Effects of linear and nonlinear dashpots forces on the dynamics of plants vibrating in a vegetation cover situation

Abstract

This paper considers the nonlinear dynamics of the oscillations of an individual plant forced by the fluctuating aerodynamic drag and significantly influenced by collisions with its close neighbors. In this study, a row of identical and flexible oscillators is considered. The flexible beams theory is used to model the equation of motion of an individual plant and then plant collisions were modelled as a simple spring, linear dashpot and nonlinear dashpot interactions between adjacent plants. The multiple scales method is used to obtain the amplitude of the plant relative to wind forcing in the resonant and nonresonant oscillations cases. Numerically, chaotic oscillations, hysteresis and coexistence of attractors have been found using the bifurcation diagram, the Lyapunov exponents and the phase portraits. The influences of both type of dashpot collisions on the dynamics behaviors of the plant have been analyzed.