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Nonlinear vibrations of unsymmetrically laminated beams. (English) Zbl 0664.73036

The purpose of this study was to develop a simple one-dimensional finite element for the nonlinear analysis of symmetrically and unsymmetrically laminated composite beams including shear deformation. The beam element has 10 degrees of freedom at each of the two nodes: the axial displacement, the transverse deflection and the slope due to bending and shear, the twisting angle, the in-phase shear rotation, and their derivatives. The formulation, the solution and procedure, and the computer program have been evaluated by solving a series of examples on the static response, free vibration, and nonlinear vibrations of isotropic and laminated beams. For unsymmetrically laminated beams, the nonlinear vibrations were found to have a soft spring behavior for certain boundary conditions as opposed to a hard spring behavior observed in isotropic and symmetrically laminated beams. The in-plane boundary conditions were found to have a significant effect on nonlinear responses.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74H45 Vibrations in dynamical problems in solid mechanics
74E30 Composite and mixture properties
74-04 Software, source code, etc. for problems pertaining to mechanics of deformable solids
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