## Operating Principle of Compressible Constrained Layer Damping and Polymeric Foam Characterisation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample** & **Manufacturer** & **Type Name** & **Base** & \begin{tabular}{c} **Density** \\ **kg m\({}^{-3}\)** \\ \end{tabular} & \begin{tabular}{c} **Porosity** \\ **-** \\ \end{tabular} & \begin{tabular}{c} **Glass Transition** \\ **Temperature** \({}^{*}\)C** \\ \end{tabular} & \begin{tabular}{c} **Cell** \\ **Diameter mm** \\ \end{tabular} \\ \hline Foam A & BASF SE & Basotect® G+ & \begin{tabular}{c} Melamine \\ resin \\ \end{tabular} & 9.0 & 0.994 & n/a & 12.5 \\ Foam B & Schaumstoffie & RG1720 & PU & 16.3 & 0.986 & \(-\)53.97 & 3.0 \\ Foam C & \begin{tabular}{c} Schaumstoffie \\ Wegerich GmbH \\ \end{tabular} & Visco5030 & PU & 48.4 & 0.960 & \(-\)17.48 & 3.1 \\ Foam D & \
\begin{tabular}{c} Aearo \\ Technologies LLC \\ \end{tabular} &
\begin{tabular}{c} ConforTM \\ CF-40 \\ \end{tabular} & PU & 96.2 & 0.919 & \(-\)2.05 & 2.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Selected physical and geometrical/morphological properties of the investigated foams [35]. shear modulus depending on compression--which determines the adaptable stiffness and damping properties of the CCLD treatment--was characterised in shear rheometric tests conducted at different frequencies and temperatures for at least eight compressions between 5% (this minimal value was determined as necessary for a reliable load introduction in the shear testing mode) and 88%. The applied experimental procedure allows a transformation of the test data to a frequency range that is much broader than the testing machine's frequency span (here 0.1... 16 Hz) using the time-temperature superposition (TTS) principle [35]. The spans of test temperatures and frequencies were selected in such a way that the measured data could be extrapolated for a fixed operating temperature of 23 \({}^{\circ}\)C into a new frequency range ending at 104 Hz, what required 2304 independent rheometric tests. Additionally, quasistatic compression tests were conducted to determine the compressive stress versus deformation describing the actuation behaviour of the CCLD being significantly slower compared to shear deformation rates during the CCLD-damped oscillations. This means that both the slow compressive actuation of the damping layer with its significant volume changes and fast shear oscillations with slight volume changes led to small fluid flow rates. Hence, the authors have assumed that the influence of damping effects connected with fluid flow in the cell skeleton can be neglected for the operation modes actuation and damping of the CCLD system at the present research stage. Such assumption is necessary for the application of the TTS as a principle pertaining originally to the behaviour of solid polymer materials. Moreover, in the literature, for example, Reference [32], it has been shown that this approach is valid for polymeric foam materials. A primary result of the conducted material characterisation is a catalogue of quantitative material data, which can be used in the CCLD design. In addition, some comparative characteristics were formulated and calculated as shown in Table 2. Both of these results, revealing a complex picture, can be used as the necessary basis for the design and calculation of structures with CCLD.