Energy-based evaluation of seismic response of structures with passive and active systems

In recent years, increased performance requirements and the strong desire for better utilization of new materials and lower costs have motivated the development of new concepts for protecting structures. Recent practical applications and research findings show that the passive and active control techniques have the potential of protecting civil engineering structures from severe earthquakes and strong winds. In this paper, application potentials of passive and active control systems to earthquake excited structures are investigated in terms of energy distribution in the structure. Dynamic behavior of a three storey shear frame structure, incorporating passive and active control systems, subjected to El Centro, Erzincan and the simulated ground motions is investigated. The well-known Kanai-Tajimi power spectral density function is used to generate the simulated ground motion. Instantaneous optimal control algorithm which minimizes a 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. A computer program which takes into account the nonlinear material property is developed for the dynamic analysis of the controlled and the uncontrolled structure. Nonlinear differential equation of the motion is solved by Wilson-θ numerical method. The numerical simulation results are presented in a comparative way for uncontrolled, passively controlled, actively controlled structures by graphical representations with hysteretic curves and the distributions of the damping energy, total kinetic energy, strain energy and seismic energy. An energy based evaluation of the example structure incorporating different combinations of passive and active systems is made.