Nonlinear dynamic analysis of flexoelectric microplates based on consistent couple stress theory under an external magnetic field

Abstract This study investigates the nonlinear dynamic behavior of rectangular flexoelectric BaTiO₃ microplates subjected to the combined action of a static magnetic field and a harmonic external force. Microscale size-dependent effects are captured using the consistent couple stress theory, combined with von Kármán nonlinear strain-displacement relations and Kirchhoff's plate theory. The governing equations of motion are derived via Hamilton's principle, reduced to a nonlinear ordinary differential equation through the Bubnov-Galerkin scheme, and solved numerically via the fourth-order Runge-Kutta method and analytically via harmonic balance. After a validation study, a parametric analysis examines thickness ratio, magnetic field intensity, flexoelectric coefficient, aspect ratio, and force amplitude. Results show the magnetic field intensity governs the response most strongly: increasing it amplifies vibration amplitude and triggers saddle-node bifurcations and jump phenomena beyond a critical intensity, while substantially lowering the resonance frequency. The flexoelectric coefficient instead acts as a stiffening mechanism, suppressing nonlinearity and raising the resonance frequency; its effect on amplitude depends on excitation level, enhancing the response under small loading but attenuating it under large excitation force. These findings identify the magnetic field and flexoelectric coupling as the two dominant factors governing the nonlinear dynamic stability of ferroelectric microplates, offering guidance for designing magnetically and electromechanically tunable microscale devices.