Analysis of multi-degree of freedom strongly non-linear mechanical systems with random input: Part II: equivalent linear system with random matrices and power spectral density matrix

✍ Scribed by S. Bellizzi; R. Bouc

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 464 KB
• Volume: 14
• Category: Article
• ISSN: 0266-8920
• DOI: 10.1016/s0266-8920(98)00010-1

✦ Synopsis

We present a method for estimating the (power spectral density) PSD matrix of the stationary response of lightly damped randomly excited multi-degree of fredom mechanical systems with strong non-linear asymmetrical restoring forces. The PSD matrix is de®ned as the mean value of the PSD matrix response of an equivalent linear system (ELS) whose damping and stiffness matrices depend on non-linear vibration modes of the associated conservative system, the frequencies and modes shapes being amplitude dependent. Based on a generalized van der Pol transformation and using a stochastic averaging principle, as developed in a companion paper, a stationary probability density function for the amplitude process is derived to characterize the ELS fully. Some possible simpli®cations of the method, such as modal reduction and/ or local linearization, are also discussed. The results obtained are in good agreement with those of direct numerical simulations taking two typical examples.