Elastic interaction between nonlinear solitary waves in granular chains and composite beams: Experiments and modelling

Abstract

We study the elastic interaction between strongly nonlinear solitary waves in lightly pre-compressed granular chains and laminated composite beams using experimental, analytical and numerical approaches. Experiments were conducted using a vertical array of 21 steel beads contacting a simply-supported composite beam at mid-span. A striker bead was dropped from a given height to initiate the propagation of a single solitary wave in the granular chain, whose interaction with the beam resulted in the propagation of multiple reflected solitary waves. The developed apparatus allowed measuring the delays and amplitudes of the reflected waves, and the obtained measurements were found in good agreement with numerical predictions based on a previously developed discrete element (DE) model. The numerical model was further simplified to derive a closed-form analytical solution for the delay of the primary reflected wave whose predictions showed no discernible differences to those obtained from the DE model. Experiments and predictions were performed on beams made of carbon fiber/epoxy and glass fiber/epoxy laminates, and the effects of beam thickness, width and flexural modulus on the characteristics of the reflected solitary waves were studied. We tested composite beams with thickness-to-length ratio in the range of 0.015 < H/L < 0.06 and found that the delays and amplitudes of the reflected nonlinear pulses are highly sensitive to the flexural modulus of the composite beam, concluding that the developed non-destructive technique is capable of measuring basic elastic properties of engineering composites, offering a reliable, time-efficient and cost-sensitive alternative to existing destructive and non-destructive test methods.