## 1 Introduction
On the other hand, in open-cell PFs (Figure 1b) the cells are interconnected to each other and the blowing agent escapes during the manufacturing process, leaving air instead. The latter structure can be chosen over the former one for its lower density, higher transpiration capability and lower thermal expansion. In this work, a vibro-acoustic analysis focusing on the estimation of the bending stiffness and sound transmission loss of a sandwich structure through the wave propagation approach is presented. The structure is made of two sheet molding compound (SMC) leaves sandwiching a layer of \"Acell 150 Foam\", an open-cell phenolic foam specifically designed for fire-resistant applications obtained through a proprietary process which allows to overcome the natural friability of the basic phenolic resin, making it suitable to machining and coupling with other materials. The manufacturing process does not use CFC, HCFC, VOC, or HFC blowing agents and the material can be recycled as a filler. The foam is currently undergoing a process of optimization by the manufacturing company, willing to improve its sound insulation capabilities while preserving its fire-resistance properties, to the aim of expanding its application in the shipbuilding industry. However, the mechanical and morphological characteristics of the structure, and of the core in particular, are difficult to know in advance, due to the modifications induced by the production process, which cannot ensure a perfectly uniform density  
Figure 1: **(a)** Example of a standard closed-cell phenolic foam. **(b)** Sample of the investigated open-cell phenolic foam. across the planar direction of the foam panel. Moreover, one of the main uncertainties when dealing with open-cell foams is that it is impossible to create a controlled interface between the core and the laminates, and to guarantee an even distribution of the glue. The aim of the work is two-fold: on the one hand, the prediction capabilities of a parametric literature model is evaluated when vibrational data measured on beam specimens are passed as input; on the other hand, the evaluation is repeated by feeding the model with the nominal data of the materials constituting the layers, so to highlight the effects of the manufacturing process on the sound insulation properties of the final product. The paper is organized as follows. Section 2 summarizes the mathematical model first proposed by [PERSON] in the early 1990s to describe the bending of sandwich beams and predict the sound transmission loss of sandwich plates. Section 3 describes the experimental techniques, the equipment, and the test specimens used in the measurement campaigns. In particular, a frequency-dependent bending stiffness of the sandwich panel is estimated by means of dynamic tests performed on two sandwich beams cut from the panel in orthogonal directions. Section 4 presents the results of the investigation, in terms of estimated bending stiffness, loss factor and sound transmission loss. The latter is compared with measurements in sound transmission suites performed according to ISO 10140-2. In Section 5, the use of the model with nominal data relative to the constituting materials instead of experimental measurements and the influence of the manufacturing process on its predictive capabilities are discussed.