Issue 29

W. Guodong, Frattura ed Integrità Strutturale, 29 (2014) 376-384; DOI: 10.3221/IGF-ESIS.29.33 377 power density as the core, and sufficiently considers the probability problem of earthquake occurring. It is very suitable for the building such as bridges, roads etc which have many structural support points with large span, and it could assist the more advanced analysis and be used as design tools. Random vibration method is taken as the design and calculation tool of structural seismic resistance by European structural seismic design code (Eurocode 8) in 1995.The highway bridge seismic design code in China also incorporates random vibration method into the calculating method of aseismic design currently. In recent years, Jia-Hao Lin [1] has proposed simple, convenient and accurate pseudo excitation method starting from computational mechanics; Jiwei Zhang etc[2]have proposed the simple calculation method of response value in structure peak under the non-stationary seismic excitation based on traditional incentive method; Yang Jiang etc [3]have proposed the pseudo-excitation algorithm with high precision which could only be obtained by a small amount of vibration mode, which is the modified absolute displacement method. So far, calculating working amount with pseudo excitation method could solve the response problem of structural linear stochastic earthquake. There is still no in-depth research for analyzing nonlinear seismic buildings. As architectural design has such response requirement to non- linear systematic random earthquake, such research method is urgently needed. Through referring to the solution of FAP numberical value by computer, this paper is to suggest simple and efficient approach of structural nonlinear pseudo excitation method, which could be applied into analyzing displacement, speed, random vibration spectrum of accelerated velocity as well as the influencing situation of axial force, thus we could realize the high accuracy and efficiency in mechanics stimulation method of nonlinear random vibration on the basis of statistical linear theory. S TATISTICAL LINEAR THEORY tatistical linear theory originated from the 1960s, R. Isaacs etc in America and L.S. Pontryagin etc in former Soviet Union had performed the initial study to this [4]. The numerical method applied in nonlinear differential game began taking shape in the 1980s, and it has developed into the method which could deal with random response problems in nonlinear dynamics system so far. For non-linear mechanics with n degree of freedom, it could be expressed with differential mode [5-7]: [ ]{y} [ {y},{y}] {F(t )} M G     (1) where [M] is the matrix of structural mass with n order; [ ({y},{y})] G  is the equivalent matrix of nonlinear restoring force and damping force. The equivalent linear equation of nonlinear system could be established according to this method: e [ ]{ } [ ]{y} [ ]{y} {F(t )} e M y C K      (2) where e e [ ][ ] C K are the equivalent viscous drag coefficient matrix and stiffness matrix respectively, the following could be obtained through direct subtract between (1) type and (2) type: e e [ ] [ ({y},{y})] [ ]{y}-[K ]{y} G C       (3) where ij ij {y} {y(c , k , t )}  the steady-state solution of type (2) is, ij ij c , k is the respective element in e e [ ][ ] C K matrix, statistical linear theory is to reasonably select the ij ij c , k in error matrix [ ]  : [[ ] [ ]] min T E    (4) where E is the mathematical expectation, the solution of type (4) could be obtained through calculation, and the equivalent linear stiffness and viscous damp of nonlinear system is derived. T HE SOLUTION OF PSEUDO - EXCITATION METHOD or stimulation method, we generally establish the equation of motion through the variable generated on the basis of particle’s relative displacement. The equation of motion is established according to d’Alembert principle, the inertia force is added on particle as load to avoid the matrix containing support quality in motion process. For the pseudo-excitation algorithm of multiple-support excitation, we could see from above solving idea that the dynamic S F