A high order Newton method to solve vibration problem of composite structures considering fractional derivative Zener model
Résumé
This paper presents a numerical method to solve the non-linear vibration problem of composite structures made of many unidirectional fibers/matrix layers. To take into account damping properties of structures, fractional derivative Zener model for complex moduli is used in each layer. The frequency dependence of these models leads to a non-linear vibration problem. To solve it, a High Order Newton (HON) solver based on homotopy and perturbation techniques is proposed. Thus, the initial non-linear problem turns into a set of linear systems, easier to solve. Numerical results obtained by the HON solver are compared with experimental and numerical results of literature.
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