Abstract
A model for 3D laminated composite beams, that is, beams that can vibrate in space and experience longitudinal and torsional deformations, is derived. The model is based on Timoshenko’s theory for bending and assumes that, under torsion, the cross section rotates as a rigid body but can deform longitudinally due to warping. The warping function, which is essential for correct torsional deformations, is computed preliminarily by the finite element method. Geometrical nonlinearity is taken into account by considering Green’s strain tensor. The equation of motion is derived by the principle of virtual work and discretized by thep-version finite element method. The laminates are assumed to be of orthotropic materials. The influence of the angle of orientation of the laminates on the natural frequencies and on the nonlinear modes of vibration is presented. It is shown that, due to asymmetric laminates, there exist bending-longitudinal and bending-torsional coupling in linear analysis. Dynamic responses in time domain are presented and couplings between transverse displacements and torsion are investigated.
Highlights
The use of composite materials in the engineering applications has been significantly increased in the last decades
The model is based on Timoshenko’s theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and deforms longitudinally due to warping [19, 20]
The displacement field is based on Timoshenko’s theory for bending [21] and it assumes that the cross section rotates as a rigid body in its own plane and deforms longitudinally due to warping [22]
Summary
The use of composite materials in the engineering applications has been significantly increased in the last decades. Improvements of the classical Bernoulli-Euler and Timoshenko beam theories have been developed in order to better approximate the cross-sectional behaviour due to axialbending coupling of the different layers. Such improvements are known as equivalent single layer (ESL) and discrete layer theories (DLT) and, as a result, the unknowns in the equation of motion are increased [16]. In ESL theories the number of unknowns is independent of the number of layers, but Mathematical Problems in Engineering z y They lead to poor approximation of the shear stresses. The model is validated by comparing the bending natural frequencies with available results from the literature, considering different orientations of the laminates and different boundary conditions. The dynamic steady-state responses of the nonlinear model are presented
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