Supersonic flutter suppression of electrorheological fluid-based adaptive panels resting on elastic foundations using sliding mode control

Abstract

Brief reviews on suppressing panel flutter vibrations by various active control strategies as well as utilization tunable electrorheological fluids (ERFs) for vibration control of structural systems are presented. Active suppression of the supersonic flutter motion of a simply supported sandwich panel with a tunable ERF interlayer, and coupled to an elastic foundation, is subsequently investigated. The structural formulation is based on the classical beam theory along with the Winkler–Pasternak foundation model, the ER fluid core is modeled as a first-order Kelvin–Voigt material, and the quasi-steady first-order supersonic piston theory is employed to describe the aerodynamic loading. Hamilton’s principle is used to derive a set of fully coupled dynamic equations of motion. The generalized Fourier expansions in conjunction with the Galerkin method are then employed to formulate the governing equations in the state space domain. The critical dynamic pressures at which unstable panel oscillations (coalescence of eigenvalues) occur are obtained via the p-method for selected applied electric field strengths (E = 0,2,4 kV mm−1). The classical Runge–Kutta time integration algorithm is subsequently used to calculate the open-loop aeroelastic response of the system in various basic loading configurations (i.e. uniformly distributed blast, gust, sonic boom, and step loads), with or without an interacting soft/stiff elastic foundation. Finally, a sliding mode control synthesis (SMC) involving the first six natural modes of the structural system is set up to actively suppress the closed-loop system response in supersonic flight conditions and under the imposed excitations. Simulation results demonstrate performance, effectiveness, and insensitivity with respect to the spillover of the proposed SMC-based control system. Limiting cases are considered and good agreements with the data available in the literature as well as with the computations made by using the Rayleigh–Ritz approach are obtained.