Normal impact of a low-velocity projectile against a taut string-like membrane

Abstract

For the impact system in which a moving projectile transversely impacts against a taut fabric band, 1-D linearized model applies because of low-velocity, sufficient pretension, and the sizes of the objects. This projectile-to-band impact model can serve as the physical prototype of applications in engineering such as cable-membrane architectures and seat belts. In this fundamental work, the response properties under central and non-central impacts are investigated analytically from the viewpoint of wave propagations, while comparisons and verifications are made with finite element (FE) analysis. For a central impact after the first separation, band can catch up with the projectile such that a contact-impact state is re-established when m is in the small interval neighbouring m = 1. For a non-central impact, the projectile would be subjected to a combination of translation and rotation due to asymmetric wave propagations. From every certain instant, the projectile is subjected to an additional rotational acceleration (principal moment) with an abrupt or zero initial value in the anti-clockwise or clockwise direction. The swing amplitude of a small-j or a flat projectile is susceptible to significant fluctuations, and vice versa. The band with a rather large off-centre ratio for the impacted zone and a rather short length of the shorter segment would facilitate a larger accumulation of swing amplitude in a single direction soon after the impact. The linearized impact models proposed can be used to well describe the small-deflection responses for the system, based on 1-D wave propagations or the dependence of quasi-static band deflection on time if the impact duration is much longer than the double wave transit time for the band.