Nonlinear Vibrations and Stability of Doubly Curved Shallow-Shells: Isotropic and Laminated Materials

Effects of curvature upon the vibration characteristics of doubly curved shallow shells are assessed in this paper. Boundary conditions of the shell are generally specified in terms of distributed elastic restraints along the edges. The classical homogeneous boundary supports can be easily simulated by setting the stiffnesses of restraining springs to either zero or infinite. Vibration problems of the shell are solved by a modified Fourier series method that each of the displacements is invariably expressed as a simple trigonometric series which converges uniformly and acceleratedly over the solution domain. All the unknown expansion coefficients are treated equally as a set of independent generalized coordinates and solved using the Rayleigh-Ritz technique. The current method provides a unified solution to the vibration problems of curved shallow shells involving different geometric properties and boundary conditions with no need of modifying the formulations and solution procedures. Extensive tabular and graphical results are presented to show the curvature effects on the natural frequencies of the shell with various boundary conditions.

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Non-linear analysis of laminated composite doubly curved shallow shells

Vietnam Journal of Mechanics ◽

10.15625/0866-7136/28/1/5478 ◽

2006 ◽

Vol 28 (1) ◽

pp. 43-55

Author(s):

Dao Huy Bich

Keyword(s):

Laminated Composite ◽

Governing Equations ◽

Shallow Shells ◽

Approximate Analytical Solutions ◽

Linear Buckling ◽

Non Linear ◽

Vibration Problems ◽

Doubly Curved ◽

Analytical Expressions ◽

Load Deflection Curve

This paper deals with governing equations and approximate analytical solutions based on some wellknown assumptions to the non-linear buckling and vibration problems of laminated composite doubly curved shallow shells. Obtained results will be presented by analytical expressions of the lower critical load, the postbuckling load-deflection curve and the fundamental frequency of non-linear free vibration of the shell.

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Investigating geometrically nonlinear vibrations of laminated shallow shells with layers of variable thickness via the R-functions theory

Composite Structures ◽

10.1016/j.compstruct.2015.02.054 ◽

2015 ◽

Vol 125 ◽

pp. 575-585 ◽

Cited By ~ 19

Author(s):

Jan Awrejcewicz ◽

Lidiya Kurpa ◽

Tatiana Shmatko

Keyword(s):

Variable Thickness ◽

Nonlinear Vibrations ◽

Geometrically Nonlinear ◽

Shallow Shells ◽

Geometrically Nonlinear Vibrations ◽

R Functions

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Nondimensional Parameters and Equations for Buckling of Anisotropic Shallow Shells

Journal of Applied Mechanics ◽

10.1115/1.2901511 ◽

1994 ◽

Vol 61 (3) ◽

pp. 664-669 ◽

Cited By ~ 25

Author(s):

M. P. Nemeth

Keyword(s):

Laminated Shells ◽

Shallow Shells ◽

Fundamental Parameters ◽

Combined Loads ◽

Vlasov Equations ◽

Shell Buckling ◽

Bifurcation Buckling ◽

Z Parameter ◽

Shear Buckling ◽

Doubly Curved

A procedure for deriving nondimensional parameters and equations for bifurcation buckling of anisotropic shallow shells subjected to combined loads is presented. First, the Donnell-Mushtari-Vlasov equations governing buckling of symmetrically laminated doubly curved thin elastic shallow shells are presented. Then, the rationale used to perform the nondimensionalization of the buckling equations is presented, and fundamental parameters are identified that represent measures of the shell orthotropy and anisotropy. In addition, nondimensional curvature parameters are identified that are analogues of the well-known Batdorf Z parameter for isotropic shells, and analogues of Dunnell’s and Batdorf s shell buckling equations are presented. Selected results are presented for shear buckling of balanced symmetric laminated shells that illustrate the usefulness of the nondimensional parameters.

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