Structural dynamics and resonance in plants with nonlinear stiffness.

Area of Science:

• Biomechanics
• Structural Dynamics
• Plant Physiology

Background:

• Most biomaterial studies focus on linear elasticity, neglecting significant nonlinear stiffness in plants.
• Plants like trees and crops are vulnerable to uprooting or snapping due to resonance with environmental forces such as wind and waves.
• Resonance amplifies plant stem and root system deflections and stresses.

Purpose of the Study:

• To investigate the impact of hardening and softening nonlinear stiffness on plant stem structural dynamics.
• To model plant stems as forced Duffing oscillators to analyze nonlinear effects on resonant behavior.
• To compare the resonant behavior of nonlinear plant models with traditional linear models.

Main Methods:

• Modeled plant stems as forced Duffing oscillators incorporating softening and hardening nonlinearities.
• Numerically calculated maximum deflection amplitudes for forcing frequencies up to twice the natural frequency.
• Analyzed the influence of parameter values across a biologically relevant range for plants.

Main Results:

• Nonlinear stiffness significantly alters resonant behavior compared to linear models.
• Hardening nonlinearity shifts resonance to higher frequencies with reduced maximum deflection amplitudes.
• Softening nonlinearity shifts resonance to lower frequencies with increased maximum deflection amplitudes.

Conclusions:

• Nonlinear stiffness in plant stems can be either beneficial or detrimental to stability, depending on environmental conditions.
• The findings highlight the importance of considering nonlinearities for accurate plant biomechanical and structural dynamic predictions.
• Damping significantly reduces deflection amplitudes and mitigates the effects of nonlinear stiffness in plant stems.