Fluid-structure interaction in noisy nonlinear systems

Homogenization;Flutter;Lyapunov Exponents;Large Deviations Theory

Singh, Prince ; Namachchivaya ; N. Sri

关键词: Homogenization;    Flutter;    Lyapunov Exponents;    Large Deviations Theory;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/50653/Prince_Singh.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The first part of this work is concerned with the application of stochastic dimensional reduction to a twelve-dimensional aeroelastic model (i.e., two degrees of freedom that characterize the aerodynamics, two auxiliary degrees of freedom, and a four dimensional real noise process).The entire analysis is done in the vicinity of a critical parameter (here the mean wind velocity) that exhibits flutter in the structure. The homogenization procedure yields a two dimensional Markov process characterized by its generator. Further simplification yields a one dimensional stochastic differential equation that characterizes the critical modes of the original system (i.e., this stochastic differential equation physically captures the essential stochastic dynamics during flutter instability). Numerical results show the convergence in law ofthe critical modes of the original system to the critical modes resulting from the homogenized one-dimensional stochastic nonlinear system for both parametric and combined excitations; in turn revealing the weak convergence of this homogenization procedure. Additionally, the top Lyapunov exponent of the homogenized system is found analytically and compares well with the exponent obtained by numerically simulating the critical modes of the original system for the case of pure horizontal turbulence. This analysis provides a transparent medium for applying the homogenization procedure that may be of particular interest to the Aerospace community when analyzing flutter instability in aircrafts. The second part of this work provides a means of assessing a ship's stability criterion in irregular waves, namely through the Mean First Passage Time (MFPT) formulation. A comprehensive description of the mathematical theory involved is presented andis applied to the ship dynamics problem. This work extends the use of the Langevin equation to encapsulate the cubic damping term and provides a Large Deviations result; this allows a vulnerability criterion to be formulated that can be used to determine the circumstances under which extreme vessel dynamics occur, and therefore, these adverse conditions can be thwarted by changing the ship's operational parameters.