Studies on structural safety in stochastically excited Duffing oscillator with double potential wells  

作　　者：Chunbiao Gan Shimin He 

机构地区：[1]Institute of Applied Mechanics, SAA, Zhejiang University, Hangzhou 310027, China [2]College of Mechanical and Energy Engineering, Zhejiang University, Hangzhou 310027, China

出　　处：《Acta Mechanica Sinica》2007年第5期577-583,共7页力学学报（英文版）

基　　金：The project supported by the National Natural Science Foundation of China10302025;The project supported by the National Natural Science Foundation of China10672140

摘　　要：The effects of the Gaussian white noise excitation on structural safety due to erosion of safe basin in Duffing oscillator with double potential wells are studied in the present paper. By employing the well-developed stochastic Melnikov condition and Monte-Carlo method, various eroded basins are simulated in deterministic and stochastic cases of the system, and the ratio of safe initial points （RSIP） is presented in some given limited domain defined by the system＇s Hamiltonian for various parameters or first-passage times. It is shown that structural safety control becomes more difficult when the noise excitation is imposed on the system, and the fractal basin boundary may also appear when the system is excited by Gaussian white noise only. From the RSIP results in given limited domain, sudden discontinuous descents in RSIP curves may occur when the system is excited by harmonic or stochastic forces, which are different from the customary continuous ones in view of the firstpassage problems. In addition, it is interesting to find that RSIP values can even increase with increasing driving amplitude of the external harmonic excitation when the Gaussian white noise is also present in the system.The effects of the Gaussian white noise excitation on structural safety due to erosion of safe basin in Duffing oscillator with double potential wells are studied in the present paper. By employing the well-developed stochastic Melnikov condition and Monte-Carlo method, various eroded basins are simulated in deterministic and stochastic cases of the system, and the ratio of safe initial points （RSIP） is presented in some given limited domain defined by the system＇s Hamiltonian for various parameters or first-passage times. It is shown that structural safety control becomes more difficult when the noise excitation is imposed on the system, and the fractal basin boundary may also appear when the system is excited by Gaussian white noise only. From the RSIP results in given limited domain, sudden discontinuous descents in RSIP curves may occur when the system is excited by harmonic or stochastic forces, which are different from the customary continuous ones in view of the firstpassage problems. In addition, it is interesting to find that RSIP values can even increase with increasing driving amplitude of the external harmonic excitation when the Gaussian white noise is also present in the system.

关 键 词：Stochastic Dulling oscillator Basin erosion Structural safety Stochastic Melnikov condition RSIP 

分 类 号：TN752[电子电信—电路与系统]