## Operating Principle of Compressible Constrained Layer Damping and Polymeric Foam Characterisation
Since the material density is an important lightweight indicator and it influences the damping as well as determines indirectly the actuation-relevant porosity of the foam, a broad range of the densities was used as an initial selection criterion of damping materials. This led to the selection of twelve open cell polyurethane (PU) foams and a single melamine foam. The loss and storage moduli were determined in preliminary rheometric tests (as described later in detail) for a single frequency of \(f\) = 1 Hz. For a further selection of suitable materials, it was judged to be advantageous that the foams could be compressed to at least 88% with a pressure of 1 bar (corresponding to the maximum possible pressure when actuated by vacuum), since major changes of the shear properties were expected in the range of high compression. Out of the foams that fulfilled this criteria, the two foams with the highest loss modulus (foam C and D) and foam B (with the lowest density and the associated high lightweight potential) as well as foam A (melanin-based; as a material with fundamentally different open cell morphology compared to PU foams) were selected. Thus, four foams were finally chosen for further investigations and characterised in detail. The CCLD-relevant properties (Table 1) were determined based on procedures described in DIN EN ISO 845:2009-10 (density), DIN EN ISO 11357-2:2014-07 (glass transition temperature) and ASTM D 3576 (cell diameter of PU foams; due to different morphology, a similar procedure was derived for the melamine foam). All experiments related to the compression behaviour and viscoelastic shear properties were conducted on cylindrical specimens using a rotatory rheometer (MCR 502, [PERSON]_) in plate-plate mode. Herein, a compressive stress up to 100 kPa was applied, anticipating a vacuum driven CCLD actuation. A detailed description of the test setup and the measurements performed can be found in Reference [35]. At first, the quasistatic through thickness compression behaviour of these materials, which determines the actuation characteristics of the CCLD, was investigated. Considering the relation between the compressive stress and strain, a non-linear behaviour with three typical regions [36] can be distinguished for all tested foams: cell wall bending, cell wall buckling and foam densification (shown exemplary for the foam D on Figure 2). As mentioned above in the selection criteria for the foams, all tested foams could be densified at least up to 88% using atmospheric pressure. In order to understand the deformation kinematics and to assess the compression reversibility at such high densifications, high-resolution in situ computed tomography (CT) enabling X-ray scanning in deformation controlled mode, was used (Figure 2). It was found that even if the tested foams were compacted to one tenth of their initial thickness, they would return to their undamaged initial structure after relief. In the scope of material characterisation and following modelling of the structural dynamic behaviour, a linear viscoelastic model of the foams as damping material was assumed. Such assumption was verified based on the analyses of raw rheometric data revealing harmonic, phase shifted stress response on applied harmonic strain. Therefore, the well established description of the viscoelastic properties using the complex shear modulus \(G^{*}=G^{\prime}+iG^{\prime\prime}\) was applied, where \(G^{\prime}\) is the stiffness related storage shear modulus and \(G^{\prime\prime}\) is the damping related loss shear modulus. The complex