American Journal of Engineering Research (AJER) 2016 American Journal of Engineering Research (AJER) e-ISSN: 2320-0847 p-ISSN : 2320-0936 Volume-5, Issue-6, pp-258-265 www.ajer.org Research Paper Open Access www.ajer.org Page 258 Flexural Wave Attenuation in A Periodic Laminated Beam Zhiwei Guo, Meiping Sheng * ,Ting Wang (School Of Marine Science And Technology, Northwestern Polytechnical University, China) ABSTRACT: The flexural wave attenuation property of a periodic laminated beam is examined in this paper. The equation of motion of a single laminated beam is firstly derived by Hamilton principle, and then the transfer matrix method and Bloch-Floquet boundary condition are applied to determine the flexural wave band-gaps of an infinite periodic laminated beam. The vibration transmission characteristic is studied by finite element method (FEM), and the numerical result shows that, the band-gaps of an infinite periodic beam from present model match very with the transmittance valleys of a finite periodic beam from FEM model, which shows good accuracy of the present theoretical model. Studies show that, the periodic laminated beam provides good vibration attenuation performance, with broad band-gap widths and strong attenuation ability, thus can be used in the vibration and noise control. The present model derived in this paper can also predict the longitudinal wave propagation property. The Euler model is also examined to give a simple model for convenient purpose in the Engineering applications. The result shows that the simplified model can be used in the low frequency band- gap prediction, while it will induce errors in the high frequency. Keywords: Flexural wave band-gap, Hamilton principle, Transfer matrix method, Periodic laminated beam. I. INTRODUCTION Vibration is a general physical phenomenon when a mechanical structure is excited. Although some vibrations bring beneficial effect, most of the vibration will induce disgusting noise or damage to the mechanical equipment. Thus in order to reduce the vibration, many methods have been proposed. One of them is using periodic structure. Periodic structure consists of periodic identical elements, alternating in the wave propagation direction [1]. It is well known that, the waves in the band-pass propagate while the waves in the band-gap attenuate, because of the Bragg-scattering effect [2] or locally resonant effect [3]. Attracted by the great potential of vibration suppression, extensive studies about periodic structure have been conducted [1, 4, 5]. As beam-type structure is widely used in the engineering applications, the structure periodicity was introduced in the beam-type structure to reduce the vibration in extensive studies. Wen [6] studied the flexural wave propagation of a periodic thin straight beam and discussed the band-gap property caused by Bragg-scattering effect. Yu [7] and Xiao [8] studied the band-gap property of a beam attached with periodic spring-mass systems from numerical simulation and experiment, which gives a physical explanation about the band-gap starting frequency and the cut-off frequency. Wen [9] studied the periodic beam attached with multi-oscillators in order to improve the band-gap performance. Liu [10] studied the periodic curved beam, and obtained some special property compared with the periodic straight beam. There are still a number of works dealing with the periodic beam in various points of view [11-14]. As the composite laminated structure provides high stiffness-to-weight ratio, high strength-to-weight ratio and many other attractive properties [15, 16], it is used widely in the aerospace and ship engineering. However, most of the previous studies about periodic beam are focused on the single layer beam, while the characteristic of periodic laminated beam is not well addressed. In order to solve the vibration control problem met in laminated structure, the wave attenuation property of the periodic laminated beam is studied in this paper. A theoretical model of a multi-layered beam is established in the paper, which will represent the wave propagation and wave attenuation performance. The generally used sandwich structure and the bi-layer structure become the special cases of the current model. The periodic model presented in this paper gives theoretical support of wave attenuation property in the periodic laminated beam and gives a new sight to the vibration control of the composite laminated structure. II. BAND-GAP FORMULATION BASED ON TIMOSHENKO THEORY Fig. 1 has shown the model of a periodic laminated beam with m layers, alternating with A i and B i . Hamilton principle is used to obtain the vibration equations of a single laminated beam.