## 3 Modelling of Lightweight Structures with Ccld Treatment
Such procedure was conducted using a material parameters obtained during the described material characterisation for an exemplary geometry of the vibrating system. The model was used in a series of simulations to estimate the CCLD potential regarding the damping capacity and its adaptation as well as to understand the physical relationships of parameters describing the system configuration. To study the influence of the base beam slenderness on the CCLD performance, the length of the base beam was kept constant at 550 mm while its thickness was varied in such a way that the slenderness took the values of 10, 20 and 100. The base beam component of the model was configured with the homogenised viscoelastic properties of a \(\left[0,90,04\right]\)s lay up of unidirectional prepreg layers (T700 carbon fibres and epoxy resin) with a low intrinsic structural damping, implemented using a loss factor typical for the material type and its lay up. The constraining layer was assumed as one unidirectional py of T700 carbon fibres and epoxy resin of the thickness 0.25 mm. The parameters of the viscoelastic layer were consecutively set according to material characterisation results for the foams shown in Table 1. The TTS principle, applied to the primary rheometric data, enabled simulations in an augmented frequency range at fixed temperatures for all considered foams. Since the shear deformation of the viscoelastic layer during the beam bending vibrations increases with the decrease of its thickness, possibly thin layers were pursued in order to maximise the damping effect. Thus, the lower thickness limit in uncompressed state was set for each foam to exactly 10 mean foam cell diameters. The normal displacement amplitude at the middle of the beam \(L/2\) as a response to a unit, normal harmonic excitation force applied in the same point was calculated for every above mentioned slenderness value and foam material. The change of the dynamic behaviour in comparison with the bare beam behaviour and the adaptation range that defines how much the vibration amplitudes can be changed using the CCLD actuation, were used as key effectiveness indicators. They are presented in detail in Figure 5 for the complete analysed frequency range on example of foam D and slenderness value of 100. Results obtained for all considered foam materials and slenderness values are compactly presented in Figure 6 for the bending modes 1, 3 and 5. It can be observed that already the application of an unactuated CCLD (Figure 5B) on the bare beam significantly increases the damping and reduces the vibration amplitudes. This can be accounted to a purely passive CLD treatment influence and it can pose a favourable fail-safe system feature in real applications. Both the adjustment range and the damping capacity reveal a complex dependency on the system configuration, varied here in terms of beam slenderness and damping material. An understandable trend showing decreasing vibration amplitudes for more slender beams can be directly seen (Figure 6A-C). This can be accounted to the decreasing ratio of base structure size to the constant CCLD treatment size. The results of the simulations described up to this point confirm the principal correctness of the initial theoretical assumptions about the adaptive dynamic behaviour of structures with the original CCLD treatment. A significant vibration damping as well as a remarkable adaptability (through effects occurring during a simple compressive actuation of the intermediate layer) were observed but both show a complex dependence on the system configuration. Nevertheless, the developed analytical modelling approach can already be used for a preliminary system design. An extensive exploration of the parameter space with the aim of detecting their possible dependencies will be part of future work. The viability of such exploration is supported through the intrinsically moderate computational effort connected with simulations using the analytical model.