A new vibration approach of an elastic oval cylindrical shell with varying circumferential thickness

Abstract

A new vibration behavior is presented for an elastic oval cylindrical shell having circumferentially variable thickness with complex radius of curvature of an isotropic and orthotropic material. Based on the framework of the Flügge’s shell theory, the transfer matrix approach and the Romberg integration method, the governing equations of motion that have variable coefficients are formulated and solved. The analysis is formulated to overcome the mathematical difficulties related to mode coupling which comes from variable curvature and thickness of shell. The vibration equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The proposed model is adopted to get the vibration frequencies and the corresponding mode shapes for symmetric and anti-symmetric modes of vibration. The sensitivity of the frequency parameters and the bending deformations to the shell geometry, ovality parameter, thickness ratio, and orthotropic parameters corresponding to different types of vibration modes of shells is investigated.

Free vibration analysis of cylindrical panels with spiral cross section

“…Suzuki et al investigated the vibration characteristics of closed noncircular thin and thick shells [21,22]. Most of the researches on closed noncircular cylinders are focused on special cross sections such as oval [23] and elliptic profiles [24][25][26]. Although some of researchers have investigated the closed noncircular cylindrical shells with arbitrary cross section, they have treated oval and elliptic shells as examples.…”

Wave‐Based Method for Free Vibration Analysis of Orthotropic Cylindrical Shells with Arbitrary Boundary Conditions

“…Lakis and Selmane [18] conducted the thin shell theory, fluid theory, and the hybrid FEM to study the influence of large amplitude vibration of orthotropic, circumferentially nonuniform cylindrical shells. Ahmed [19] analyzed the isotropic and orthotropic cylindrical shell with variable circumferentially thickness and complex curvature radius by Flugge's shell theory. e transfer-matrix method and the Longberg integral method were proposed in the establishment of the motion control equation.…”

Stability of clamped-clamped periodic functionally graded material shells conveying fluid

“…The dynamic behavior of cylindrical shells conveying fluid is of substantial practical applications, for instance, in heat exchangers, hydraulic systems, power plants and nuclear reactor systems, etc. It is not surprising, therefore, that the dynamic problems of fluidconveying shells have been extensively investigated both theoretically (Tang and Paı¨doussis, 2009;Ahmed, 2010Ahmed, , 2012Sofiyev and Kuruoglu, 2013) and experimentally (Zhang et al, 2000;Liu et al, 2009;Chebair et al, 1989;Karagiozis et al, 2005Karagiozis et al, , 2008.…”