Dynamic modelling and analysis of a biological circular membrane

Abstract

This paper presents the nonlinear dynamics of a biological circular membrane subjected to an electrically-induced mechanical loading condition. A continuum mechanics-based analytical model is developed to predict the dynamic response of the membrane for an applied electro-mechanical load. A crucial bi-stability feature is studied using the snap-through instability. The effect of bi-stability on the dynamics of a particular membrane system is characterised. The free and forced vibrations, including chaos for the critical conditions, are illustrated using the Poincaré map and Lyapunov stability criteria. Parametric studies are subsequently performed for varying sinusoidal voltages to determine the membrane multi-frequency resonance activity and stability parameters. As a result, the perturbation of the membrane exhibits two natural frequencies. Also, the system response transits from a soft duffing oscillator to a hard duffing oscillator with increased perturbation energy. The parametric study is also extended to varying sinusoidal pressure.