An Analytical Model for the Interaction of Mass Inclusions in Heterogeneous (HG) Blankets

The heterogeneous (HG) blanket is a passive treatment used to reduce the low frequency transmission of sound through partitions. HG blankets, glued onto a structure, consist of an elastic medium with embedded mass inhomogeneities that mechanically replicate a mass-spring-damper system to reduce efficient radiating structural modes at low frequencies. The elastic layer typically used has sound absorption properties to create a noise control device with a wide bandwidth of performance. The natural frequency of an embedded dynamic vibration absorber is determined by the mass of the inhomogeneity as well as by its effective stiffness due to the interaction of the mass inclusion with the elastic layer. A novel analytical approach has been developed to describe in detail the interaction of the mass inclusions with the elastic layer and the interaction between the masses by evaluating special elastomechanical concepts. The effective stiffness is predicted by the analytical approach based on the shape of the mass inclusions as well as on the thickness and material properties of the layer. The experimental validation is included and a simplified direct equation to calculate the effective stiffness of a HG blanket is proposed. Furthermore, the stress field inside the elastic material will be evaluated with focus on the stresses at the base to assess the modeling of one or more masses placed on top of the elastic layer as dynamic vibration absorbers. Finally, the interaction between two (or more) masses placed onto the same layer is studied with special focus on the coupling of the masses at low distances between them.