Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust Ultra-thin films effects on vibro-acoustic behaviour of laminated plate including a viscoelastic core Belaid Bouzouane a , Ameni Ghorbel b , Ali Akrout b, ⁎ , Moez Abdennadher b , Taoufik Boukharouba a , Mohamed Haddar b a Advanced Mechanics Research Laboratory (LMA), Houari Boumediene Sciences and Technology University, Alger, Algeria b Mechanics, Modelling and Production Research Laboratory (LA2MP), Engineering National School of Sfax, University of Sfax, Sfax, Tunisia ARTICLE INFO Keywords: Laminated plate Ultra-thin adhesive films Viscoelastic layer Finite element Eigenmodes Vibro-acoustic behaviour ABSTRACT In this paper, the vibro-acoustic behaviour of a laminated glass plate composed of two elastic skins, a viscoelastic core and two ultra-thin adhesive films; is investigated. Here, the coupled dynamic model is derived by mixing the classical plate’s theories (Mindlin and Kirchhoff models) and the specific behaviour law for the ultra-thin films, previously introduced in our published works in Applied Acoustics Journal [1], with an integral equation formulation for the acoustic radiation of the studied structure. The discretized coupled dynamic equation as- sociated to the energy functional is solved in order to determine the vibratory and acoustic efficiency of the designed laminate. For this purpose, a numerical validation of the finite element model is achieved by using the calculated results corresponding to a standard sandwich plate. In order to predict the vibro-acoustic responses, a modal recombination method is developed by taking into account the external fluid radiation. Hence, the effects of many parameters on some vibro-acoustic indicators (deflection, strain energy, transmission loss) such as core thickness, geometrical property, modal damping and boundary condition are presented and discussed. Especially, the influence of the ultra-thin adhesive films due to the coupling with the viscoelastic core on both dynamic and vibro-acoustic behaviours of the laminate is presented and analyzed. 1. Introduction Laminated plates represent one of the best techniques used to solve sound and vibration problems which constitute a veritable nuisance to the environment due to the continuous creation of noise sources. For this reason, laminated glass structure is requested in many application fields, for example: building constructions, automotive, aircraft and naval industry [2–6]. In order to improve the technical performance of the laminate, several researchers have analyzed the vibro-acoustic be- haviour of dynamic systems. In this context, Das et al. [7] have con- trolled the acoustic response of a laminated composite plate inside a vehicular cabin in order to improve the comfort of operators in surface transportation vehicles. Also, Narayanan et al. [8] established a closed- form expression of the transmission loss factor in terms of the viscoe- lastic core parameters for a damped standard sandwich panel. More- over, Wang et al. [9] discussed the weighted effects of the sandwich panel in order to optimize the average sound transmission loss for a high frequency range. Consequently, we remark that the majority of research works dealing with the dynamic or the vibro-acoustic beha- viour have studied a standard sandwich structure which contains two elastic skins and a viscoelastic core such as presented in the works of Wang et al. [10], Foin et al. [11], Larbi et al. [12], Assaf [13], Assaf et al. [14] and Abdennadher et al. [15]. Furthermore, for the numerical prediction techniques, several methods were established in the literature such as the Statistical Energy Analysis (SEA) [16], the finite element method (FEM) [17,18] and the boundary element method (BEM) [19]. Here, the finite element method (FEM) is adopted to establish the discretized coupled dynamic equation. Then, it seems interesting to investigate the vibro-acoustic perfor- mance of a given structure by considering a laminated plate which the associated dynamic model is developed by taking into account some kinematical hypothesis allow obtaining a closer real structure beha- viour. Actually, for many industrial applications, the layers of the sandwich plate are joined with adhesive ultra-thin films inducing in- terfacial shear stresses and tangential slip on the interface of the com- ponents [20]. Then, based on the laminate model established by Akrout et al. [21], and as presented in our work recently published; Ghorbel et al. [1], the studied laminate model was developed by combining the Kirchhoff [22] and Mindlin [23] plate theories with a specific beha- viour rule of the ultra-thin adhesive film which introduces the https://doi.org/10.1016/j.apacoust.2018.04.008 Received 3 May 2017; Received in revised form 22 January 2018; Accepted 5 April 2018 ⁎ Corresponding author. E-mail address: ali_akrout2005@yahoo.fr (A. Akrout). Applied Acoustics xxx (xxxx) xxx–xxx 0003-682X/ © 2018 Elsevier Ltd. All rights reserved. Please cite this article as: BOUZOUANE, B., Applied Acoustics (2018), https://doi.org/10.1016/j.apacoust.2018.04.008