| Joint probability density function of the stochastic responses of nonlinear structures |
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| 作者姓名： | 陈建兵 李杰 |
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| 作者单位： | School of Civil Engineering, Tongji University, No. 1239 Siping Road, Shanghai 200092, China |
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| 摘 要： | The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.
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| 关 键 词： | 非线性结构 随机响应 联合概率密度函数 随机振动理论 有限差分法 |
| 文章编号： | 1671-3664（2007）01-0035-13 |
| 收稿时间： | 2006-12-10 |
| 修稿时间： | 2007-02-16 |
Joint probability density function of the stochastic responses of nonlinear structures |
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| Chen?Jianbing,Li?Jie.Joint probability density function of the stochastic responses of nonlinear structures[J].Earthquake Engineering and Engineering Vibration,2007,6(1):35-47. |
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| Authors: | Chen Jianbing Li Jie |
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| Institution: | School of Civil Engineering, Tongji University, No. 1239 Siping Road, Shanghai 200092, China |
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| Abstract: | The joint probability density function (PDF) of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established.The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined.A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a frame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation. |
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| Keywords: | stochastic response nonlinearity joint probability density function probability density evolution method number theoretical method finite difference method |
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