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Nonlinear flexural vibrations of composite shallow open shells
Author(s) -
Adam Christoph
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610123
Subject(s) - isotropy , nonlinear system , shell (structure) , flexural strength , vibration , equations of motion , materials science , shear (geology) , plate theory , geometry , mechanics , structural engineering , physics , classical mechanics , composite material , mathematics , optics , engineering , quantum mechanics
This paper addresses geometrically nonlinear flexural vibrations of open doubly curved shallow shells composed of three thick isotropic layers. The layers are perfectly bonded, and thickness and linear elastic properties of the outer layers are symmetrically arranged with respect to the middle surface. The outer layers and the central layer may exhibit extremely different elastic moduli with a common Poisson's ratio ν . The considered shell structures of polygonal planform are hard hinged supported with the edges fully restraint against displacements in any direction. The kinematic field equations are formulated by layerwise application of a first order shear deformation theory. A modification of Berger's theory is employed to model the nonlinear characteristics of the structural response. The continuity of the transverse shear stress across the interfaces is specified according to Hooke's law, and subsequently the equations of motion of this higher order problem can be derived in analogy to a homogeneous single‐layer shear deformable shallow shell. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)