Optimal design for rubber concrete layered periodic foundations based on the analytical approximations of band gaps and mapping relations

The seismic performance of rubber concrete-layered periodic foundations are significantly influenced by their design, in which the band gaps play a paramount role. Aiming at providing better designs for these foundations, this study first proposes and validates the analytical formulas to approximate the bounds of the first few band gaps. In addition, the mapping relations linking the frequencies of different band gaps are presented. Furthermore, an optimal design method for these foundations is developed, which is validated through an engineering example. It is demonstrated that ensuring the superstructure's resonance zones are completely covered by the corresponding periodic foundation's band gaps can achieve satisfactory vibration attenuation effects, which is a good strategy for the design of rubber concrete layered periodic foundations.