## 1 Introduction
[14] investigated the properties of sandwich panels with two steel laminates and a phenolic foam core under uniformly distributed load, by testing full specimens according to vacuum chamber loading method and examining the failure mechanisms step-by-step. A simplified theoretical model, based on Timoshenko composite beam theory and validated by the experimental tests and by finite-element analysis, was given for the calculation of bending moment, shear force, deformation, load-bearing capacity and local buckling at a design stage. [PERSON] et al. [15] investigated the heat transfer in wooden layered roofs in relation to the fire hazard when exposed to a heat source, showing that the position of the layers affects the temperature distribution. The vibro-acoustic analysis of a sandwich structure can encompass different theoretical, experimental, and numerical aspects and methodologies, some of which were described by [PERSON] et al. in their review [16]. Sound transmission loss \(STL\) and radiation efficiency \(\sigma\) are commonly used indicators of the coupling between vibrating structures and a surrounding fluid. Other parameters, such as the group velocity, the wavenumber and the modal density, are the subject of dedicated studies because they allow to derive \(STL\) and \(\sigma\) and they carry additional information on the vibrational field. These parameters can be obtained through mathematical models, as in [PERSON] and [PERSON] [17], but also experimentally measured with contact methods based on accelerometers (see for instance Tronchin [18]) or non-contact techniques as in [PERSON] et al. [19]. Finally, the study of the point and transfer mobility to predict the structure-borne sound power is of practical interest when vibrations are transmitted by a mechanical vibrating source, causing noise [20]. Common types of core are honeycomb structures, made of aluminum, paper, or plastic. Foam cores are another frequent choice due to their low weight and good insulation properties, and they can be realized in several different materials, including metal and polymer-based compounds. Polyurethane (PUR), polyethylene (PE), and polystyrene (PS) are widely used as core materials, but they have limited high-temperature resistance [21] and, when exposed to fire, they deteriorate, ignite, and release toxic gases. A valid alternative in this respect is represented by phenolic resins, which show excellent fire properties [22] including low, non-toxic future generation. Phenolic foam (PF) is a thermosetting cellular material that is widely used in the construction industry. The environmental life-cycle impact of phenolic foam items is to be considered, especially because of its potential scale of application [23]. As all conventional foams, phenolic foams are obtained by mixing a liquid resin, a blowing agent and an acid catalyst, with further additives that can be added to the mixture to provide the material with certain desired characteristics. Very common blowing agents used to be volatile organic compounds (VOCs) or chlorofluorocarbons (CFCs) like trichlorofluoromethane, also known as CFC-11. In the late 1980s, following the Montreal Protocol, CFCs and HCFCs were phased out because proven ozone-depleting substances, thus they were partially replaced by hydrofluorocarbons (HFCs) like HFC 365 mfc/227 ea blends. Recently, HFCs have also been phased down after the Kigali Amendment to the Montreal Protocol and the European F-gas regulation, due to their relatively high global warming potential (GWP) [24]. PFs can be manufactured in either closed-cell or open-cell structures. In closed-cell PFs, the cells that form the structure of the material are sealed from each other and contain the blowing agent on a long-term basis (Figure 1a), thus, they are widely used for insulation purposes, especially in external wall, pipework and equipment insulation systems, for their good thermal properties and moisture resistance.