Dynamic modelling and analysis of a biological circular membrane
Subrat Kumar Behera, Rashi Aditi Ranjan, Deepak Kumar, Somnath Sarangi, Ranjan Bhattacharyya
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.