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- Title
Stochastic dynamics of mechanical systems with impacts via the Step Matrix multiplication based Path Integration method.
- Authors
Sykora, Henrik T.; Kuske, Rachel; Yurchenko, Daniil
- Abstract
In this work we propose the Step Matrix Multiplication based Path Integration method (SMM-PI) for nonlinear vibro-impact oscillator systems. This method allows the efficient and accurate deterministic computation of the time-dependent response probability density function by transforming the corresponding Chapman–Kolmogorov equation to a matrix–vector multiplication using high-order numerical time-stepping and interpolation methods. Additionally, the SMM-PI approach yields the computation of the joint probability distribution for response and impact velocity, as well as the time between impacts and other important characteristics. The method is applied to a nonlinear oscillator with a pair of impact barriers, and to a linear oscillator with a single barrier, providing relevant densities and analysing energy accumulation and absorption properties. We validate the results with the help of stochastic Monte-Carlo simulations and show the superior ability of the introduced formulation to compute accurate response statistics.
- Subjects
NONLINEAR oscillators; MATRIX multiplications; IMPACT (Mechanics); PROBABILITY density function; DISTRIBUTION (Probability theory); HARMONIC oscillators
- Publication
Nonlinear Dynamics, 2024, Vol 112, Issue 11, p9095
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-024-09513-y