共查询到18条相似文献,搜索用时 171 毫秒
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用广义谐和函数导出了含分数导数型阻尼的Duffing振子在谐和与宽带噪声联合作用下的随机平均方程,然后用有限差分法求解了平均FPK方程得到系统的随机稳态响应,研究了分数阶数对随机跳跃分岔影响。最后,通过与原方程MonteCarlo数字模拟结果的比较,验证了所得结果的正确性。 相似文献
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拟可积哈密顿系统中噪声诱发的混沌运动 总被引:4,自引:0,他引:4
研究拟可积哈密顿系统在谐和与噪声激励联合作用下的混沌运动。通过对噪声性质的假定,并利用动力系统理论,给出了高维梅尔尼科夫方法应用于随机拟可积哈密顿系统的推广形式。根据这种推广的方法,研究了谐和与高斯白噪声激励联合使用下两自由度拟可积哈密顿系统 同宿分岔,得出了系统发生混沌运动的参数阈值,并由此讨论了噪声对系统的混沌运动的影响。蒙特-卡罗方法模拟、李雅普诺夫指数等数值结果表明,这种推广的方法是有效的。 相似文献
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研究了单自由度非线性单边碰撞系统在窄带随机噪声激励下的次共振响应问题。用Zhuravlev变换将碰撞系统转化为速度连续的非碰撞系统,然后用随机平均法得到了关于慢变量的随机微分方程。在没有随机扰动情形,得到了系统响应幅值满足的代数方程;在有随机扰动的情形下,给出了系统响应稳态矩计算的迭代公式。讨论了系统阻尼项、非线性项、随机扰动项和碰撞恢复系数等参数对于系统响应的影响。理论计算和数值模拟表明,系统响应幅值将在激励频率接近于次共振频率时达到最大。而当激励频率逐渐偏离次共振频率时,系统响应迅速衰减。 相似文献
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提出了一种基于拟不可积Hamilton系统随机平均法和随机动态规划原理的控制策略,它可以对受高斯白噪声激励的拟不可积Hamilton系统进行非线性随机最优控制,以使系统的响应最小化,利用拟不可积Hamilton系统随机平均法可以将受控的拟不可积Hamilton系统降维成一维的It随机微分方程,利用随机动态规划原理可以为系统响应最小化问题建立动态规划方程,在控制力为有界的条件下,从动态规划方程中可以确定出最优控制规律,受控系统的响应是通过求解与It6随机微分方程相联系的FPK方程得到的,用一个例子阐述了这一随机最优控制策略的实施过程。 相似文献
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本文研究一类阻尼为线性,弹性恢复力为非线性的振动系统在随机外部激励作用下的随机分叉。文中采用广义稳态势和方法,求解系统响应的稳态联合概率密度函数。在此基础上根据由不变测度定义的随机分叉,讨论了具有权式分叉的确定性非线性系统在随机扰动下分叉行为。 相似文献
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IntroductionForlinearviscoelasticsystemsunderbothadditiveandmultiplicativebroad_bandexcitationexcitations,Ariaratnam[1]studiedthestochasticstabilityofthesystembyusingthemethodofstochasticaveragingprocedure .Itwasshownthatthevisco_elasticforcecontributedtowarddamping ,hence ,stabilityofthesystem .However,thestiffnesseffectofthevisco_elasticcomponentwasnotfullyaccountedfor.FurthermoreAriaratnam[2 ]studiedthestochasticstabilityofthesystembutthemodelislinear.Inthetheoryofnonlinearrandomvibration… 相似文献
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IntroductionThestudyoftheresponseofnonlinearsystemstonarrow_bandrandomexcitationofconsiderableimportance.Forexample ,theexcitationofsecondarysystemwouldbeanarrow_bandrandomprocessiftheprimarysystemcouldbemodeledasasingle_degree_of_freedomsystemwithlightdampingsubjecttowide_bandexcitation .Inthetheoryofnonlinearrandomvibration ,mostresultsobtainedsofarareattributedtotheresponseofnonlinearoscillatorstowide_bandrandomexcitation .Incomparison ,resultsontheeffectofnarrow_bandexcitationonnonlinearos… 相似文献
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在随机振动的研究中,研究较多的是系统在宽带噪声作用下的响应问题,对于非线性系统特别是多自由度非线性系统在窄带随机噪声作用下的响应问题则研究较少。本文研究了三自由度非线性系统在窄带随机噪声激励下的主共振响应和稳定性问题。用多尺度法分离了系统的快变项,给出了系统响应的振幅和相位角满足的方程。用摄动法讨论了系统随机项对系统响应的影响。当随机扰动较小时,在一定的参数范围内,对应于不同的初值,系统具有两个均方响应值,随机饱和现象也存在。当随机扰动增大时,系统可从一个大的响应突跳为一个小的响应,或从一个小的响应突跳为一个大的响应,即存在随机跳跃现象。数值模拟表明本文提出的方法是有效的。 相似文献
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The principal resonance of a 3-DOF nonlinear system to narrow-band random external excitations is investigated. The method of multiple scales is used to derive the equations for modulation of amplitude and phase. The behavior, stability and bifurcation of steady-state responses are studied by means of qualitative analysis. The effects of damping, detuning, and excitation intensity on responses are analyzed. The theoretical analyses are verified by numerical results. Both theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may change from a limit cycle to a diffused limit cycle. Under some conditions, co-existence of two kinds of stable steady-state solutions, saturation and jump phenomena may occur. The stationary probability density function of responses for the co-existence case is obtained approximately. 相似文献
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The resonant resonance response of a single-degree-of-freedom non-linear vibro-impact oscillator, with cubic non-linearity items, to combined deterministic harmonic and random excitations is investigated. The method of multiple scales is used to derive the equations of modulation of amplitude and phase. The effects of damping, detuning, and intensity of random excitations are analyzed by means of perturbation and stochastic averaging method. The theoretical analyses verified by numerical simulations show that when the intensity of the random excitation increases, the non-trivial steady-state solution may change from a limit cycle to a diffused limit cycle. Under certain conditions, impact system may have two steady-state responses. One is a non-impact response, and the other is either an impact one or a non-impact one. 相似文献
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Rong HaiWu Xu WeiWang Xiangdon Meng GuangFang Tong 《International Journal of Non》2002,37(6):1017-1028
The principal resonance of two-degree-of-freedom non-linear system to narrow-band random external excitation is investigated. The method of multiple scales is used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response are studied by means of qualitative analysis. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that when the intensity of the random excitation increases, the nontrivial steady state solution may be changed from a limit cycle to a diffused limit cycle. Under some conditions the system may have two steady state solutions, saturation and jumps may exist. 相似文献