Nonlinear vibrations of unsymmetrically laminated beams

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-plane shear rotation, and their derivatives. The formulation, the solution 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.

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