Vibration isolation of machine foundations by periodic trenches

A unified method is proposed for screening the ground-transmitted vibrations generated by machine foundations. The method is based on the solid-state phenomenon of Bragg resonance, which leads to the fact that periodic shallow trenches are capable of reflecting a considerable amount of wave energy if they are carefully designed to have a tuned periodicity with the propagating modes. The method of multiple scales is used to derive the coupled-mode equations, describing the interaction of propagating waves with the tuned periodic trenches. Reflection coefficients are calculated to evaluate the effectiveness of the trenches in reducing wave amplitudes.