On the effects of using nonlinear springs in mono-coupled periodic structures

Abstract

Abstract Many strategies are employed to control structural vibration. One of them is to design structural elements in a periodic arrangement to obtain the so-called bandgap effect. For infinite periodic structures, bandgaps are defined as frequency ranges where waves do not propagate. These result from internal resonances or wave reflections due to Bragg scattering. This paper investigates the longitudinal vibration of a finite periodic array of rods connected to linear and nonlinear springs, in which Bragg scattering occurs. The analysis uses the transmissibility of a single cell, which can provide insight into the behaviour of the entire structure. The influence of the nonlinearities is studied by way of approximate dynamic stiffness functions obtained from the harmonic balance method. It is found that grounded hardening springs can marginally improve the bandgap width, although this improvement may be challenging to exploit in practical rod-like systems. The series-spring configuration is also discussed and is shown to be limited by multivalued responses and possible stiffness instability when softening nonlinearities are used. Experimental results on the linear structures together with nonlinear finite element simulations to support the analytical expressions and the consequent conclusions.