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

Measurement Point Selection and Modal Damping Identification for Bladed Disks

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90656/1/AIAA-2011-1783-756.pd

Reduced Order Modeling for Nonlinear Vibration Analysis of Mistuned Multi-Stage Bladed Disks with a Cracked Blade

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90668/1/AIAA-2011-2065-784.pd

Damage detections in nonlinear vibrating thermally loaded plates

In this work, geometrically nonlinear vibrations of fully clamped rectangular plates subjected to thermal changesare used to study the sensitivity of some vibration response parameters to the presence of damage and elevated temperature. The geometrically nonlinear version of the Mindlin plate theory is used to model the plate behaviour.Damage is represented as a stiffness reduction in a small area of the plate. The plates are subjected to harmonicloading leading to large amplitude vibrations and temperature changes. The plate vibration response is obtained by a pseudo-load mode superposition method. The main results are focussed on establishing the influence of damage on the vibration response of the heated and the unheated plates and the change in the time-history diagrams and the Poincaré maps caused by damage and elevated temperature. The damage criterion formulated earlier for nonheated plates, based on analyzing the points in the Poincaré sections of the damaged and healthy plate, is modified and tested for the case of plates additionally subjected to elevated temperatures. The importance of taking into account the actual temperature in the process of damage detection is shown

The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows

The Gauss--Newton with approximated tensors (GNAT) method is a nonlinear model reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with residual minimization; it delivers computational efficency by a hyper-reduction procedure based on the `gappy POD' technique. Originally presented in Ref. [1], where it was applied to implicit nonlinear structural-dynamics models, this method is further developed here and applied to the solution of a benchmark turbulent viscous flow problem. To begin, this paper develops global state-space error bounds that justify the method's design and highlight its advantages in terms of minimizing components of these error bounds. Next, the paper introduces a `sample mesh' concept that enables a distributed, computationally efficient implementation of the GNAT method in finite-volume-based computational-fluid-dynamics (CFD) codes. The suitability of GNAT for parameterized problems is highlighted with the solution of an academic problem featuring moving discontinuities. Finally, the capability of this method to reduce by orders of magnitude the core-hours required for large-scale CFD computations, while preserving accuracy, is demonstrated with the simulation of turbulent flow over the Ahmed body. For an instance of this benchmark problem with over 17 million degrees of freedom, GNAT outperforms several other nonlinear model-reduction methods, reduces the required computational resources by more than two orders of magnitude, and delivers a solution that differs by less than 1% from its high-dimensional counterpart

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