Locally resonant 1-D periodic structures : theory and application

Noise control in the aerospace eld is a relevant and challenging problem. One of the most common and problematic noise source are the vibrations transmitted directly to the cabin from gearbox, rotors and engines through structural linking components. Helicopter's struts, that link the fuselage to the gearbox, are a straightforward example of these delicate structural elements: they have to be as sti as possible to support the gearbox at the most severe ight conditions, but such requirement is in contrast with the goal of isolating the two parts in order to reduce the transmitted vibrations. Many active and passive control techniques were developed in the last centuries to face such problem. Moreover, the need for passive damping techniques arises from the complexities that are brought to the structures by active control systems as well as by the increase of weight and energy supplies required to implement such controls. The following thesis is concerned with 1-D structures (rods and beams) with periodically attached dynamic vibration absorbers as an e ective passive control system for vibration transmission and, in particular, the application of such technique to helicopter struts is investigated. Periodic structures have been widely studied in the last decades showing very interesting wave ltering properties, elastic waves, in fact, cannot propagate freely within some frequency ranges, the so called band gaps. Such unique wave ltering characteristic is combined with the dynamic vibration absorber property of reducing a determined frequency. The study is performed by using an exact analytical approach based on a combination of the spectral element method and periodic structure theory. An explicit expression is provided for the calculation of propagation constants and thus the complex band structures, and it is further developed to examine the e ects of various system parameters on the band-gap behavior, including the position, width and wave attenuation performance of all the band gaps. At last, the actual vibration reduction is shown through the transmittance function of a nite structure, pointing out how this control strategy can be an e ective, simple and light solution to the vibration transmission issue.