A Dynamical Systems Approach to Damage Evolution Tracking, Part 1: Description and Experimental Application

2002 ◽  
Vol 124 (2) ◽  
pp. 250-257 ◽  
Author(s):  
David Chelidze ◽  
Joseph P. Cusumano ◽  
Anindya Chatterjee
Keyword(s):  
Dynamical System ◽  
Systems Approach ◽  
Experimental System ◽  
Restoring Force ◽  
Tracking Method ◽  
Flow Equations ◽  
Scale Modeling ◽  
Damage Process ◽  
Modeling Strategy ◽  
Battery Discharge

In this two-part paper we present a novel method for tracking a slowly evolving hidden damage process responsible for nonstationarity in a fast dynamical system. The development of the method and its application to an electromechanical experiment is the core of Part 1. In Part 2, a mathematical model of the experimental system is developed and used to validate the experimental results. In addition, an analytical connection is established between the tracking method and the physics of the system based on the idea of averaging and the slow flow equations for the hidden process. The tracking method developed in this study uses a nonlinear, two-time-scale modeling strategy based on the delay reconstruction of a system’s phase space. The method treats damage-induced nonstationarity as evolving in a hierarchical dynamical system containing a fast, directly observable subsystem coupled to a slow, hidden subsystem. The utility of the method is demonstrated by tracking battery discharge in a vibrating beam system with a battery-powered electromagnetic restoring force. Applications to systems with evolving material damage are also discussed.

A Dynamical Systems Approach to Damage Evolution Tracking, Part 2: Model-Based Validation and Physical Interpretation

2002 ◽  
Vol 124 (2) ◽  
pp. 258-264 ◽  
Author(s):  
Joseph P. Cusumano ◽  
David Chelidze ◽  
Anindya Chatterjee
Keyword(s):  
Systems Approach ◽  
Experimental System ◽  
Flow Equation ◽  
Slow Flow ◽  
Tracking Method ◽  
Hidden Variable ◽  
System A ◽  
Damage Tracking ◽  
Relationship Of ◽  
The Relationship

In this paper, the hidden variable damage tracking method developed in Part 1 is analyzed using a physics-based mathematical model of the experimental system: a mechanical oscillator with a nonstationary two-well potential. Numerical experiments conducted using the model are in good agreement with the experimental study presented in Part 1, and explicitly show how the tracking metric is related to the slow hidden variable evolution responsible for drift in the fast system parameters. Using the idea of averaging, the slow flow equation governing the hidden variable evolution is obtained. It is shown that the solution to the slow flow equation corresponds to the hidden variable trajectory obtained with the experimental tracking method. Thus we establish in principle the relationship of our algorithm to any underlying physical process. Based on this result, we discuss the application of the tracking method to systems with evolving material damage using the results of some preliminary experiments.

Feedback Control of Turbulence

1994 ◽  
Vol 47 (6S) ◽  
pp. S3-S13 ◽  
Author(s):  
Parviz Moin ◽  
Thomas Bewley
Keyword(s):  
Feedback Control ◽  
Turbulent Flows ◽  
Systems Approach ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Flow Equations ◽  
Active Feedback ◽  
Active Feedback Control ◽  
Mathematical Techniques

A brief review of current approaches to active feedback control of the fluctuations arising in turbulent flows is presented, emphasizing the mathematical techniques involved. Active feedback control schemes are categorized and compared by examining the extent to which they are based on the governing flow equations. These schemes are broken down into the following categories: adaptive schemes, schemes based on heuristic physical arguments, schemes based on a dynamical systems approach, and schemes based on optimal control theory applied directly to the Navier-Stokes equations. Recent advances in methods of implementing small scale flow control ideas are also reviewed.

scholarly journals BACH FLOWS OF PRODUCT MANIFOLDS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250039 ◽  
Author(s):  
SANJIT DAS ◽  
SAYAN KAR
Keyword(s):  
Dynamical System ◽  
Fixed Point ◽  
Ricci Flow ◽  
Flow Characteristics ◽  
Geometric Flow ◽  
Flow Equations ◽  
First Order ◽  
Bach Tensor ◽  
Point Condition ◽  
Future Work

We investigate various aspects of a geometric flow defined using the Bach tensor. First, using a well-known split of the Bach tensor components for (2, 2) unwarped product manifolds, we solve the Bach flow equations for typical examples of product manifolds like S2 × S2, R2 × S2. In addition, we obtain the fixed-point condition for general (2, 2) manifolds and solve it for a restricted case. Next, we consider warped manifolds. For Bach flows on a special class of asymmetrically warped 4-manifolds, we reduce the flow equations to a first-order dynamical system, which is solved exactly to find the flow characteristics. We compare our results for Bach flow with those for Ricci flow and discuss the differences qualitatively. Finally, we conclude by mentioning possible directions for future work.

Research on Numerical Integration Algorithm for MDOF Pseudo-Dynamic Test

2012 ◽  
Vol 204-208 ◽  
pp. 4820-4826
Author(s):  
Xin Guo ◽  
Li Hua Zhu ◽  
Tian Li Wang
Keyword(s):  
Dynamic Test ◽  
Experimental System ◽  
Test System ◽  
Unconditional Stability ◽  
Comparison Study ◽  
Restoring Force ◽  
Integration Algorithm ◽  
Integration Algorithms ◽  
Simulation Results ◽  
Force Characteristics

This paper focuses on two integration algorithms used for pseudo-dynamic test, explicit Newmark algorithm and implicit alpha-C algorithm. The comparison study between the test and simulation results shows that: the non-uniform distribution of mass, restoring force characteristics and higher frequency vibration modality are simulated more accurately using the alpha-C algorithm than using explicit Newmark algorithm. The alpha-C algorithm also leads to high iterative accuracy and unconditional stability. Replacing the explicit Newmark algorithm in original experimental system by implicit alpha-C algorithm, the MDOF pseudo dynamic test system can be realized successfully.

scholarly journals FOUR–DIMENSIONAL BRUSSELATOR MODEL WITH PERIODICAL SOLUTION

2020 ◽  
Vol 6 (1) ◽  
pp. 3
Author(s):  
Odiljon S. Akhmedov ◽  
Abdulla A. Azamov ◽  
Gafurjan I. Ibragimov
Keyword(s):  
Dynamical System ◽  
Chemical Reactions ◽  
Main Property ◽  
External Source ◽  
Closed Trajectory ◽  
Dimensional Model ◽  
Tracking Method ◽  
Positive Orthant ◽  
Brusselator Model ◽  
Periodical Solution

In the paper, a four-dimensional model of cyclic reactions of the type Prigogine's Brusselator is considered. It is shown that the corresponding dynamical system does not have a closed trajectory in the positive orthant that will make it inadequate with the main property of chemical reactions of Brusselator type. Therefore, a new modified Brusselator model is proposed in the form of a four-dimensional dynamic system. Also, the existence of a closed trajectory is proved by the DN-tracking method for a certain value of the parameter which expresses the rate of addition one of the reagents to the reaction from an external source.

scholarly journals The Multi-Scale Infrastructure for Chemistry and Aerosols (MUSICA)

2020 ◽  
Vol 101 (10) ◽  
pp. E1743-E1760 ◽  
Author(s):  
Gabriele G. Pfister ◽  
Sebastian D. Eastham ◽  
Avelino F. Arellano ◽  
Bernard Aumont ◽  
Kelley C. Barsanti ◽  
...  
Keyword(s):  
Atmospheric Chemistry ◽  
Atmospheric Modeling ◽  
Atmospheric Composition ◽  
Earth System ◽  
Policy Makers ◽  
Multi Scale ◽  
Scale Modeling ◽  
Consistent Manner ◽  
Limited Scale ◽  
Modeling Strategy

ABSTRACTTo explore the various couplings across space and time and between ecosystems in a consistent manner, atmospheric modeling is moving away from the fractured limited-scale modeling strategy of the past toward a unification of the range of scales inherent in the Earth system. This paper describes the forward-looking Multi-Scale Infrastructure for Chemistry and Aerosols (MUSICA), which is intended to become the next-generation community infrastructure for research involving atmospheric chemistry and aerosols. MUSICA will be developed collaboratively by the National Center for Atmospheric Research (NCAR) and university and government researchers, with the goal of serving the international research and applications communities. The capability of unifying various spatiotemporal scales, coupling to other Earth system components, and process-level modularization will allow advances in both fundamental and applied research in atmospheric composition, air quality, and climate and is also envisioned to become a platform that addresses the needs of policy makers and stakeholders.

scholarly journals Study of Combined Multi-Point Constraint Multi-Scale Modeling Strategy for Ultra-High-Performance Steel Fiber-Reinforced Concrete Structures

Materials ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 5320
Author(s):  
Zuohua Li ◽  
Zhihan Peng ◽  
Jun Teng
Keyword(s):  
Reinforced Concrete ◽  
Energy Balance ◽  
High Performance ◽  
Steel Fiber ◽  
Fiber Reinforced Concrete ◽  
Steel Fiber Reinforced Concrete ◽  
Multi Scale ◽  
Scale Modeling ◽  
Multi Scale Modeling ◽  
Modeling Strategy

Compared with normal strength concrete (NSC), ultra-high-performance steel fiber-reinforced concrete (UHPFRC) shows superior performance. The concrete damage plasticity (CDP) model in ABAQUS can predict the mechanical properties of UHPFRC components well after calibration. However, the simulation of the whole structure is seriously restricted by the computational capability. In this study, a novel multi-scale modeling strategy for UHPFRC structure was proposed, which used a calibrated CDP model. A novel combined multi-point constraint (CMPC) was established by the simultaneous equations of displacement coordination and energy balance in different degrees of freedom of interface nodes. The advantage is to eliminate the problem of the tangential over-constraint of displacement coordination equation at the interface and to avoid stress iteration of the energy balance equation in the plastic stage. The expressions of CMPC equations of typical multi-scale interface connection were derived. The multi-scale models of UHPFRC components under several load cases were established. The results show that the proposed strategy can well predict the strain distribution and damage distribution of UHPFRC while significantly reducing the number of model elements and improving the computational efficiency. This study provides an accurate and efficient finite element modeling strategy for the design and analysis of UHPFRC structures.

Identification of a Two Degree of Freedom Experimental System Using a Force Appropriation Approach

1997 ◽  
Author(s):  
P. A. Atkins ◽  
J. R. Wright
Keyword(s):  
Cross Coupling ◽  
Experimental System ◽  
Single Mode ◽  
Degree Of Freedom ◽  
Restoring Force ◽  
Linear Mode ◽  
Force Method ◽  
Experimental Systems ◽  
Coupling Terms ◽  
Two Degree Of Freedom

Abstract The identification of nonlinear multi degree of freedom systems involves a significant number of nonlinear cross coupling terms, whether the identification is carried out in spatial or modal domains. One possible approach to reducing the order of each identification required is to use a suitable pattern of forces to drive any mode of interest. For a linear system, the force pattern required to drive a single mode is derived using a Force Appropriation method. This paper presents a method for determining the force pattern necessary to drive a mode of interest of a nonlinear system into the nonlinear region whilst the response is controlled to remain in proportion to the linear mode shape. Such an approach then allows the direct nonlinear modal terms for that mode to be identified using the Restoring Force method. The method for determining the relevant force patterns is discussed. The implementation of the method for experimental systems is considered and experimental results from a two degree of freedom ‘benchmark structure’ are presented. Two methods of estimating the mass for a restoring force identification are compared.

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