Christina Hamlet, University of North Carolina, Chapel Hill


Nonlinear Model for Periodically Forced Deformations in Plant Stems and Trunks


Abstract: Although most biomaterials are characterized by strong stiffness nonlinearities, the majority of studies of plant biomechanics and structural dynamics focus on the linear elastic range of their behavior. In this presentation, the effects of hardening (elastic modulus increases with strain) and softening (elastic modulus decreases with strain) nonlinearities on the structural dynamics of plant stems are investigated. A number of recent studies suggest that trees, crops, and other plants often uproot or snap when they are forced by gusting winds or waves at their natural frequency. This can be attributed to the fact that the deflections of the plant, and hence mechanical stresses along the stem and root system, are greatest during resonance. To better understand the effect of nonlinear stiffness on the resonant behavior of plants, plant stems have been modeled as forced Duffing oscillators with softening or hardening nonlinearities. The results of the mathematical models are compared to experimental measurements of forced oscillations taken from trees and the literature.


Advisors: Laura Miller (University of North Carolina)