Abstract: The development of modern industry inspires higher requirements for material properties and structural dimensions. The design of electromechanical devices is increasingly biased towards miniaturization, high frequency and intelligence. The most recent studies demonstrate that composite materials with magnetoelectric coupling can not only achieve mutual conversion of magnetic, mechanical, and electrical energy with high magnetoelectric conversion efficiencies, but can also avoid direct contact between the structure and the mechanical driving source to achieve non-contact control, which is crucial for the creation of multifunctional micro and nanoscale devices. Based on the multi-physics structural analysis framework developed by Mindlin, this paper studies the dynamic electromechanical coupling response of a sandwich plate composed of a flexoelectric dielectric layer and two symmetric piezomagnetic layers induced by external transverse magnetic fields. The macroscopic piezomagnetic and curvature-induced flexoelectric theories are employed and the classical electromechanical coupling theory is extended to centrosymmetric materials. The dynamic numerical examples of the sandwich plate driven by a sinusoidal global magnetic field and a uniformly distributed local magnetic field show that the magnitudes of displacement and potential are frequency dependent. When the excitation frequency reaches the natural frequency, the amplitude reaches the maximum. In addition, the distribution of symmetrical piezomagnetic layer tends to improve the electromechanical coupling performance of multilayer composite plates. Both the theoretical model and numerical results provide new ideas for the optimization design of magnetic-controlled electromechanical devices.