Stochastic Stability of Flow-Induced Vibration

stochastic stability;flow-induced vibration;perturbation;Civil Engineering

Zhu, Jinyu

University of Waterloo

关键词: stochastic stability;    flow-induced vibration;    perturbation;    Civil Engineering;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/3643/1/Thesis.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

Flow-induced structural vibration is experienced in many engineering applications, such as aerospace industry and civil engineering infrastructures. One of the main mechanisms offlow-induced vibration is instability which can be triggered by parametric excitations orfluid-elastic forces. Experiments show that turbulence has a significant impact on thestability of structures. The objective of this research is to bridge the gap betweenflow-induced vibration and stochastic stability of structures.The flow-induced vibration of a spring-supported circular cylinder is studiedin this research. The equations of motion for thecylinder placed in a cross-flow are set up, in which the vortex force is modeled by abounded noise because of its narrow-band characteristics.Since the vibration in the lift direction is more prominent in the lock-in region,the system is reduced to one degree-of-freedom, i.e., only the vibration ofthe cylinder in the lift direction is considered. The equation of motion for thecylinder can be generalized as a two-dimensional system excited by a bounded noise.Stochastic analysis is usedto determine the moment Lyapunov exponents and Lyapunov exponents for the generalizedsystem. The results are then applied to study the parametric instability of a cylinder inthe lock-in region.Fluidelastic instability can occur when the cylinder is placed in a shear flow. Theequations of motion are established by using the quasi-steady theory to model thefluid-elastic forces. To study the turbulence effect on the stability of the cylinder,a real noise or an Ornstein-Uhlenbeck process is used to model the grid-generatedturbulence. Theequations of motion are randomized resulting in a four-dimensional system excited by areal noise. The stability of the stochastic system is studied by determining themoment Lyapunov exponents and Lyapunov exponents. Parameters of the system and the noiseare varied to investigate their effects on the stability. It is found thatthe grid-generated turbulence can stabilize the system when the parameters takecertain values, which agrees with the experimental observations.Many flow-induced vibration problems can be modeled by a two degrees-of-freedom systemparametically excited by a narrow-band process modeled by a bounded noise. Thesystem can be in subharmonic resonance, combination (additive or differential) resonance,or both if the central frequency of the bounded noise takes an appropriate value.The method for a single degree-of-freedom systemis extended to study the stochastic stability of the two degrees-of-freedom system. Themoment Lyapunov exponents and Lyapunov exponents for the three cases are obtained usinga perturbation method. The effect of noise on various types of parametric resonance,such as subharmonic resonance, combination additive resonance, and combinedsubharmonic and combination additive resonance, is investigated.The main contributions of this thesis are stochastic stability analysis ofone-degree-of-freedom systems and two-degree-of-freedom systems.Stability analysis for systems under the excitation of real noise and bounded noiseis carried out by determining the moment Lyapunov exponents and Lyapunov exponents.Good agreement is obtained between analytical results and those obtained from Monte Carlo simulations.In the two degrees-of-freedom case,the effect of free stream turbulence on cylinder vibration and its stability is examined.