An inverse method for characterization of dynamic response of 2D structures under stochastic conditions

The reliable estimation of the wavenumber space(k-space)of the plates remains a longterm concern for acoustic modeling and structural dynamic behavior characterization.Most current analyses of wavenumber identification methods are based on the deterministic hypothesis.To this end,an inverse method is proposed for identifying wave propagation characteristics of twodimensional structures under stochastic conditions,such as wavenumber space,dispersion curves,and band gaps.The proposed method is developed based on an algebraic identification scheme in the polar coordinate system framework,thus named Algebraic K-Space Identification(AKSI)technique.Additionally,a model order estimation strategy and a wavenumber filter are proposed to ensure that AKSI is successfully applied.The main benefit of AKSI is that it is a reliable and fast method under four stochastic conditions:(A)High level of signal noise;(B)Small perturbation caused by uncertainties in measurement points’coordinates;(C)Non-periodic sampling;(D)Unknown structural periodicity.To validate the proposed method,we numerically benchmark AKSI and three other inverse methods to extract dispersion curves on three plates under stochastic conditions.One experiment is then performed on an isotropic steel plate.These investigations demonstrate that AKSI is a good in-situ k-space estimator under stochastic conditions.

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

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.

BSDEs with stochastic Lipschitz condition:A general result

We prove a general existence and uniqueness result of solutions for a backward stochastic differential equation(BSDE)with a stochastic Lipschitz condition.We also establish a continuous dependence property and a comparison theorem for solutions to this type of BSDEs,thus strengthening existing results.

SMALLEST g-SUPERSOLUTION WITH CONSTRAINT

In this paper the existence and uniqueness of the smallest g-supersolution for BSDE is discussed in the case without Lipschitz condition imposing on both constraint function and drift coefficient in the different method from the one with Lipschitz condition.Then by considering (ξ,g) as a parameter of BSDE,and ( ξ α,g α) as a class of parameters for BSDE,where α belongs to a set A,for every α ∈A there exists a pair of solution { Y α,Z α } for the BSDE,the properties of sup α ∈A{ Y α } which is also a solution for some BSDE is studied.This result may be used to discuss optimal problems with recursive utility.

SOME MULTIVARIATE DMRL AND NBUE DEFINITIONS BASED ON CONDITIONAL STOCHASTIC ORDER

Two classes of multivariate DMRL distributions and a class of multivariate NBUE distributions are introduced in this paper by using conditional stochastic order.That is, a random vector belongs to a multivariate DMRL class of life distributions if its residual life(defined as a conditional random vector)is decreasing in time under convex or linear order.Some conservation properties of these classes are studied.

STOCHASTIC LAYER OF DUFFING'S EQUATION NEAR ITS SUBHARMONIC RESONANT ORBIT

In this Paper,the stochastic layer of Duffing's equation hosed on the chosen resonance is investigated.A general method is provided for studying the stochastic layer near the assigned resonant orbit. Several approximate critical conditions are given for the theoretical predictions of that stochastic layer. For non-dissipative Duffing's equation, two critical conditions are obtained when its global stochastic layer occurs and vanishes for the given resonance. In addition, a limit critical condition has been presented when all Possible resonances exist risible in the stochastic layer.Our results are compared with the critical conditions resulting from both Chirikov overlap method and renormalization techniques. Finally, using the cirtical conditions, numerical simulations are Performed to check our theoretical predictions of the stochastic layer based on the given resonance.