Critical load, dynamic characteristics and parametric instability of electrorheological material-based adaptive beams

This study derives formulae for the critical load, natural frequency, and loss factor of a simply supported adaptive beam with embedded electrorheological fluid. The parametric instability and dynamic response of the beam subjected to a periodic axial force are investigated. The theoretical model is developed from DiTaranto sandwich beam theory and extended to a transverse vibration model. Galerkin’s method is applied to simplify the governing equation of motion to the form of Mathieu equation. The incremental harmonic balance (IHB) method is employed to determine the parametric instability of the electrorheological material-based adaptive beams. The fourth-order Runge–Kutta method is used to analyze the dynamic response of the adaptive beams. The effects of electric field, core thickness ratio, and length of beam on the critical load, natural frequencies, loss factor, and parametric instability are investigated. The influence of the static load parameter factor on the parametric instability is also addressed.