Simulating the Stochastic Response of Mechanical Systems Influenced by Noise

Motivation: Mechanical systems like the blades of turbomachinery can exhibit transitions between multiple stable vibration modes due to the effect of random external perturbations; in certain applications, high energy vibrating modes are undesired, and it is of interest to be able to estimate the probability transitions into or out of these undesired modes will occur.

Objective: Quantify the probability a physics based model of a Mechanical system with multiple vibrating modes will transition between modes due to noise.

Results: Using the Path Integral Method as a building block, and the Duffing oscillator as a physical model of the blades of turbomachinery, I developed a methodology to simulate the stochastic response of the system due to the effect of noise. From these simulations, I showed how one can extract the probability of transition between stable modes as a function of time. These results were peer reviewed and published in Chaos Journal in 2021.

My Role: All work described in this section was designed, programmed, analyzed, and published by Lautaro Cilenti.

Evolution of the stochastic response (probability density functions) of the mechanical system at four periods in time. The pdf values (z-vertical- axes) indicate the density (related to likelihood) of possible responses with a particular displacement (x) and velocity (dx/dt) at that time.
A contour diagram of the probability a physics based model of a mechanical system remains in an undesired high energy mode (high amplitude basin) as a function of nondimensionalized time (t/T) and noise intensity (σ)