Longitudinal wave propagation in a one-dimensional quasi-periodic waveguide

Abstract

The paper deals with the analysis of wave propagation in a general one-dimensional (1D) non-uniform waveguide featuring multiple modulations of parameters with different, arbitrarily related, spatial periods. The considered quasi-periodic waveguide, in particular, can be viewed as a model of pure periodic structures with imperfections. Effects of such imperfections on the waveguide frequency bandgaps are revealed and described by means of the method of varying amplitudes and the method of direct separation of motions. It is shown that imperfections cannot considerably degrade wave attenuation properties of 1D periodic structures, e.g. reduce widths of their frequency bandgaps. Attenuation levels and frequency bandgaps featured by the quasi-periodic waveguide are studied without imposing any restrictions on the periods of the modulations, e.g. for their ratio to be rational. For the waveguide featuring relatively small modulations with periods that are not close to each other, each of the frequency bandgaps, to the leading order of smallness, is controlled only by one of the modulations. It is shown that introducing additional spatial modulations to a pure periodic structure can enhance its wave attenuation properties, e.g. a relatively low-frequency bandgap can be induced providing vibration attenuation in frequency ranges where damping is less effective.

Research on the vibration transmission characteristics of quasi-periodic impedance layered structure constructed by magnetorheological fluid

“…on this feature, periodic structures are widely applied in engineering applications, such as vibration and noise control, as well as filtering [2,3]. In addition, many research workers have also investigated the wave transmission in quasi-periodic structures [4,5]. Quasi-periodic structure is a type of transition pattern between periodic and disordered structures.…”

Silver-mean canonical quasicrystalline-generated phononic waveguides

“…Recently, elastodynamics of composite beams following a quasiperiodic pattern has gained considerably attention (see e.g. [13,14,15,16]). In particular, the non-standard dispersive properties of a class of two-phase periodic structured rods whose unit cells are generated according to the Fibonacci substitution rule have been presented [13,17,18].…”