Flexoelectric effect is a novel electro-mechanical coupling effect that has drawn a lot of attention in the past few decades. Compared with piezoelectric materials, flexoelectric materials have the inherent characteristics of gradient coupling effect between electric field and elastic field. Since no complex pre-polarization process is required, the flexoelectric materials do not have depolarization or aging problems during the trial period. Similar to piezoelectricity, flexoelectricity exhibits two different effects: direct and converse flexoelectric effect. The direct flexoelectric effect indicates that the strain gradient produces an electrical response, and can be used in sensor design and energy harvesting. The converse flexoelectric effect represents mechanical stress or strain caused by inhomogeneous electric field or polarization gradient, and then as a response, the induced membrane force and the corresponding control moment will occur in the structure. This study will take the mechanic electric coupling characteristics of flexoelectric effect as the core, establish the dynamic equation, deduce the modal response of plate structure under the effect of flexoelectric and obtain the relationship between modal response and electric field gradient. To validate the theoretical method, a finite element model of flexoelectric actuated plate will be established in the commercial software COMSOL Multiphysics. With no existing flexoelectric module, the finite element model of flexoelectric plate will be built based on the original dynamic model. A non-uniform electric field is firstly constructed in COMSOL with the electrostatic module. The influence of different structural parameters on the vibration control effect caused by flexoelectric excitation will be analyzed and optimized, which will provide a theoretical basis for the application of flexoelectric materials in the vibration control of novel smart structures.

In this letter, a simple balanced directional coupler with high common-mode (CM) suppression is designed by using a single-layer substrate-integrated waveguide (SIW). The SIW can be considered a naturally balanced structure.The CM noises are able to be intrinsically suppressed when differentially excited along the symmetric H-plane of SIW. The coupling window with tapered transition is designed for broadening the bandwidth of 3-dB coupling. The microstrip differential feeding structure with inductive vias and inductive matching section enables planar integration and better impedance matching. Finally, a SIW balanced directional coupler operating at 14-16 GHz is designed and fabricated. Measured results are in good agreement with simulated ones.

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