Research on the design of phononic crystal shaft bandgaps based on lumped mass method

Abstract

Phononic crystals tend to mature in the research of forward problems due to their unique bandgap characteristics, but it is difficult to realize reasonable parameter design at specific bandgap frequencies in practical engineering applications. Thus, based on the lumped mass method, a research method for the inverse problem of phononic crystal shaft bandgaps is proposed in this paper. On the basis of the discretization model, the relationship between polynomials and the characteristic of bandgaps is discussed through derivation of the dispersive polynomial, and the feasible regions of the corresponding parameters are solved according to the bandgap existence criterion established by the characteristic rules for analytical verification. The results show that the bandgap existence criterion for frequency points and frequency bands can accurately and effectively invert the relevant parameters that meet the requirements, and the method is of great practical significance for promoting the development of phononic crystal shaft parameter design under the target bandgap in engineering applications.