical Shells

“…Linear free vibrations of corrugations in the direction of the angular coordinates of cylindrical shells were investigated in [3,[7][8][9]. In [1,4,11] their geometrically nonlinear vibrations were investigated. Various applied shell theories were used for this purpose.…”