K. Soldatos

Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels

Abstract The free vibration problem of a homogeneous isotropic thick cylindrical shell or panel subjected to a certain type of simply supported edge boundary conditions is considered. For this problem, the governing equations of three-dimensional linear elasticity are employed and solved by using a new iterative approach which, in practice, leads to the prediction of the exact frequencies of vibration. In the particular case of a flat plate or a complete shell, excellent agreement is achieved between results based on the present approach and corresponding results based on other exact analyses available in the literature. For certain cylindrical panel geometries, comparisons are also made between corresponding numerical results based on the present analysis and certain two-dimensional shell theories.

Buckling and vibration of cross-ply laminated non-circular cylindrical shells

The free vibration problem of a thin composite cross-ply laminated non-circular cylindrical shell subjected to an axial compression is studied. The equations of motion are derived, in the framework of the Donnell-type theory, in terms of the shell middle surface displacement components. The differential equations of motion have variable coefficients and they are solved by employing Galerkins method. As an application, the problem of the free vibrations and buckling of cross-ply laminated oval cylinders is studied. Numerical results for antisymmetric and unsymmetric cross-ply laminated shells of graphite-epoxy are presented and discussed.

A refined laminated plate and shell theory with applications

Abstract The present paper is concerned with the development and certain applications of a refined shear deformable theory suitable for the dynamic analysis of laminated anisotropic plates as well as cylindrical shells of either circular or non-circular configuration. The theory accounts for parabolic variation of transverse shear strains and it is capable of satisfying zero shear traction boundary conditions at the external shell or plate surfaces, and makes no use of transverse shear correction factors. It can be considered as a transverse shear deformable analogue of the classical laminate Donnell-type and Love-type shell theories while, through certain new definitions of force and moment resultants, the higher order moment and transverse shear force resultants occurring acquire some pysical substance. Under certain conditions, some dynamical problems studied earlier by the present author are considered as applications of the refined theory developed. As a further application, the present theory is employed for the study of the free vibration problem of antisymmetric angle-ply laminated closed circular cylindrical shells. This problem is solved by two different mathematical techniques; namely, the helical modal pattern approach and an approach based on Galerkins method. Numerical results based on both solutions obtained are presented and compared and the efficiency of both approaches, with regard to the prediction of the natural frequencies of vibration, is discussed.

INFLUENCE OF THICKNESS SHEAR DEFORMATION ON FREE VIBRATIONS OF RECTANGULAR PLATES, CYLINDRICAL PANELS AND CYLINDERS OF ANTISYMMETRIC ANGLE-PLY CONSTRUCTION

Abstract This paper is concerned with the influence of thickness shear deformation and rotatory inertia on the free vibrations of antisymmetric angle-ply laminated circular cylindrical panels. Two kinds of thickness shear deformable shell theories are considered. In the first one, uniformly distributed thickness shear strains through the shell thickness and, therefore, thickness shear correction factors are used. In the second theory a parabolic variation of thickness shear strains and stresses with zero values at the inner and outer shell surfaces is assumed. The analysis is mainly based on Loves approximations but, for purposes of comparison, Donnells shallow shell approximations are also considered. For a simply supported panel, the equations of motion of the aforementioned theories, as well as of the corresponding classical theories, are solved by using Galerkins method. For a family of graphite-epoxy angle-ply laminated plates and circular cylindrical panels, numerical results are obtained, compared and discussed and some interesting conclusions are made regarding the shell theories considered as well as the mathematical method employed.

Dynamic behavior of a cylindrical shell subjected to a thermal gradient

SummaryThe presence of a thermal gradient considerably affects the dynamic characteristics of shell structures.In this study an attempt is made to discover the influence of a thermal gradient along the length of a cylindrical shell on its dynamic behaviour. The formulation of the problem is based on Donnells linear theory and the mathematical analysis on the Bubnov-Galerkin method. Finally, numerical results are presented for simply supported and clamped shells.ZusammenfassungDie dynamischen Charakteristika der Schalenstruktur werden durch das Auftreten des thermischen Gradienten beträchtlich beeinflußt.In dieser Arbeit wird versucht, die Rolle des thermischen Gradienten entlang der Erzeugenden einer zylindrischen Schale hinsichtlich des dynamischen Verhaltens der Schale zu untersuchen.Die Formulierung des Problems und die mathematische Analyse haben als Basis die lineare Theorie von Donnell und die Methode von Bubnov-Galerkin. Numerische Ergebnisse für einfach gelagerte und eingespannte Schalen werden vorgelegt.

Dynamic analysis of thin elastic noncircular conical shells

SummaryThe geometry of the middle surface lines of curvature of a thin conical shell, whose cross-section is bounded by a certain closed convex plane curve, is studied. Then, for such a shell, several sets of linear and nonlinear equations of motion are derived in terms of its middle surface orthogonal line-of-curvature coordinate system. As an application of the presented analysis, the free vibration problem of thin circular and elliptical frustums is investigated by means of linear Donnell-type equations of motion. These equations are expressed in terms of the shell middle surface displacement components and they are solved approximately by means of Galerkins method. Numerical results are presented for frustums with clamped both edges.

Dynamic behaviour of a simply supported circular cylindrical panel subjected to an initial bending moment

Abstract The vibration of cylindrical panels with simply supported boundary conditions in the presence of an initial bending moment is investigated. The analysis is based on the theory of Herrmann and Armenakas. The results for the stability and free vibration of the panels are obtained as special cases.