振动与冲击
振動與遲擊
진동여충격
Journal of Vibration and Shock
2015年
19期
49-56
,共8页
随机平均法%奇异边界%随机P分叉图%随机极限环图
隨機平均法%奇異邊界%隨機P分扠圖%隨機極限環圖
수궤평균법%기이변계%수궤P분차도%수궤겁한배도
stochastic averaging method%singular boundary%stochastic P-bifurcation diagram%stochastic limit cycle diagram
在非线性悬挂轮对系统中加入了 Gauss 白噪声参激，通过 Hamilton 系统理论和随机微分方程理论，将系统转化为拟不可积 Hamilton 系统伊藤随机微分方程组，根据拟不可积 Hamilton 系统的随机平均法，把该方程组降维为一维扩散的平均伊藤随机微分方程，使原系统的解依概率收敛到一维伊藤扩散过程。通过分析一维扩散奇异边界的性态得到了随机全局稳定性的条件。最后对系统的 D 分叉和 P 分叉行为进行了研究，并画出了随机 P 分叉图和随机极限环图。结果表明，随机项的作用使系统的临界速度发生漂移，随着噪声项强度增大，临界速度显著降低。P 分叉后系统表现为最大可能意义上的随机极限环振荡，而 D 分叉后统表现为概率1意义下不稳定的非极限环随机振荡。
在非線性懸掛輪對繫統中加入瞭 Gauss 白譟聲參激，通過 Hamilton 繫統理論和隨機微分方程理論，將繫統轉化為擬不可積 Hamilton 繫統伊籐隨機微分方程組，根據擬不可積 Hamilton 繫統的隨機平均法，把該方程組降維為一維擴散的平均伊籐隨機微分方程，使原繫統的解依概率收斂到一維伊籐擴散過程。通過分析一維擴散奇異邊界的性態得到瞭隨機全跼穩定性的條件。最後對繫統的 D 分扠和 P 分扠行為進行瞭研究，併畫齣瞭隨機 P 分扠圖和隨機極限環圖。結果錶明，隨機項的作用使繫統的臨界速度髮生漂移，隨著譟聲項彊度增大，臨界速度顯著降低。P 分扠後繫統錶現為最大可能意義上的隨機極限環振盪，而 D 分扠後統錶現為概率1意義下不穩定的非極限環隨機振盪。
재비선성현괘륜대계통중가입료 Gauss 백조성삼격，통과 Hamilton 계통이론화수궤미분방정이론，장계통전화위의불가적 Hamilton 계통이등수궤미분방정조，근거의불가적 Hamilton 계통적수궤평균법，파해방정조강유위일유확산적평균이등수궤미분방정，사원계통적해의개솔수렴도일유이등확산과정。통과분석일유확산기이변계적성태득도료수궤전국은정성적조건。최후대계통적 D 분차화 P 분차행위진행료연구，병화출료수궤 P 분차도화수궤겁한배도。결과표명，수궤항적작용사계통적림계속도발생표이，수착조성항강도증대，림계속도현저강저。P 분차후계통표현위최대가능의의상적수궤겁한배진탕，이 D 분차후통표현위개솔1의의하불은정적비겁한배수궤진탕。
Here,Gauss-White-noise parametric random excitation was input in a nonlinear suspended wheelset system. According to Hamilton system and the stochastic differential equation theory,the system could be expressed as a quasi-non-integrable Hamiltonian system in form of Ito stochastic differential equation.The equation was reduced to one dimensional diffusion Ito average stochastic differential equations with the stochastic averaging method.So,the solution to the original system converged in probability an one-dimensional Ito diffusion process.The global stochastic stability conditions were obtained by analyzing the modality of the singular boundary of the one-dimensional diffusion.At last,the stochastic P-bifurcation and D-bifurcation behaviors of the system were studied.The stochastic P-bifurcation diagram and the stochastic limit cycle one were plotted.The results showed that the random excitation can drift forward the system critical speed and the system critical speed significantly decreases when the intensity of random excitation increases;the P-bifurcation leads to the most possible limit cycle of the system,while the D-bifurcation leads to an unstable non-limit cycle of the system in the sense of probability 1.
