Noncircular Cylindrical Shells Research Articles

On thickness shear deformation theories for the dynamic analysis of non-circular cylindrical shells

This paper is concerned with the problem of free vibrations of homogeneous isotropic non-circular cylindrical shells, including the effects of thickness shear deformation and rotatory inertia. For this problem the equations of motion of two first approximation shell theories are derived. Both theories are transverse shear deformable analogues of the classical Love-type theory. The first theory involves thickness shear correction factors while the second one assumes a parabolic variation for thickness shear strains and stresses, with zero values at the inner and outer shell surfaces. The equations of both theories are solved, for the case of a simply supported non-circular cylindrical shell and, as an application, the free vibration problem of a simply supported oval cylindrical shell is considered. From comparisons made between corresponding numerical results based on both theories, as well as the classical Love-type theory, a superiority of the theory assuming parabolic variation of thickness shear is concluded.

Free Vibrations of Noncircular Cylindrical Shells Having Circumferentially Varying Thickness

An exact method using power series expansions is presented for solving free vibration problems for noncircular cylindrical shells having circumferential thickness variation. The method is used to obtain the first known results for this class of problems. Frequencies and mode shapes are presented for a set of elliptical cylindrical shells having second degree thickness variation in each quadrant.

A Spline Finite Element Method for the Solution of the Clamped Shallow Cylindrical Shell Problem

AbstractThe paper deals with a spline finite element method for the solution of the problem of the clamped shallow noncircular cylindrical thin elastic shell. An error estimate for the approximate solution is given.

On the existence of a solution of the clamped shallow noncircular cylindrical shell problem

The existence and uniqueness of a solution of the continuous Galerkin variational problem of ‘shallow’ noncircular open cylindrical thin elastic shells clamped along straight and curvilinear edges have been established.

Collapse of long, noncircular, cylindrical shells under pure bending

This paper describes an extension of a method developed in a previous paper to determine the moment carrying capacity of elastoplastic noncircular cylindrical shells with infinite length by the finite element method. As a result of the shape change in the cross section of a shell during deformation, the bending moment reaches a global maximum value and then decreases as the bending curvature further increases. The shell would consequently collapse at the maximum moment. However, a bifurcation buckling may occur before the maximum moment can be developed. This bifurcation buckling could induce collapse of the shell under a moment less than the maximum. Determination of the likelihood that the bifurcation buckling would generate shell collapse may be made from the initial post-buckling behavior. An initial post-buckling analysis based on the J 2 deformation theory of plasticity has been developed in this paper. The finite element method with one spatial variable is used to locate the bifurcation point as well as to analyze the initial post-buckling behavior. Numerical examples of cylindrical shells with various cross-sectional shapes are shown. In particular, for a shell of square cross section, the moment at the bifurcation is much lower than the maximum value; however, the initial post-buckling analysis reveals that the state of equilibrium is still stable. Deep post-buckling analysis is required to determine the moment carrying capacity of a shell with such cross section.

Numerical solution of problems on the deformation of open flexible noncircular cylindrical shells of variable stiffness

Numerical solution of problems on the deformation of open flexible noncircular cylindrical shells of variable stiffness

Free vibration of non-circular cylindrical shells with longitudinal interior partitions

An analysis is presented for the free vibration of a simply supported non-circular cylindrical shell with longitudinal interior partitions. For this purpose, the governing equations of vibration of a non-circular cylindrical shell including a plate as special case are written in a matrix differential equation by using the transfer matrix in the circumferential direction. Once the matrix has been determined, the entire structure matrix is obtained by the product of the transfer matrix of the shell and the point matrix at the joint of the structure matrix. The method is applied to approximately elliptical cylindrical shells with an interior plate, and the natural frequencies and the mode shapes of vibration are calculated numerically, giving the results.

Stability of noncircular cylindrical shells under axial compression

Stability of noncircular cylindrical shells under axial compression

Free vibration of non-circular cylindrical shells with variable circumferential profile

An analysis is presented of the free vibration of non-circular cylindrical shells with a variable circumferential profile expressed as an arbitrary function. The applicability of thin-shell theory is assumed and the governing equations of vibration of a non-circular cylindrical shell are written in a matrix differential equation by using the transfer matrix of the shell. Once the transfer matrix has been determined by numerical integration of the matrix equation, the natural frequencies and mode shapes of vibration are calculated numerically in terms of the matrix elements. The method is applied to cylindrical shells of three or four-lobed cross-section, and the effects of the length of the shell and the radius at the lobed corners on the vibration are studied.

Some optimal and inverse problems for orthotropic noncircular cylindrical shells

In this paper, we consider problems of optimal control involving stressed or strained states of orthotropic, noncircular cylindrical shells. It is assumed that the thickness of the shell is variable. The thickness and the radius of curvature of the directrix of the shell are assumed to be the controls. Existence of solutions for the optimal control problems considered is shown. In particular, existence of solutions for the problem of the minimal weight shell and the problem of nearest-to-equal-strength shell is shown. We present results on the approximation of the optimal control problems by a sequence of finite-dimensional problems, which may be reduced to nonlinear programming problems.

A flugge-type theory for the analysis of anisotropic laminated non-circular cylindrical shells

For a generally anisotropic laminated thin elastic non-circular cylindrical shell, subjected to a combined loading, the equations of motion of a second approximation Flugge-type theory are derived and expressed in terms of the shell middle-surface displacement components. As an application, for the free vibration problem of a cross-ply laminated non-circular cylindrical shell subjected to S2 simply supported edge boundary conditions, these equations are solved by employing the method of Galerkin. For a family of regular antisymmetric cross-ply laminated oval shells, numerical results are obtained and discussed. Comparisons are also made between some of the obtained results and corresponding results obtained from the solution of the quasi-shallow shell Donnell-type equations of motion.

Radiation from noncircular cylindrical shells in a fluid

Radiation from noncircular cylindrical shells in a fluid

Vibrations of Noncircular Cylindrical Shells

In this paper, we show a method for analyzing free vibrations of thin cylindrical shells with noncircular cross sections which have been used in chemical plants, atomic plants, flight structures and so on. This method is a general one applicable to various noncircular cylindrical shells. As the first step, we obtain an exact solution of a noncircular cylindrical shell with freely supported ends. By the numerical calculations, we obtain natural frequencies and mode shapes of elliptical cylindrical shells and clarify their characteristics.

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 Galerkin's 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.

Asymptotic formula for the natural frequencies of noncircular cylindrical fluid-filled shells

An exact asymptotic formula is proved for the natural frequencies of noncircular cylindrical shells. It turns out that the spectrum dissociates asymptotically into four series corresponding to different kinds of state of stress. Natural frequency modes are written down in the form of rapidly oscillating functions corresponding to a quasi-transverse state of stress.

Intrinsic oscillation of noncircular cylindrical shell with discrete masses

Intrinsic oscillation of noncircular cylindrical shell with discrete masses

Free vibration of non-circular cylindrical shell panels

In the free vibration analysis of clamped non-circular cylindrical shell panels, a matrix method has been used to solve the governing differential equations, which have variable coefficients. The effect of the curvature, thickness ratio and aspect ratio on the natural frequencies has been studied. The results obtained for circular cylindrical panels are compared with other available results. The convergence of the solution is found to be good.

The vibrations of non-circular cylindrical shells with initial stresses

The differential equations which govern the vibrations with initial stresses of thin non-circular cylinders of arbitrary curvature are obtained by a variational approach. The initial stresses which are considered are stresses produced by axial loads, torsion, and normal pressure. The solution procedure is presented and numerical results are presented for the free vibrations of freely supported oval cylinders without initial stress. Frequency factors of oval cylinders are compared with those of circular cylinders as the length, thickness, and non-circularity are varied. The equivalence of the solutions for the free vibrations with and without initial axial stress is also established.

Noncircular Cylinder Vibration by Multilocal Method

A modified multilocal difference scheme is presented for the free vibration analysis of nonhomogeneous orthotropic noncircular cylindrical shells with simply supported curved edges. The problem is formulated in terms of 10 first-order ordinary differential equations and in the finite-difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to more accurate results than those obtained by other multilocal and ordinary difference schemes reported here-to-fore in the literature.

Investigation of the free vibrations of noncircular cylindrical shells: PMM vol. 37, n≗6, 1973, pp. 1125–1134

An asymptotic method of integrating the free vibrations equations of a noncircular cylindrical shell, freely supported along the curvilinear edges, is proposed. The qualitative singularities of the vibrations associated with the fact that the shell is essentially noncircular are clarified. Numerical results are presented for the free vibrations frequencies and modes of a box shell which are compared to the results of the asymptotic analysis. It is supposed that the variability of the stress and strain states is great.