Non-linear vibration analysis of visco-elastically damped composite structures by multilevel finite elements and asymptotic numerical method

Composites Part C: Open Access

Elias Belouettar-Mathis¹  Salim Belouettar²  Ahmed Makradi²  Hakim Boudaoud³  El Mostafa Daya⁴  Guillaume Robin⁴ 

[1] Centrale Marseille, 38 Rue Frédéric Joliot Curie, 13013 Marseille, France;Luxembourg Institute of Science and Technology, Luxembourg;Université de Lorraine, Equipe de Recherche des Processus Innovatifs, EA-3767, F-54000 NANCY, France;Université de Lorraine, LEM3, LabEx DAMAS, F-57000 METZ, France;

关键词: Vibrations;    Damping;    Multiscale finite element method (FE2);    Asymptotic Numerical Method;    Nonlinear homogenization;    Automatic differentiation;   

DOI  :  

来源: DOAJ

【 摘 要 】

Composite materials and structures are inherently in-homogeneous across multiple scales. Multi-scale modelling offers opportunities to apprehend the coupling of material behaviour and characteristics from the micro- to meso- and macro-scales. In this paper, a multi-scale finite element method (FE2) is proposed to compute the modal properties of visco-elastic heterogeneous composite materials in terms of damping frequencies and modal loss factors. In the proposed FE2-based vibration analysis, two finite elements (FE) calculations are carried out in a nested manner, one at the macro-scale and the other at the micro-scale. Unlike conventional analysis, the developed analysis does not require homogenized constitutive properties because these are derived from the micro-scale FE simulations at the representative volume element (RVE) level. The non-linearity at the micro-scale is accounted by using a frequency dependent Young’s modulus. The Asymptotic Numerical Method (ANM) and its automatic differentiation is used to solve the non-linear numerical problem. ANM consists of solving an analytical non-linear problem with a path-following (or continuation) method associated with a high-order perturbation technique. Compared with existing methods, the originality of the proposed approach lies in its ability to account for the frequency dependence of Young’s modulus in visco-elastic microstructure. Using the automatic differentiation makes the proposed approach enough flexible and generic to deal with damped and undamped vibration analyses of composite materials structures.

【 授权许可】

Unknown