Dynamic response of non-linear systems to poisson-distributed pulse trains: Markov approach

• Published in: Structural safety Vol. 8; no. 1; pp. 223 - 238
• Main Authors: Iwankiewicz, Radosław, Nielsen, Søren R.K., Thoft-Christensen, Palle
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.1990
• Subjects: Markov process; Monte Carlo method; Poisson process; random excitation; vibrations; Markov process; Monte Carlo method; random excitation; Poisson process; vibrations
• ISSN: 0167-4730; 1879-3355
• DOI: 10.1016/0167-4730(90)90042-N

The dynamic response of non-linear systems with algebraic non-linearities to Poisson-distributed trains of impulses and general pulses is considered. The displacement and velocity response of the system form in that case a Poisson-driven Markov vector process. The differential equations governing the joint response moments are obtained by making use of a generalized Ito's differential rule which is valid for this kind of problems. Two closure techniques are used to truncate the hierarchy of moment equations: an ordinary and a modified cumulant-neglect closure technique. Transient response statistics such as the mean value and the variance are evaluated numerically. Verification of the obtained approximate analytical results against Monte Carlo simulations shows that the ordinary cumulant-neglect closure technique is appropriate in the case of non-linear systems subject to Poisson-distributed impulses and general pulses if the mean arrival rate of impulses is not very low, i.e. if the departure of the excitation from the Gaussian process is not very large. Otherwise, i.e. in the case of a low mean arrival rate of impulses, the modified cumulant-neglect closure scheme provides better results.