Investigation of seismic wave reaction of spatial structure
The stochastic behavior of the spatial structure under seismic action was studied on the basis of theories and methods of nonlinear mechanics, finite elements, traveling wave and wavelet analysis. The spatial concrete structure in the form of a square plate, which rests on four columns rigidly fixed in the foundation was presented. A probabilistic simulation of acceleration of seismic action with different magnitudes using the statistical method of Ruiz and Penzien was performed. The effect of horizontal seismic displacement in the soil on the design was taken into account with the help of simulation of a transverse bending traveling wave in the form of an initial imperfection of the four columns of the structure. Mathematical models of non-stationary stochastic vibrations structure in the form of a system of second-order differential equations in generalized coordinates were formed on the basis of the Dahlberger-Lagrange method. The influence of the traveling waves and surface pressure on the static characteristics structure was estimated. The nonlinear static problem by the Newton-Ruffson method and the stability problem by Lanczos method were solved. A modal analysis of the spatial structure without and with traveling waves and surface pressure by the Lanczos method was carried. Realizations of dynamic characteristics of the structure: acceleration, velocity and displacement were obtained by the direct method of numerical integration of Runge-Kutta of the fourth order. The wavelet analysis of the seismic acceleration and structure reactions to the seismic action of different magnitudes was performed using discrete orthogonal (Dobesh4) and continuous nonorthogonal (Morle) one-dimensional complex wavelet functions. Wavelet-spectrograms and Fourier-images of the seismic acceleration and of the structure reactions were presented. The expediency of accounting for the flexural traveling waves in a spatial structure in the study of its seismic behavior was estimated.
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