Analysis of active damping in composite laminate cylindrical shells of revolution with skewed PVDF sensors/actuators

This paper presents the third of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. In particular, the initial problem reviewed is the case of a homogeneous cylindrical shell of variable thickness that is of an axisymmetric nature. The equilibrium equations as first introduced by Donnell over seventy years ago are discussed and reviewed in establishing a basis for embarking upon a solution that utilizes finite difference methods to solve the resulting equilibrium and compatibility equations. The ultimate objective of these calculations is to achieve a quantitative assessment of the critical buckling load considering the small axisymmetric deviations from the nominal cylindrical shell wall thickness. Clearly in practice, large diameter, thin wall shells of revolution that form stacks are never fabricated with constant diameters and thicknesses over the entire length of the assembly. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. The results obtained by finite difference method agree well with those published by Elishakoff and Williams for the prediction of buckling load.

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FREE VIBRATIONS OF COMBINED HEMISPHERICAL–CYLINDRICAL SHELLS OF REVOLUTION WITH A TOP OPENING

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455413500235 ◽

2013 ◽

Vol 14 (01) ◽

pp. 1350023 ◽

Cited By ~ 6

Author(s):

JAE-HOON KANG

Keyword(s):

Present Method ◽

Thin Shell ◽

Natural Frequencies ◽

Cylindrical Shells ◽

Ritz Method ◽

Three Dimensional ◽

Free Vibrations ◽

Two Dimensional ◽

Algebraic Polynomials ◽

Shells Of Revolution

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of joined hemispherical–cylindrical shells of revolution with a top opening. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur, uθ and uz in the radial, circumferential, and axial directions, respectively, are taken to be periodic in θ and in time, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the joined shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies. Natural frequencies are presented for different boundary conditions. The frequencies from the present 3D method are compared with those from 2D thin shell theories.

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Bending of Cord Composite Laminate Cylindrical Shells

Journal of Applied Mechanics ◽

10.1115/1.1544541 ◽

2003 ◽

Vol 70 (3) ◽

pp. 364-373 ◽

Cited By ~ 2

Author(s):

A. J. Paris ◽

G. A. Costello

Keyword(s):

Cylindrical Shell ◽

Differential Equations ◽

Closed Form ◽

Composite Laminate ◽

Circular Cylindrical Shell ◽

Cylindrical Shells ◽

Axisymmetric Loading ◽

Shell Axis

A theory for the bending of cord composite laminate cylindrical shells is developed. The extension-twist coupling of the cords is taken into account. The general case of a circular cylindrical shell with cord plies at various angles to the shell axis is considered. The differential equations for the displacements are derived. These equations are solved analytically in closed form for a shell subjected to axisymmetric loading and no in-plane tractions. The results of the current study are compared with the commonly used Gough-Tangorra and Akasaka-Hirano solutions.

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