Chapter Four - Critical Excitation for Acceleration Response

Abstract

This chapter discusses a probabilistic critical excitation method for acceleration responses of nonproportionally damped structural systems to nonstationary inputs. Recently, acceleration responses are considered important from the viewpoint of the protection and maintenance of functionality in buildings. Therefore, it is natural and desirable to develop critical excitation methods for acceleration. In contrast to most of the conventional critical excitation methods, a stochastic acceleration response at a point is treated as the objective function to be maximized. The power and the intensity of the excitations are fixed, and the critical excitation is found under these restrictions. The key to finding the new nonstationary random critical excitation for nonproportionally damped structural systems is the order exchange in the double maximization procedure with respect to time and to the power spectral density (PSD) function. Various numerical examples have been incorporated in this chapter. These examples demonstrate the effectiveness and validity of the present critical excitation method. They also reflect that there exist peculiar time-varying characteristics of the generalized nonstationary transfer function multiplied by the envelope function of the input motion model. It is concluded that the damping installation in upper stories is effective in reducing the acceleration.