Forecasting Bifurcation of Parametrically Excited Systems: Theory & Experiments

A system is parametrically excited when one or some of its coefficients vary with time. Parametric excitation can be observed in various engineered and physical systems. Many systems subject to parametric excitation exhibit critical transitions from one state to another as one or several of the system parameters change. Such critical transitions can either be caused by a change in the topological structure of the unforced system, or by synchronization between a natural mode of the system and the parameter variation. Forecasting bifurcations of parametrically excited systems before they occur is an active area of research both for engineered and natural systems. In particular, anticipating the distance to critical transitions, and predicting the state of the system after such transitions, remains a challenge, especially when there is an explicit time input to the system. In this work, a new model-less method is presented to address these problems based on monitoring transient recoveries from large perturbations in the pre-bifurcation regime. Recoveries are studied in a Poincare section to address the challenge caused by explicit time input. Numerical simulations and experimental results are provided to demonstrate the proposed method. In numerical simulation, a parametrically excited logistic equation and a parametrically excited Duffing oscillator are used to generate simulation data. These two types of systems show that the method can predict transitions induced by either bifurcation of the unforced system, or by parametric resonance. We further examine the robustness of the method to measurement and process noise by collecting recovery data from an electrical circuit system which exhibits parametric resonance as one of its parameters varies

The effects of viscoelastic fluid on kinesin transport

Kinesins are molecular motors which transport various cargoes in the cytoplasm of cells and are involved in cell division. Previous models for kinesins have only targeted their in vitro motion. Thus, their applicability is limited to kinesin moving in a fluid with low viscosity. However, highly viscoelastic fluids have considerable effects on the movement of kinesin. For example, the high viscosity modifies the relation between the load and the speed of kinesin. While the velocity of kinesin has a nonlinear dependence with respect to the load in environments with low viscosity, highly viscous forces change that behavior. Also, the elastic nature of the fluid changes the velocity of kinesin. The new mechanistic model described in this paper considers the viscoelasticity of the fluid using subdiffusion. The approach is based on a generalized Langevin equation and fractional Brownian motion. Results show that a single kinesin has a maximum velocity when the ratio between the viscosity and elasticity is about 0.5. Additionally, the new model is able to capture the transient dynamics, which allows the prediction of the motion of kinesin under time varying loads.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98600/1/0953-8984_24_37_375103.pd

Sensitivity Enhancement of Modal Frequencies for Sensing using System Augmentation and Optimal Feedback Auxiliary Signals

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76542/1/AIAA-2008-2085-567.pd

Exploiting Chaotic Dynamics for Detecting Parametric Variations in Aeroelastic Systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76656/1/AIAA-9556-135.pd

Damage detection in nonlinear systems using system augmentation and generalized minimum rank perturbation theory

A damage detection method is developed for nonlinear systems using model updating. The method uses a nonlinear discrete model of the system and the form of the nonlinearities to create an augmented linear model of the system. A modal analysis technique that uses forcing that is known but not prescribed is then used to solve for the modal properties of the augmented linear system after the onset of damage. Due to the specialized form of the augmentation, nonlinear damage causes asymmetrical damage in the updated matrices. Minimum rank perturbation theory is generalized so that it may be applied to the augmented system and can handle these asymmetrical damage scenarios. The method is demonstrated using numerical data from several nonlinear mass–spring systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/49014/2/sms5_5_037.pd