Compressible Constrained Layer Damping (CCLD) is a concept for a novel semi-active damping solution for vibration mitigation. In this case, the constrained layer consists of a compressible damping material with the thickness that can be adjusted in operando using fluid actuation. This changes both the material properties and the amount of vibration-induced shear deformation, enabling a tuning of the structural dynamic behaviour of the overall structure according to the excitation parameters. The CCLD can be applied to the entire surface of the vibrating structure or as patch only partially. This work demonstrates the potential of the damping measure by experiments carried out on a curved sample structure with partial CCLD coverage that increases the structure mass by less than 5~%. The structure was excited by an electrodynamic shaker operating in a frequency range of 45-450 Hz, while the vibration velocity was measured by a laser scanning vibrometer. By adjusting the CCLD in operando, it was possible to significantly reduce the maximum vibration amplitudes as well as the spatial mean velocity of the sample structure over the entire frequency range. In addition to the experimental investigations, a multi-step simulation technique was proposed and investigated. The developed model calculates the compression of the constrained layer resulting from the fluid actuation and applies its viscoelastic parameters accordingly. In a second step, it calculates the resulting frequency-dependent dynamic behaviour of the structure. The model implements the results of a comprehensive characterisation of the compression- and frequency-dependent viscoelastic shear properties of a compressible damping material. The simulation results show a good agreement with the measured results. In the future, a fully parameterised simulation model will be used for an extensive parameter study to identify the optimal design parameters (size, position, material of the CCLD patch, etc.) and to develop guidelines for the CCLD design.