Effects of a Non-Sinusoidal Wind on Plants

In this paper, we elaborate a nonlinear theory of plants suggested to both fifth nonlinearities and non-sinusoidal wind effects modeled by the sinus cardinal function known as a good model used to approximate the Dirac function (behavior). By using the plan beam theory and the multiple time scales method, we find that the interactions between plants and wind are governed by the coupled differential system of equations. Through analytical and numerical techniques, we observe in the non-resonance state, that the effects of wind on the plant are worthless while its harmonic oscillations with their corresponding stability boundaries are tackled in the resonance case. Owing to the rang of the control parameters, we also examine periodic, quasi-periodic and chaotic behavior of the system. Our investigations show that judicious choice of some system’s parameters can avoid the plant rupture during violent storms. For applications, numerical simulations carry out with the physical parameters of Pinus Pinastr Ait., corn plant and those of Raphia Vinifera lead to very interesting results showing the wideness applicability of the results established within this paper.