Stretch-dependent electromagnetic properties of circular membrane: A dynamic analysis

Electromagnetic Active (EMA) membranes are advanced materials that combine electromagnetic properties with active functionalities, creating flexible and responsive surfaces. Dynamic analysis plays a vital role in understanding their behavior under fluctuating electromagnetic fields and mechanical loads, ensuring optimal performance, stability, and adaptability in practical applications. A key determinant of EMA membrane performance is their electrical and magnetic breakdown strength, which dictates the maximum electric and magnetic fields the membrane can endure before failure. Building on these ongoing advancements, this work presents a novel analytical framework for investigating the nonlinear dynamics of electromagneto-active circular membranes, incorporating stretch-dependent variations in permittivity and permeability. Using a continuum physics-based Gent model, the study provides key insights into the influence of electro-magneto-mechanical loading on stability, resonance, and energy dynamics, advancing the design of smart membranes for diverse applications. The acquired results provide important initial insights into how the nonlinear behavior of the membrane is affected by both DC and AC dynamic actuation modes. There is variation in equilibrium stretch and natural frequency for different models (constant, linear, and nonlinear) of permittivity and permeability. Notably, we find that with an increase in pre-stress and strain stiffening parameter, there is an increase in the amplitude and energy of the system for considered stretch-dependent nonlinear models of permittivity and permeability. In addition, the stability, periodicity, beating phenomena, and resonant behavior of the actuator are assessed using phase diagrams, Poincaré maps, and time–history response. These findings are crucial for enhancing the performance and design of smart membranes, unlocking new possibilities for a wide range of applications.