Statistical Study of Complex Eigenvalues in Stochastic Systems

In this research we analyze the complex modes arising in multiple degree-of-freedom nonproportionally damped discrete linear stochastic systems. The complex eigenvalues 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 show n that the approach can predict the probability density function with good accuracy when compared with independent Monte-Carlo simulations.