Nonlinear dynamics of circular microplates on displacement-dependent porous PDMS foundations for capacitive ultrasonic transducers

Abstract This study develops a comprehensive nonlinear mathematical model for the dynamic behavior of a circular microplate supported by a porous polydimethylsiloxane (PDMS) foundation with displacement-dependent porosity, relevant to capacitive micromachined ultrasonic transducers (CMUTs). The model integrates nonlinear elasticity, effective medium theory to capture dielectric variation, and accounts for the influence of displacement-dependent porosity on the system’s stiffness and electrostatic coupling. Employing dimensionless formulation and energy-based harmonic balance methods, the analysis addresses primary and secondary resonance phenomena and highlights how porous PDMS significantly reduces actuation voltage and enhances vibration amplitude and acoustic pressure compared to conventional air-gap models. Numerical simulations demonstrate the critical role of displacement-dependent porosity in improving CMUT performance, offering an effective mathematical framework for the design and optimization of soft, porous elastomeric foundations in ultrasonic devices.