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


   The effects of the Gaussian white noiseexcitation on structural safety due to erosion of safe basin inDuffing oscillator with double potential wells are studied inthe present paper.By employing the well-developed stochas-tic Melnikov condition and Monte-Carlo method,variouseroded basins are simulated in deterministic and stochasticcases of the system,and the ratio of safe initial points(RSIP)is presented in some given limited domain defined by thesystem s Hamiltonian for various parameters or first-passagetimes.It is shown that structural safety control becomes moredifficult when the noise excitation is imposed on the system,and the fractal basin boundary may also appear when thesystem is excited by Gaussian white noise only.From theRSIP results in given limited domain,sudden discontinu-ous descents in RSIP curves may occur when the system isexcited by harmonic or stochastic forces,which are differ-ent from the customary continuous ones in view of the first-passage problems.In addition,it is interesting to find thatRSIP values can even increase with increasing driving ampli-tude of the external harmonic excitation when the Gaussianwhite noise is also present in the system.……