Interactive inverse design of periodic non-uniform/inhomogeneous rod structures based on q-learning method

The existing researches on controlling the longitudinal waves through periodic rods with frequency bands mainly focus on the analysis of band structures together with their influences by various geometrical/material parameters and on the corresponding forward design via passive/active modulations. This paper originally proposes the interactive inverse design method by virtue of the Q -Learning algorithm for catering required objectives with introducing the cross-sectional nonuniformity and material inhomogeneity to the constituent components in periodic rods. Firstly, theoretically analyzing the frequency bands of periodic non-uniform/inhomogeneous rods with linear variations to the cross-sectional area and to the Young ' s modulus and material density, is presented using transfer matrix method (TMM). After verifying the analysis method by comparing it with the finite element method (FEM) for obtaining band structures in three kinds of exemplified periodic rods with non -uniform/ inhomogeneous components, the effects of non -uniformity and inhomogeneity of components on the frequency bands are discussed. These effects provide qualitative judgment criteria to the results of inverse design. Secondly, the inverse design method by the Q -learning algorithm for periodic non-uniform/inhomogeneous rods is proposed as the optimization objective is the maximum of the first bandgap width. The optimization results of the periodic rods with only non -uniformity, with only inhomogeneity or with both non -uniformity and inhomogeneity are provided to validate the accuracy and efficiency of the proposed Q -Learning algorithm that has the advantages of obtaining the optimal result from any initial states and giving the evolutionary path along the gradient to the objective. It should be pointed out that our proposed inverse design method can actually be extended for other optimization objectives and to other kinds of periodic structures for controlling diversified elastic waves.