Linear and nonlinear computation of the crack of a whip

Abstract

This article deals with two different finite element computations of the crack of a whip. The first model is based on linear wave equation of a taut string in a uniformly rotating coordinate system, using two nodes elements. The string preload is constant over time, but the centrifugal force along the whip gradually decreases toward the free tip according to the circumferential velocity. The starting point of the whip is excited by a sinusoidal half-wave displacement. The second nonlinear model describes the whip with truss elements capable of large displacements in the plane. The whip is excited by specifying its initial velocity and moving its starting point along a given line. A realistic fan-shaped image of the whip positions can be produced. Both models are suitable for modeling supersonic speeds of the whip tip, i.e. a whip crack.