ANALYTICAL, NUMERICAL AND EXPERIMENTAL STUDY OF THE DYNAMICAL RESPONSE OF A MULTI- LAMINATED PERIODIC BAR Policarpo, H. 1 ; Ribeiro, A. R. 2 ; Neves, M. M. 2,* 1 DEM, Instituto Superior Técnico, Av. Rovisco Pais, 1049 – 001 Lisboa, Portugal 2 IDMEC-IST, Instituto Superior Técnico, Av. Rovisco Pais, 1049 – 001 Lisboa, Portugal E-mail *: maneves@dem.ist.utl.pt SUMMARY: This article presents a study on the effect of using multi-laminated periodic bars to separate two adjacent eigenfrequencies creating wide resonance gaps at useful frequencies. Three complementary approaches are considered: analytical, numerical and experimental. The objective is to control, in a passive form, longitudinal vibration transmissibility in specific and wide enough frequency ranges of interest. For useful frequencies the selection of appropriate material pairs is of great importance as it is shown. We propose the use of pairs of steel and cork agglomerate, since this choice allows the design of attenuators for low frequencies by a usual linear-elastic prediction based on the Finite Element Method (FEM). In this particular case, it requires knowing the storage modulus of cork, which is also treated in this article. An interesting relation between the modal analysis (finite medium), the harmonic analysis (finite medium) and the Bloch wave theory (infinite medium) is proposed for which no reference was found in the researched literature. The analytical and numerical models are verified and validated experimentally. Throughout the experimental validation process, a methodology to determine the storage modulus of cork was used. Finally, a structural improvement problem allowed obtaining an even wider resonance gap in the required frequency interval. KEYWORDS: Passive Isolation, Vibration, Multi-laminated Bar, Cork Agglomerates, Structural Modification. 1. INTRODUCTION Multi-laminated structures have received considerable attention and extensive efforts have been made to analyze the propagation of waves in periodic structures. Among these efforts is the unified approach of Brillouin for the dynamic analysis of a wide variety of periodic structures [1]. Apart from their unique filtering characteristics, the ability of periodic structures to transmit waves from one location to another, within the pass-bands, can be greatly reduced when the ideal periodicity is disrupted or disordered [2]. Among the pioneering efforts is also the work of Mead and his co-workers [3] which includes many of the original contributions in the analysis and characterization of the wave propagation in periodic structures. To study structures built with infinite periodicity repetition, Bloch's theorem [4] also related with Lyapunov-Floquet’s theorem [4] can be used to obtain a characterization of longitudinal waves leading to the corresponding dispersion relation. For structures with finite periodic repetition a description of the basics can be found in [6]-[9]. In this study multi-laminated periodic bars are used to separate two adjacent eigenfrequencies creating wide resonance gaps at useful frequencies. For this purpose, three different but complementary approaches are considered: the analytical, the numerical and the experimental. The main objective is to control, in a passive form, longitudinal vibration transmissibility in specific and wide enough frequency ranges of interest, designated as resonance gap, also referred to as attenuation region. The present study is motivated by the lack of work reported in low frequency ranges, for these types of structures even though they have been widely researched over the years. The layout of the materials and the contrasting ratio of their properties (specifically, the wave propagation speed) determine the widths and locations of the resonances gaps [10]. Thus, for low frequency ranges is required a high contrasting ratio of the properties of the materials. Steel and cork or cork agglomerates present such high contrasting ratio of properties [11], which associated to the lack research of cork agglomerates in this area, reinforces this study’s motivation. The multi-laminated periodic bar is here used since it allows obtaining a significant wider resonance gap between some selected adjacent eigenfrequencies, relatively to the homogeneous bar or to helicoidal springs which generally present uniformly spaced resonances. The reason for using steel–cork agglomerate multi-