Equivalent force modeling of macro fiber composite actuators integrated into non-homogeneous composite plates for dynamic applications

Smart structures with integrated macro fiber composite (MFC) piezoelectric transducers have been increasingly investigated in engineering. A simple but elaborate system model of such smart structure not only can predict system dynamics, but also can reduce challenges in application. Therefore, the equivalent force (EF) modeling approach is presented to model the plate-type structures with integrated piezoelectric actuators in a semi-analytical fashion: analytical EF is applied to finite element (FE) structural models. The EF is derived from the bending effort balance between the equivalent loads, and the equivalent loads are developed by introducing the spatial distribution into a generalized Hamilton's principle. The proposed approach is validated by cantilever aluminum beams with integrated MFC actuators and it is consistent with existing alternative approaches from literature. Then, it is validated on a non-homogeneous composite plate for dynamic applications: a laminated composite plate with integrated MFC actuators was manufactured and both an impact test and MFC drive test were elaborately carried out. The modal validation shows the high fidelity of the EF model and the predicted velocity frequency responds functions (FRFs) agree well with experimental measurement. Being applicable to both numerical and analytical modeling approaches, the EF is actually assigned to the out-plane displacement on the structure and distributed along the edges of the actuators. Therefore, it is convenient to use in EF models. The rotational degrees of freedom could also be eliminated in the EF models without losing structure complexity, since they neither link to the electromechanical coupling nor have a significant kinetic contribution to the system. (paper)