Free vibrations of simply supported cylindrical shells of oval crosssection

Abstract

A Flii'gge-type theory is employed in studying the dynamic characteristics of simply supported shells of oval cross section. The components of displacement are expressed in a double Fourier series of the axial and circumferential coordinates and substituted into the equations of motion. This leads to four different typical, algebraic, eigenvalue problems from which the frequencies and shapes of four types of harmonic modes are determined. These modes are either symmetric or antisymmetric with respect to the principal axes of the cross section of the shell. A comparison of the dynamic characteristics of oval cylindrical shells obtained on the basis of the Donnell, Love, Sanders, and Flu'gge theories is presented. It is shown that the deviations in the results of these theories increase with increasing noncircularity. NomenclatureA mn ,B mn ,C mn , D m,n> E m, n > F m"n = Fourier coefficients D = (\/\2)Eh 3 /(-v 2 ) E = Young' s modulus t -time u,v,w = axial, circumferential, and radial components of displacement of a point on the median surface of a shell, respectively U m ,V m , W m = displacement functions for axial wave number m ?>ij = Kronecker delta e = ovality parameter v = Poisson's ratio

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

“…The best collection of documents can be found in Leissa [4], in which more than 500 publications are analyzed and discussed in both linear and non-linear vibration cases. Other related literatures for the vibration of homogeneous oval cylindrical shells can be found in [5][6][7][8][9][10][11]. On the other hand, there are a few publications that studied the vibration characteristics of the isotropic and orthotropic corrugated cylindrical shells, e.g., [12][13][14][15][16][17], whereas Tsiolkovsky [18] was the first one to see that the corrugated shells can be used in lighter-than-air engineering.…”

Simplified equations and solutions for the free vibration of an orthotropic oval cylindrical shell with variable thickness

“…The vibration problems of the cylindrical shells of the oval profile are rather limited and are due to the difficulty introduced in governing equations of motion. Some researchers conducted their studies using different methods and theories to such problems with constant or variable thickness such as . A treatise on the use of the transfer matrix approach for mechanical science problems was presented by Tesar and Fillo .…”

New approach to investigation of resonant vibrations of noncircular shells based on the theory of coupled waveguides

“…Noncircular cylindrical shells are relatively simple structures that are widely used for their own sake as well as for describing physical processes in more complex structures, especially in aeronautical and oceanic engineering applications; see [Armenakas and Koumousis 1983;Kumar and Singh 1993;Suzuki et al 1996;Ganapathi and Haboussi 2003]. Some recent applications of elliptical or oval-type noncircular shells include modeling structure-borne vehicle interior noise in simplified reduced-scale vehicle models, where they form flexible parts of the model structures [Krylov et al 2003;.…”