Vibroacoustic metamaterial distribution optimization for increased sound insulation and mass reduction

Locally resonant metamaterials enhance sound and vibration reduction within specific frequency ranges when attached to a base plate. Typically, these metamaterials are designed with periodically distributed elements across the surface, maintaining subwavelength spacing. Using periodic boundary conditions simplifies calculations and reduces the computational power needed compared to finite-sized models. However, no other practical background states that the elements should be distributed evenly in the whole available space for maximum metamaterial effectiveness. The effectiveness of each resonant element depends on the displacement amplitude of the base plate, making elements placed in areas with lower vibration amplitude less effective than those in higher vibration regions. This work presents a topological optimization of the distribution of locally resonant elements and experimental validation of the concept. The Method of Moving Asymptotes is employed to minimize the number of resonant elements while preserving the initial sound reduction achieved by periodic metamaterials. Calculations were conducted in COMSOL Multiphysics with MATLAB, using a combined analytical and numerical approach for mechanical impedance and sound insulation simulation. Vibroacoustic measurements, such as Sound Reduction Index measurements in the reverberation chamber, were conducted in order to validate the simulation results.