Dynamic deflection control of reinforced concrete frame under earthquake load with piezoelectric layer

Piezoelectric materials are a type of smart materials that are of interest to many researchers in various engineering sciences due to their extraordinary properties such as converting mechanical energy into electrical energy and vice versa. In this article, the determination and control of the dynamic deformation of a one-span concrete frame with a piezoelectric layer coating on beams and columns under seismic load is discussed. In order to control the dynamic deformation of the concrete frame, a proportional-derivative controller has been used in such a way that a piezoelectric layer is considered as an actuator and a layer as a sensor. The governing equations for the beam and column components of concrete frame are obtained by using high-order shear theory, calculating energy relations, applying Hamilton's principle and considering the applied voltage on piezoelectric materials. In order to solve the dynamic coupled equations, the numerical method of differential quadrature method has been used and finally, with the help of Newmark method, the dynamic deformation of the concrete frame is calculated. After validating the results, the effect of various parameters such as voltage applied to the piezoelectric layer, piezoelectric type controller, thickness of the piezoelectric layer on dynamic deformation were investigated. Here, the optimal values of controller parameters, including proportionality coefficient and derivative coefficient, were obtained as 3.824 and 5.812, respectively. The results show that the use of the controller leads to a reduction of 72 and 65 percent of the lateral and vertical dynamic deflection of the frame, respectively.