Continuous Wavelet and Fourier Transform Methods for the Evaluation of the Properties of Critical Excitation

A designer needs to design a structure with the aim of obtaining the maximum possible load expected for the structure during its lifetime. In this paper, with regards to the information obtained from the earthquakes, the critical earthquakes were computed for a shear frame building, equipped with a belt truss system and subjected to two constraint scenarios. For this purpose, a nonlinear optimization problem has been solved, in which the objective function was the maximization of the roof displacement. In the first constraint scenario, the computed critical earthquake was known as the first state critical earthquake. In addition, for the second constraint scenario, the earthquake was named as the second state critical earthquake. In the first scenario, the energy and peak ground acceleration was considered as the constraints, while in the second scenario, the upper bound Fourier spectrum was added to these constraints. Finally, properties of the initial and critical earthquakes were investigated using the Fourier analysis method and continuous wavelet transform. The numerical results showed that the Fourier spectrum of the first critical earthquake was 6.86 times higher than the maximum values for the same parameter for other earthquakes at a frequency near the first natural frequency of the structure. Also, using time-frequency curve, it was shown that duration of the strong ground motion of all earthquake places within the dominant duration of the frequencies of the same earthquake was more than 10 sec.