Wavelet analysis of seismic wave reaction of frame building
The application of new and effective wavelet methods to the analysis of seismic responses of structures is a time-consuming task. The article investigates the effectiveness of a new numerical approach to calculating the seismic response of a multi-storey frame building. The approach is based on the theory and methods of nonlinear mechanics, method of traveling wave and wavelet analysis. Seismic loads are represented as random realizations of accelerations of soil with different magnitudes, obtained by the statistical model of Ruiz and Penzien. Another component of seismic loads is the wave response of the building to horizontal seismic movement of the ground. A mathematical model of non-stationary stochastic oscillations of a building has the form of a system of second-order differential equations in generalized coordinates. The model is constructed with the use of a finite element method. The wave response of the building is represented by transverse bending waves in columns whose amplitude corresponded to the magnitude of the seismic action. The static behavior and stability of the framed building under the action of surface pressure on the floor slabs were investigated in nonlinear formulation by the Newton-Rafson method. The modal analysis of the building was performed using the Lanzos method. The dynamic behavior of the building was investigated using the fourth-order Runge-Kutta method. The wavelet analysis of realizations of seismic impact and seismic reactions of a framed building was performed with the use of discrete orthogonal (Daubechies 4) and continuous non-orthogonal (Morlet) one-dimensional complex wavelet functions. Visualization of the seismic impact and seismic response of the building is presented in the form of wavelet spectrograms and Fourier images. The expediency of taking into account the transverse bending waves in the columns of a multi-storey frame building when studying its seismic behavior is confirmed. This is especially true for frame buildings with many spans because of the dependency of the wave speed in the columns on the number of floor slabs resting on them.
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