IJRET: International Journal of Research in Engineering and Technology ISSN: 2319-1163 __________________________________________________________________________________________ Volume: 02 Issue: 07 | Jul-2013, Available @ http://www.ijret.org 1056 DETERMINATION OF THE EQUIVALENT ELASTIC COEFFICIENTS OF THE COMPOSITE MATERIALS BY THE VIBRATORY ANALYSIS R. Tchatchou Metchunzin 1 , G.E. Ntamack 2 , K. Mansouri 3 , S. Charif D'Ouazzane 4 1,2 Groupe de Mécanique et des Matériaux, GMM, Département de Physique, Faculté des Sciences, Université de Ngaounderé, Cameroun, tchatchoumr@yahoo.fr, guyedgar@yahoo.fr 3 Laboratoire des Signaux, Systèmes Distribués et Intelligence Artificielle (LSSDIA) ENSET de Mohammédia, Université Hassan II Mohammédia Casablanca, Maroc, khmansouri@hotmail.fr 4 Laboratoire de Mécanique, Thermique et Matériaux, LMTM, Ecole Nationale de l’Industrie Minérale, ENIM, B.P. 753 Rabat, Maroc, charif.enim@hotmail.com Abstract We must first find a behaving law of a material, before using it in the structure. The establishment of this law in the case of a composite material requires the knowledge of his elastic equivalent coefficient. In this work, we will present the vibratory technic with which we can extract the equivalent elastic coefficients of some composite materials. The relationships we have obtained through this analysis permits to evaluate the equivalent elastic coefficients of composite materials as a function of their self throb. Those relationships are first validated with the determination of mechanical characteristics of conventional materials. After that, equivalent elastic coefficients of some composite materials are evaluated. Simulated results we have obtained are discussed in comparison of Voigt and Reuss boundaries. Keywords: Composite materials, Vibration, Self throb, Young’s Modulus, Finite Elements Method. -----------------------------------------------------------------------***----------------------------------------------------------------------- 1. INTRODUCTION Composite materials are used in many industrial areas automobile, aeronautic, building, medicine between many others. Their mechanical performances depend on the used charge and matrix, but also on the quality of the interface between the components [1, 2, 3]. An important axis in the research on the composite materials concerns the evaluation of their behaving law that is the relationship which links stress and strain. In this work, we propose a rapid technical characterization of composite materials from the vibratory analysis. This technique is based on the determination of relationships between mechanical properties of materials and their vibratory characteristics from the Lagrange motion equations and the analytical methods of the transversal vibrations of structures [4]. In other to validate those relationships, we will calculate at once, known mechanical characteristics of some conventional materials. After, we will evaluate numerically elastic properties of some stratified composite materials. The discussion on the obtained results will be done according to Reuss [5] and Voigt [6] boundaries results. 2. THEORETICAL MODEL The aim of this work is to determine elastic coefficients of sandwich composite materials [7] having the morphology of those of the following figure 1: Figure 1: Stratified heterogeneous composite material Usually when composite materials are used in structures, they are supposed homogeneous. For this reason one can represent them by the following scheme of figure 2: y x b L h z