Statistical Study of Complex Eigenvalues in Stochastic Systems

Seifedine Kadry ； Hussam Kassem ； Mohamad Smaili ； Abdo Abou Jaoude

《Research Journal of Applied Sciences, Engineering and Technology》 2卷3期 (2010/05) Pp. 233-238

並列摘要

In this research we analyze the complex modes arising in multiple degree-of-freedom non-proportionally damped discrete linear stochastic systems. The complex eigen values intervene when unstable states like resonances, happened. Linear dynamic systems must generally be expected to exhibit non-proportional damping. Non-proportionally damped linear systems do not possess classical normal modes but possess complex modes. The proposed method is based on the transformation of random variables. The advantage of this method which give us the probability density function of real and imaginary part of the complex eigenvalue for stochastic mechanical system, i.e. a system with random output (Young's modulus, load). The proposed method is illustrated by considering numerical example based on a linear array of damped spring-mass oscillators. It is shown that the approach can predict the probability density function with good accuracy when compared with independent Monte-Carlo simulations.

並列關鍵字

Complex modes ； discrete linear stochastic systems ； non-proportionately damped ； probabilistic transformation method