Analytical and numerical study on bandgap and transmission of periodical truss structures based on phononic crystal theory

Abstract Truss structures with obvious periodical repetition in civil engineering are commonly used in long-span bridges and large-span buildings. Based on phononic crystal theory, periodical repetition structures have the potential to develop elastic wave bandgaps, which conduct noise attenuation or novel nondestructive testing. However, there needs to be more current knowledge about the engineering truss structures bandgaps and their potential applications. This study investigates the elastic wave bandgaps and transmission characteristics of two typical engineering truss structures analytically and numerically. We first decoupled the unit cells from the large truss structures. Then, we proposed a standard analytical model to get the dispersion relationship of the truss structures. The analytical dispersion relationship is verified by the finite element method. The results show that truss structure A could generate a bandgap from 1032 to 2065 Hz, while truss structure B could generate bandgaps from 982 to 1980 Hz. The mode analysis further reveals that the bandgap mechanism is Bragg scattering rather than local resonator. We verified the elastic wave transmission characteristics through frequency domain analysis, which agrees well with the bandgaps. To exhibit how the bandgap of the truss structures conducts noise attenuation and potential applications in nondestructive testing, we employ two case studies to illustrate the propagation of noise waves and the novel nondestructive testing for periodical truss structures. The results show that the two truss structures could attenuate noise waves. Defects in truss structures could conduct abnormal transmission, which could be applied in novel nondestructive testing.