随机介质中的弱阻尼振动
The Weak Damped Oscillation in a Random Medium
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摘要: 本文应用小参数法讨论了形式如(t)+K2(t)x(t)=-εf(,t)的具有随机系数的随机微分方程,其中K(t)是一个随机过程,ε是阻尼系数.它是一个小参数.文章给出了求解的方法,还介绍了求解的统计特性的方法.并对f(,t)=2,K(t)=k0[1+εV(t)]的情形作了具体的计算.Abstract: The paper gives a solution of the random differential equation with random coefficient, that is (t)+K2(t)x(t)=-ef(,t),where K(t) is a random process and e is a damp coefficient, it is a little parameter.
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[1] Karal,F,C,and J.B,Keller,Elastic,electromagnetic and other waves in a random medium,J.Math.Phys.,5(1964),537-547. [2] Chen,K.K.and T,T.Soong,Covariance properties of waves propagating in a random medium,J.Acoust,Soc.Amer.,49(1971),1639-1642. -
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