## 2 Description of the Methodology  
A vibro-acoustic analysis for a chain cover of a four-stroke four-cylinder diesel engine was performed through an FEM-BEM coupled approach. Such a hybrid approach--selected as an alternative to an FEM-FEM approach--is particularly advantageous when considering a free field acoustic emission, because with BEM it suffices to model the vibrating finite boundary, being null the  
Figure 1: (**a**) Fiat Power Train (FPT) Small Diesel Engine (SDE); (**b**) Finite element model (FEM) model of the engine.  
contribution of integrals evaluated on the infinite boundary (Sommerfeld condition). Moreover, even for closed-domain acoustic emission problems, there can be computational advantages by coupling FEM and BEM approaches [17].  
In [17], the reader can find detailed explanations about the way in which the interface between FEM and BEM approaches is realized (e.g., with reference to mapping of results from the FE-mesh to the BE-mesh with corresponding interpolation errors caused by such a data transfer process).  
The vibration analysis is executed using FEM, whereas BEM is adopted for the simulation of the free field acoustic emission because it is more computationally efficient than FEM (BEM does not need to model the remote boundary at infinity as provided by the Sommerfeld radiation condition). A free field FE-based acoustic simulation would also be possible, but special FEM elements (infinite finite elements) would be necessary in this case.  
The interface between the programs is realized by automatic data exchange tools available in the Virtual Lab environment following a theoretical approach detailed in [17] and synthetically reported in Section 4.  
The BE approach combined with the acoustic transfer vector (ATV) technique in principle allows the acoustic emission to be evaluated in a shorter computational time when considering different engine regimes and various stiffening configurations.  
Having to map a vibrational scenario from a refined FEM mesh to a coarse BEM mesh, some minor interpolation errors are introduced by the interfacing process.  
Components showing a direct structural interaction with the chain cover were explicitly included in the FEM model: tappet cover, head, crankcase, sub-crankcase with bearing caps, and oil pan.  
The FEM overall model (Figure 1b) consisted of 546,155 linear elements with a size of 6 mm and 507,978 nodes, whereas the chain cover was modelled by using quadratic elements with a size of 3 mm.  
The overall FEM engine model is only adopted for a free-free modal analysis from which to extract the chain cover modal basis.  
The modal analysis basis of the chain cover was extracted, leveraging on the results provided by the modal analysis of the overall engine. Afterwards, applying the vibrational excitations experimentally measured at the bolted connections between the chain cover and the engine block, a modal-based forced response analysis was performed for the chain cover.  
The interface between chain cover and engine block was modelled using tie constraints everywhere except for the connection bolts where rigid elements (RBE2) are used. Equipment for the experimental vibrational measurements was available and consequently exploited to get a realistic assessment of the vibrational input to the chain cover.  
The vibration numerical results were compared with corresponding experimental measurements.  
The BEM model (Figure 2) was based on a discretization involving the component surface (outer \"skin\" of the component) and consisted of 1300 surface linear elements and 1385 nodes.  
Figure 2: Boundary element method (BEM) model of the chain cover.  
The objective of this work was the evaluation of noise emission from the sole chain cover: in this respect, the BEM discretization was only applied to the component under examination.  
The environmental acoustic pressure distribution was calculated by the BEM model, and then compared with the related experimental acquisitions.