A fully nonlinear dynamic formulation for rotating composite beams: Nonlinear normal modes in flapping

作者：Arvin Hadi; Lacarbonara Walter^*

来源：Composite Structures, 2014, 109: 93-105.

DOI：10.1016/j.compstruct.2013.10.044

• Composite multilayer beams
• Rotating beams
• Geometrically exact approach
• Method of multiple scales
• Effective nonlinearity coefficient
• Individual nonlinear normal modes

The geometrically exact equations of motion of pretwisted rotating composite beams parametrized by one space coordinate are derived from three-dimensional theory. The mechanical formulation is based on the special Cosserat theory of rods which does not place any restriction on the geometry of deformation besides the rigidity of the cross-sections. The constitutive relations for the composite beams are obtained within the context of three-dimensional theory. The Taylor expansion of the equations of motion - further specialized to the case of unshearability - is carried out about the equilibrium caused by centrifugal forces to obtain the linearized and third-order perturbed forms of the governing equations. The Galerkin approach is employed to project the linearized equations of motion and solve for the linear free vibration characteristics. Subsequently, the method of multiple scales is applied directly to the perturbed equations of motion to investigate the nonlinear flapping modes and their frequency variations with the amplitude and the angular speed. These modes are investigated away from internal resonance conditions found as the critical angular speeds for which nonlinear interactions between different modes may occur. Results obtained by the Galerkin method are compared with those obtained via a finite element discretization.

• 出版日期2014-3