The application of stochastic perturbation method to viscoelastic problems does n't result in the emergence of undesirable secular terms although the viscoelastic constitutive relation is time-dependent 盡管粘彈性本構(gòu)關(guān)系具有時(shí)間相依性,其隨機(jī)攝動(dòng)格式并不存在“長(zhǎng)期項(xiàng)”的影響。
As 4ws system is a typical system with stochastic perturbations, which are from the road surface unevenness and side wind and ca n't be described by deterministic function, the probability and statistics theory must be used in such research 由于汽車四輪轉(zhuǎn)向系統(tǒng)是典型的一個(gè)存在隨機(jī)擾動(dòng)的系統(tǒng),振源主要就是路面的不平度和地面的側(cè)風(fēng),這類擾動(dòng)不能用確定性的時(shí)間或空間函數(shù)去描述,只能用概率統(tǒng)計(jì)的方法去研究。
By virtue of the stochastic bifurcation theory, the transition of the atom movement at a crack tip in fatigue damage system is investigated . using the singular point theory of one-dimensional diffusion process and the stochastic averaging approach of energy envelope, a micro-model to describe the atom movement at the crack tip in homoclinic bifurcation fatigue damage system, which is in the presence of stochastic perturbation, is established . after the study on the characteristic of the diffusion exponent, the drift exponent and the character exponent of the fatigue damage diffusion process on singular boundary, the bifurcation behavior of a homoclinic bifurcation fatigue damage system, which is in the presence of parametric white noise, is examined 采用隨機(jī)分叉理論,探討疲勞損傷系統(tǒng)裂尖粒子運(yùn)動(dòng)性質(zhì)突變.利用一維擴(kuò)散過(guò)程的奇點(diǎn)理論,并結(jié)合能量包絡(luò)的隨機(jī)平均法,建立了隨機(jī)擾動(dòng)的疲勞損傷同宿分叉系統(tǒng)裂尖粒子運(yùn)動(dòng)模型,通過(guò)研究奇異邊界的擴(kuò)散指數(shù)、漂移指數(shù)以及特征指數(shù)特性,考查疲勞損傷裂尖粒子運(yùn)動(dòng)的同宿分叉系統(tǒng)受參激白噪聲影響的分叉行為
Secondly, the response problem of a random structure under evolutionary random excitation is solved by the stochastic perturbation method combined with the unified approach . our derivation is based on the following three indispensable assumptions : 1, the random perturbations must be small fluctuations; 2, the random parameters of the system are mutually independent; 3, the random parameters and the random excitation are mutually independent too 2)將統(tǒng)一解法與隨機(jī)攝動(dòng)法相結(jié)合,推導(dǎo)中采用了三個(gè)不可或缺的假設(shè):(1)隨機(jī)攝動(dòng)是一個(gè)小量;(2)系統(tǒng)各個(gè)隨機(jī)參數(shù)是相互獨(dú)立的;(3)系統(tǒng)的隨機(jī)參數(shù)與所受的隨機(jī)激勵(lì)是統(tǒng)計(jì)獨(dú)立的。
In this method, a new perturbation technique called linearization-correction method was used to linearize the nonlinear equations in the model, and then the wavelet precise integration method was used to calculate the sensitivity of the response . at last the stochastic perturbation method is used to analyse the variance and expectation of sediment concentration, rate and depth of flow . the calculated result was high agreement with that result of monte carlo method 在該方法中,采用了一種擬攝動(dòng)法對(duì)模型中的非線性方程進(jìn)行線性化,然后采用小波配置法對(duì)模型方程進(jìn)行空間離散,最后用隨機(jī)有限元方法求得模型中水流速度,水深和泥沙濃度的統(tǒng)計(jì)特性,計(jì)算結(jié)果和montecarlo法模擬結(jié)果吻合得很好。
It is said that the stochastic perturbation method basically could not fulfil the requirement of dynamical random response problems . however, so far in the dissipative systems, this is not the case . thirdly, the unified approach is combined with the orthogonal polynomial approximation 3)將統(tǒng)一解法,與正交多項(xiàng)式逼近方法結(jié)合起來(lái),指出文獻(xiàn)中流傳的采用正態(tài)pdf來(lái)描述隨機(jī)結(jié)構(gòu)參數(shù)的缺陷,并先后提出了拱形概率密度與更具有一般性的?pdf模型,并分別與chebyshev多項(xiàng)式逼近、gegenbauer多項(xiàng)式逼近相配合,構(gòu)成了一套具有廣泛適應(yīng)性的解法。