K-space Analysis of Complex Large-scale Periodic Structures

During its operational mission, a transportation mean is subject to broadband acoustic, aerodynamic and structure-borne excitations. The transportation means, such as aircrafts, space launchers, ships, cars, trains, etc., are designed to accomplish a primary goal, usually to transfer a payload (passengers, goods, satellites, for example) from a point to another, always keeping a high level of comfort, safety and survivability of the payload. National and international regulations about noise pollution are more and more stringent; scientists and industrial players are facing with these challenges developing new materials and new design choices.

Composite materials, complex geometries and new design concepts are investigated, making the analysis and the prediction of the vibroacoustic response of these structures a huge challenge. The complexity makes the derivation of analytical models harder to obtain; the use of numerical tools is of crucial importance. One of the most employed method is the Finite Element (FE) modeling, but the huge amount of degrees of freedom together with a high computational cost limits its use in the low frequency range. In the last decades, different methods are derived to obtain the dispersion characteristics of the structures; one of the most common is the Wave Finite Element Method (WFEM), that is based on the wave propagation. This method has been applied on various simple and complex structures, deriving both 1D and 2D formulations, extended also to curved structures.

Recently, an energetic approach has been derived starting from the Prony’s method, the Inhomogeneous Wave Correlation (IWC) method. This approach has its applicability in the mid-high frequency range, where the modal overlap is quite high. The IWC method is based on the projection of the wavefield on an inhomogeneous traveling wave. The dominant wavenumber, at each frequency, is obtained by maximization of the correlation function between the projected wavefield and the inhomogeneous wave. 

In this context, an extended version of the IWC method is derived, allowing to describe the dispersion curves of complex structures: periodic narrow plates, composite plates, ribbed panels, composite curved shells and curved stiffened structures. The method has the advantage to be applied in an operational environment, making use of sparse acquisition locations. A complete dispersion characteristics analysis is conducted, even in presence of periodic elements and vibration-control devices, describing the directly correlated band-gaps in certain frequency regions and general vibration level attenuation. A numerical and experimental estimation of the structural damping loss factor is computed. A description of the local dynamics in presence of small-scale resonators, of the periodicity effect and the identification of the multi-modal behavior are also captured.

All the results of the numerical simulations are experimentally validated on complex large-scale meta-structures, such as a 3D-printed sandwich panel, a curved composite laminated sandwich panel and a aluminum aircraft sidewall panel. The effect of industrially-oriented 3D-printed small-scale resonators on the vibro-acoustic response of the considered structures is conducted, taking in account both diffuse acoustic field and mechanical excitations.