TY - GEN TI - Probability density determination by means of Gibbs entropy probability density T3 - DYMAMESI 2019 - Dynamics of Machines and Mechanical Systems with Interactions AU - Náprstek, Jiří AB - A method of random response investigation of a nonlinear dynam-ical system is discussed. In particular, the solution of the probability density of a single/multi-degree of freedom (SDOF/MDOF) system response is investigated. Multiple stable equilibrium states with possible jumps of the snap-through type among them are considered. The system is Hamiltonian with weak damping excited by a set of non-stationary Gaussian white noises. The solution, which is based on the Gibbs principle of the maximum entropy of probability, can be employed in various branches of engineering. The search for the extreme of the Gibbs entropy functional is formulated as a constrained optimization problem. The secondary constraints follow from the Fokker-Planck equation (FPE) for the system considered or from the system of ordinary di_erential equations for the stochastic moments of the response derived from the relevant FPE SN - 978-80-87012-70-3 UR - http://hdl.handle.net/11104/0294422 UR - http://www.nusl.cz/ntk/nusl-394143 A2 - Fischer, Cyril LA - eng KW - Fokker-Planck equation KW - probability density principle KW - maximum entropy KW - Gibbs entropy functional PY - 2019 PB - Ústav teoretické a aplikované mechaniky, Prosecká 76, 190 00 Praha 9, http://www.itam.cas.cz/ ER -