Issue 29

W. Guodong, Frattura ed Integrità Strutturale, 29 (2014) 376-384; DOI: 10.3221/IGF-ESIS.29.33 380 Computational Analysis In order to verify the validity of pseudo excitation method directly solved with absolute displacement ， this paper is to linearize system through applying statistical linearization method, then analyze it through applying the random vibration module and harmonious response module in finite element software. Linearization procedure and its solution could refer to literature [8], which has well solved the response problem of nonlinear system with multi-degree of freedom under random excitation through taking full advantage of computer characteristics and combining FAP numerical method. FAP is the numerical method of statistical linearization method, and could compile corresponding computer program code with various algorithmic languages conveniently. This paper has compiled the procedure of FAP algorithm through applying FORTRAN 90, thus to realize the linearization of structure. For the pseudo excitation method directly solved with absolute displacement in this paper, the Full method in harmonic response analysis could be applied. Vibration isolation bearing is constructed through applying combin40 (it is the combination of mutually paralleled spring slider and damper, and cascaded with a clearance controller), its rigidity is k = 6×106N/, the former 150 order mode of vibration is taken during modal analysis, modal participation quality is as high as 97%, by which to guarantee the sufficient accuracy of algorithm. When applying pseudo excitation method directly solved with absolute displacement, mass 21 -big mass unit is added on 4 support nodes of model base, big mass unit is in rigid connection with support node, the mass takes 106 times of main bridges mass, then the constraint of freedom degree along x, y direction is released. According to the method proposed by above theory, every mass block is exerted with fictitious force, then harmonic response analysis is performed, the pseudo-excitation response after taking into account nonlinearity is obtained, and then the power spectral density matrix of absolute displacement is obtained according to type (14). The power spectrum inputted in calculation applies the practical seismic spectrum [10] obtained through GB50011 -2001 modifying response spectrum’s model iteration proposed by literature [3]. The consistent ground motion parameters: Fortification of 7 degree, Ⅲ site, the first group designs earthquake grouping, the wave velocity takes 100m/s, coherence function adopts L － W model, the overall structure adopts Rayleigh damping, four nodes in base are taken out for performing consistent stimulus in three direction (the four nodes in base are: the constraint nodes at left end of bridge, the constraint nodes at right end of bridge as well as the constraint nodes on both sides of the centerline at the base of cable support tower along transverse direction of bridge). Contrastive Analysis Through applying the traditional principle of random vibration solution ， we perform solution through random vibration method, time-history method, spectra analysis respectively. Its projects are the respective effect of displacement, velocity and acceleration on power spectral density, by which to compare absolute displacement method. The Comparison between Absolute Displacement Method and Random Vibration Method The charts in Fig. 3 are to respectively represent that the main span of cable-stayed bridge, the power spectral density of back span are influenced by several factors in the case, where the linear points denote random vibration method, the dashed points denote absolute displacement method. We could see from calculation results that after system linearization, the calculation result of two algorithms is basically consistent, and we find that there is also similar rule between the response power spectral density of other girders and main tower nodes through research, which demonstrates the validity of absolute displacement method. Furthermore, through observation and contrast, we find that the value of displacement, velocity and the density value of acceleration response power spectral obtained through calculating with absolute displacement method are smaller than the value obtained through calculating with random vibration method. We analyze from the area surrounded by curve and the abscissa that the mean square value of seismic random vibration wave obtained through calculation with absolute displacement method is on the smaller side, namely the energy acting on cable- stayed bridge is too small, and it demonstrates that random vibration method is a kind of seismic analysis method, which is conservative in relative speaking. As the frequency range of inputted acceleration power spectrum density is 0.48-15.9 Hz, the figure does not represents the curved section whose frequency range is 0-0.48 Hz .Essentially, the inputted stimuli will make response power spectral density of structure have a sharp increase near the zero frequency. The average power spectral density model would reasonably reduce dynamic low frequency component of earthquake, when f =0, the power spectral density is generally 0 [9]. For displacement and velocity response power spectrum, the value is very small behind f ≥Hz, thus it is not represented in the figure. For acceleration response spectrum, its value represents a certain range of volatility after f ≥Hz, the changing curve is shown as Fig. 3 (c), (f).