Materials with superior damping properties are used to reduce the effects of vibration in machine tools, thereby increasing precision at high feed rates. Sandwich materials utilize the stiffness of the face sheets to prevent deformation while minimizing acceleration forces due to their low density. Additionally, the choice of the core material can drastically alter the composite's damping properties. One candidate for the core that addresses the high damping requirements of machine tools is a particle-filled hollow sphere structure (PHSS). The porous structure consists of sintered hollow steel spheres filled with aluminum oxide particles and adhered with epoxy. The porosity ensures low density, and the energy-absorbing collisions in the particle fillings increase damping. Furthermore, varying the manufacturing parameters of the spheres allows for adjustment of the material properties. Accelerating the design of task-specific PHSSs requires predicting their effective properties accurately, in order to dimension the machine as a whole. In this contribution, we present an approach to determining the effective behavior of microstructured materials, focusing on damping characteristics. Specifically, we use the geometric representation of a microstructure and FFT-based homogenization methods to compute the frequency response function. Our primary interest lies in the damping behavior of PHSSs and the underlying parameters. We present the utilized homogenization approach, where we apply it to a previously developed geometric representation of the PHSS microstructure.