An analytical model for the propagation of bending waves on a plant stem due to vibration of an attached insect Dedicated to Ellen Cocroft

A mathematical model is presented to examine the propagation of bending waves on a plant stem that are induced by vibratory excitation from an attached insect. This idealized model represents the insect body as a mass and the legs as a linear spring along with a general time-varying force that is assumed to act in parallel with the spring. The spring connects the mass to a stem modeled as a beam having uniform geometric and material properties. The linearly elastic beam is assumed to undergo pure vibratory bending and to be infinitely long in each direction. The equations that govern the insect-induced, coupled motions of both the beam and the mass are solved for arbitrary time varying forces produced by the insect's legs. Solutions for the frequency response indicate that the response is dominated by frequency components near the natural resonant frequency of the attached insect while at higher frequencies the amplitude of the response is strongly influenced only by the properties of the stem.