Energy distributions in actively and passively controlled nonlinear structures

In this study, the energy distributions of actively or passively controlled multistory nonlinear shear structures are investigated. Nonlinear differential equations of motion of the structure and the energy equations are derived for an uncontrolled and a controlled structure. A computer program which takes into account the nonlinearity of the material is developed and used for the dynamic analysis of the controlled and the uncontrolled structure. As numerical examples, two different structures are examined with six different control cases. These structures are a three-story and a twelve-story shear structure. In the dynamic analysis, the Erzincan and El Centro earthquakes are used. Active and passive controls are obtained by implementing base isolation and a mass damper into the structure. In addition, a hybrid structural control case is examined by implementing base isolation with an active mass damper to the structure. In total, six different passive and active control cases are investigated. An instantaneous optimal control algorithm, which minimizes the performance index defined as a time-dependent quadratic scalar functional instead of a quadratic integral functional and takes into account only the current state, is used as an active control algorithm. The results are given as force-displacement, acceleration, and energies in a comparative way for uncontrolled and controlled structures. The results show that the responses of the structure are reduced and the structural behavior is improved by using structural control.