Optimal Design Approach for One-dimensional Rubber-Concrete Periodic Foundations based on Analytical Approximations of Band Gaps

Abstract

This research presents an optimal design approach for one-dimensional rubber-concrete periodic foundations based on the proposed analytical approximations and mapping relations of the first few band gaps. The presented design approach can search for the optimal solution in a global sense through effectively cooperating the band gaps with the superstructure’s resonance frequencies. Firstly, analytical approximation formulas for the first few band gaps, mapping relations among frequency points inside the band gaps, and special approximations for the first band gap of one-dimensional rubber-concrete periodic foundations are proposed and verified. Furthermore, inspired by the proposed analytical approximations and the mapping relations, an optimal design approach for one-dimensional rubber-concrete periodic foundations is presented and applied to a practical example, whose optimality is demonstrated both theoretically and numerically