000004545 001__ 4545
000004545 005__ 20141118192705.0
000004545 0177_ $$2doi$$a10.3850/978-981-07-2219-7_P276

000004545 0247_ $$210.3850/978-981-07-2219-7_P276
$$adoi
000004545 04107 $$aeng
000004545 046__ $$k2012-05-23
000004545 100__ $$aChen, Jianbing
000004545 24500 $$aNonlinear Response Analysis of Structures Subjected to Random Ground Motions

000004545 24630 $$n5.$$pProceedings of the 5th Asian-Pacific Symposium on Structural Reliability and its Applications
000004545 260__ $$bResearch Publishing, No:83 Genting Lane, #08-01, Genting Building, 349568 SINGAPORE
000004545 506__ $$arestricted
000004545 520__ $$2eng$$aThe explicit expression of random ground motion is incorporated into the probability density evolution method to implement stochastic seismic analysis. Recently, two kinds of stochastic harmonic function (SHF) representations of stochastic processes have been proposed. For instance, the first kind (SHF-I) representation of the ground motion acceleration takes the form
 X<sub>g</sub>(t)=∑<sup>N</sup><sub>i=1</sub>A(Ω<sub>i</sub>)cos(Ω<sub>i</sub>t+∅<sub>i</sub>)
 where <font face="symbol">WΩ</font><sub>i</sub>'s are independent random frequencies, of which the probability densities are consistent with the target PSD function in the sub-interval, ∅<sub>i</sub>'s are mutually independent random variables uniformly distributed over [0, 2π] (Chen & Li, 2011).
 Inserting Eq.(1) into the equation of motion of a nonlinear MDOF structure subjected to random ground motion yields
 MŸ+CY+f(Y)=-MIX<sub>g</sub>(Θ,t) 
 Thus, based on the probability density evolution method the following generalized density evolution equation could be obtained 
 ∂p<sub>zΘ</sub>(z,θ,t)/∂t+∑<sup>m</sup><sub>j=1</sub>Ż<sub>j</sub>(θ,t)∂p<sub>zΘ</sub>(z,θ,t)/∂z<sub>j</sub>=0 
 where p<sub>zΘ</sub>(z,θ,t) is the joint PDF of the augmented state (Z,Θ) and Z(t) is the the physical quantities of interest, e.g. displacements, stresses, and internal forces, etc (Li & Chen, 2008; 2009).
 Then a 9-story shear frame exhibiting strong nonlinearity under random ground motion is studied to illustrate the methodology. The Clough-Penzein spectrum is adopted as the target power spectrum density, which could be reproduced by SHFs exactly (Figure 1). The results validate that the proposed method could achieve tradeoffs between accuracy and computation efforts (Figures 2 and 3).

000004545 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000004545 653__ $$aStochastic harmonic function, Probability density evolution method, Nonlinear structure.

000004545 7112_ $$a5th Asian-Pacific Symposium on Structural Reliability and its Applications$$cSingapore (SG)$$d2012-05-23 / 2012-05-25$$gAPSSRA2012
000004545 720__ $$aChen, Jianbing$$iXu, Jun$$iLi, Jie
000004545 8560_ $$ffischerc@itam.cas.cz
000004545 8564_ $$s373322$$uhttps://invenio.itam.cas.cz/record/4545/files/P276.pdf$$yOriginal version of the author's contribution as presented on CD, .
000004545 962__ $$r4180
000004545 980__ $$aPAPER