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Abstract: This paper focuses on the effect of variabilities on the diffusion matrix. The reflection and transmission coefficients for two deterministic waveguides connected through an uncertain coupling element with a single random variable is addressed. Based on hybrid numerical tools called the wave finite element/stochastic finite element method (WFE/SFEM), a formulation is developed and validated. The statistics of energetic coefficients are investigated and explicitly formulated. The coupling loss factors (CLFs), which is one of the important parameters in statistical energy analysis (SEA), is also evaluated regarding the mechanical and geometrical inhomogeneities in the coupling element. Numerical validations are performed using Monte Carlo simulations. [Copyright &y& Elsevier]

The paper describes a methodology for computing the sound transmission loss of any flat, curved and cylindrical, homogeneous and periodic structure, under any type of acoustic and/or aerodynamic load. An approximate excitation model is introduced to reproduce uncorrelated and spatially-correlated loads using a wavenumber integration of surface waves. Then, a wave finite element formulation is developed and interfaced with the excitation models in order to cover industrially-relevant case studies. Analytical, numerical and experimental transmission losses are presented for validation purposes. Finite size effects are also taken into account using a spatial windowing and a cylindrical analogy, for curved structures. Different periodic-cell designs are also compared and investigated under turbulent boundary layer and diffuse acoustic field excitations. [ABSTRACT FROM AUTHOR]

The stochastic response of periodic flat and axial-symmetric structures, subjected to random and spatially-correlated loads, is here analysed through an approach based on the combination of a wave finite element and a transfer matrix method. Although giving a lower computational cost, the present approach keeps the same accuracy of classic finite element methods. When dealing with homogeneous structures, the accuracy is also extended to higher frequencies, without increasing the time of calculation. Depending on the complexity of the structure and the frequency range, the computational cost can be reduced more than two orders of magnitude. The presented methodology is validated both for simple and complex structural shapes, under deterministic and random loads. [ABSTRACT FROM AUTHOR]

This paper presents a rapid and accurate numerical tool for the energy flow evaluation in a periodic substructure from the near-field to the far-field domain. Here we suppose that the near-field part contains a point source characterized by the injected power in the structure. The near-field part is then modeled by Finite Element Method (FEM) while the periodic structure and the far-field part are regarded as waveguides and modeled by an enhanced Wave and Finite Element Method (WFEM). Enhancements are made on the eigenvalue scheme, the condensation of the unit cell and the consideration of a reduced wave basis. Efforts are made to adapt substructures modeled by different strategies in a multi-scale manner such that the final matrices dimensions of the built-up structure are largely reduced. The method is then validated numerically and theoretically. An application is presented, where a structural dynamical system coupled with periodic resistive piezoelectric shunts is discussed. [ABSTRACT FROM AUTHOR]

• New designs based on multi-layer core systems to control vibroacoustic properties. • Multi-layer core systems allowing to easily compare structures with the same mass. • The flexural behavior is modified with the trigger of transition frequencies. • Strong improvement of STL compared to sandwich panels made of one single core. • Strong improvement of STL while maintaining the mass constant. The present work deals with multi-layer rectangular core topology systems built up by stacking layers made of different rectangular core geometries. Multi-layer systems have been intensively studied in terms of mechanical performances whereas their vibroacoustic behavior, acoustic efficiency and design is however still an open issue. Several design parameters should be considered to fully understand the dynamic and acoustic behaviour of such structures. Therefore, this paper focuses on controlling the transition frequency and the Sound Transmission Loss (STL) by modifying geometrical parameters of the unit cell, while keeping the mass constant. Infinite panels and real wavenumbers will be considered in the study. The Wave Finite Element Method (WFEM) is used to obtain the targeted indicators. The proposed designs give the opportunity to shift the transition frequency and to control the flexural waves propagating in the structure. Besides, the STL is highly improved in the full frequency range of interest compared to a standard sandwich panel made of a single core. [ABSTRACT FROM AUTHOR]

• Tailoring of the structural elastic waves' propagation versus the acoustic one. • Shifted and Folded walls core designs are proposed for sandwich complex structures. • Broadband increased transmission loss keeping the mass of the system constant. • Experimental verification of trends using 3D-printed panels with the designed cores. Two types of sandwich panels are designed by using the periodic structure theory. A double-wall panel with mechanical links and a sandwich panel with rectangular core are studied. An oriented optimization of the elastic bending waves' propagation versus the acoustic wavenumbers is achieved by using shifted core walls and by keeping the mass and stiffness of the system constant. Standard and optimized configurations are 3D-printed and sound transmission measurements are carried out by using a facility with an uncoupled reverberant-anechoic configuration. The experimental evidences of enlarged bending band-gaps and deformation mechanisms are proved using a reverse approach based on the acoustic radiation of the panels. [ABSTRACT FROM AUTHOR]

Video Abstract • A stochastic quadratic eigenvalue formulation for the periodic media is presented. • The longitudinal and flexural waves in the 1D and 2D periodic media are simulated. • In the case of flexural wave, only out of plane flexural wave are generated. • The formulation offers huge computational advantages over the Monte Carlo simulation. Periodic structures have properties of controlling mechanical waves. These solutions are used in aircraft, trains, submarines, space structures, where high level of robustness has to be ensured in presence of uncertainty in the numerical models. The paper presents a stochastic formulation for the Bloch analysis of periodic structures, based on the quadratic 1D and 2D forms of the Wave Finite Element method. In 1D case, numerical examples of periodic rod and metamaterial rod systems are considered; for the 2D case, homogeneous and periodic plates are considered. In both cases, the effect of uncertainties on wavenumber variation is studied. The accuracy and performance of the developed method is compared with Monte Carlo Simulation (MCS) results. It is found that the uncertainties affects the wavenumber scattering. Maximum variation of wavenumber occurs at the band gap edge frequencies and trends are increasing in higher frequency. In terms of computational cost, the presented formulation offers advantages over MCS. The obtained computational cost savings can be a remarkable achievement for the optimization and reliability study under uncertainties of complex structures. [ABSTRACT FROM AUTHOR]