主题：Non-linear 6D response statistics of a rotating shaft subjected to colored noise by path integration
a Jeffcott-type rotor with non-linear restoring force, under uniaxial colored noise excitation. The latter type of dynamic system is of wide use in stability studies of rotating machinery.
System response statistics are studied by applying the path integration (PI) method. The Jeffcott rotor response statistics are then obtained by solving the Fokker–Planck-Kolmogorov (FPK) equation for a 6D dynamic system. The resulting response probability distributions can serve as an engineering input for a wide range of design issues, e.g. estimates of characteristic values, extreme value statistics and system reliability. Assessment of transverse random vibrations of shafts in rotating machinery may be of practical importance for applications with substantial environmental dynamic loads on supports, particularly in transport/vehicle engineering. Colored noise is a step forward compared to white noise excitation forces, but it raises the mechanical system dimension from 4D to 6D.The major advantage of path integration, relative to direct Monte Carlo simulation, is that path integration yields high accuracy in the probability distribution tail. Improved implementation of the PI algorithm was applied, specifically, the fast Fourier transform (FFT) was used to simulate the additive noise of the dynamic system. PI was accelerated by using a Monte Carlo based estimate of the joint PDF as a initial input. Finally, the key feature of this work is the advance to 6D problems, where very little PI research has been done. The obvious reason is of course the formidable computation load arising from decent 6D mesh. In the presentation a practical solution to the latter challenge is discussed, enabling 6D PI calculation on an ordinary desktop within a reasonable amount of time. Using modern computational hardware with a decent GPU (Graphic Processing Unit) will significantly facilitate 6D calculation, making it accessible for engineering problems.
Arvid Naess教授为挪威科技大学（NTNU）教授、挪威皇家科学（技术）院院士、挪威皇家科学与文学院院士、美国土木工程学会2010年“弗洛登瑟尔奖”得主。主要研究方向概率统计、随机振动和结构可靠性等。目前，Arvid Naess教授担任多个国际期刊的副主编和编委，发表论文100余篇。