AN ANALYTIC METHOD TO ESTIMATE THE RESPONSE SPECTRUM OF THE SYNTHETIC RECORDS WITH EVOLUTIONARY SPECTRUM

According to Priestley (1965), a real-valued stochastic evolutionary process can be defined as in the general form of Fourier-Stieltejes as follows:(...)where A(t,w) is a deterministic complex-valued modulating function and Z(ω) is a random complex-valued function. If the Fourier Transform of A(t,w)exp(iwt ) on w axis is available, Equation 1 expression can be stated in time domain by the means of the convolution integral given that:(...)Waezi and Rofooei (2016, 2017) introduced double frequency model (DFM) for stochastic generation of nonstationary acceleration records. The proposed model is capable of considering two large and one small dominant frequencies for efficient capturing of the recorded strong motion’s power spectrum. A high-pass filtered time-varying double-frequencies model with time-variant parameters is introduced to develop a frequency-wise, non-stationary process. This model can be described by the Equation 3:(...)where h (t,t ) , m(t ) and s (t) represent the impulse response function of the filter, modulating function and the instantaneous standard deviation of the integral in the bracket, respectively: Also, w(t ) and s 2 (t ) are a white noise with power 0 S and the evolutionary variance of the process, respectively. It is shown in this paper that in case of slowly varyingH (t ,w) , which is the evolutionary transfer function of h (t,t ) , one can write:(...)

کلیدواژه ها:

Priestley’s evolutionary process ، Peak factor ، Synthetic ground motion ، Power spectral density