Abstract: In this work a theory of nonlinear chaotic dynamics of multi-layer beams consisting of equally distance located layers coupled only via the boundary conditions is proposed. Wavelet analysis is applied to study a chaotic phase synchronization of vibrating multi-layer beams. Two-layer beam package serves as an example of application of the given theoretical background, where three types of the nonlinearities (geometric, physical and design) are used. 1. Introduction Investigation of chaotic dynamics of one-layer structures, as well as control of various regimes of such structures is reported in numerous papers and monographs including works of the authors of this paper [1-9]. However, chaotic dynamics of mechanical structures consisting of multi-layer beams coupled only via the boundary conditions and problems related to the phase synchronization and its control has not been reported in the existing literature. In addition, we apply here to the so far stated problems Winkler’s hypothesis regarding a transversal contact of thin walled structures. In the case of static problems we acknowledge important results reported by Kantor [10], which are further used in this paper. 2. Problem formulation Consider a package composed of multi-layer beams shown in Figure 1. In the general case, beams may have arbitrary thickness as well as arbitrary material properties, but in order to simplify the considerations we consider beams of equal thickness, width and length (h, a, b), as well as with the same physical parameters: Young modulus E(x, z, 0 , i e ), Poisson’s coefficient , shear modulus 0 G (x, z, 0 , i e ), and the specific material density . Nonlinear dynamics and chaotic synchronization of contact interactions of multi-layer beams J. Awrejcewicz, .V. Zhigalov , V.. Krysko-jr., U. Nackenhorst, I.V. Papkova, A.V. Krysko 283