scholarly journals Trace properties of certain damped linear elastic systems

2013 ◽  
Vol 2 (4) ◽  
pp. 711-721
Author(s):  
David L. Russell ◽  
Keyword(s):  
Linear Elastic ◽  
Elastic Systems

Control of Elastic Systems via Passivity-Based Methods

2004 ◽  
Vol 10 (11) ◽  
pp. 1699-1735 ◽  
Author(s):  
A. G. Kelkar ◽  
S. M. Joshi
Keyword(s):  
Flexible Structures ◽  
Robotic Manipulators ◽  
Mathematical Concept ◽  
Controller Synthesis ◽  
Control Laws ◽  
Linear Elastic ◽  
Elastic Systems ◽  
Different Types ◽  
Linear Controllers ◽  
Synthesis Approach

In this paper we present a controller synthesis approach for elastic systems based on the mathematical concept of passivity. For nonlinear and linear elastic systems that are inherently passive, robust control laws are presented that guarantee stability. Examples of such systems include flexible structures with col-located and compatible actuators and sensors, and multibody space-based robotic manipulators. For linear elastic systems that are not inherently passive, methods are presented for rendering them passive by compensation. The “passified” systems can then be robustly controlled by a class of passive linear controllers that guarantee stability despite uncertainties and inaccuracies in the mathematical models. The controller synthesis approach is demonstrated by application to five different types of elastic systems.

On the Stability of Elastic Systems Subjected to Nonconservative Forces

1964 ◽  
Vol 31 (3) ◽  
pp. 435-440 ◽  
Author(s):  
G. Herrmann ◽  
R. W. Bungay
Keyword(s):  
Critical Loads ◽  
Kinetic Method ◽  
Euler Method ◽  
Parameter Instability ◽  
Linear Elastic ◽  
Elastic Systems ◽  
Nonconservative Loading ◽  
The Stability ◽  
Two Degree Of Freedom ◽  
Increasing Load

Free motions of a linear elastic, nondissipative, two-degree-of-freedom system, subjected to a static nonconservative loading, are analyzed with the aim of studying the connection between the two instability mechanisms (termed divergence and flutter by analogy to aeroelastic phenomena) known to be possible for such systems. An independent parameter is introduced to reflect the ratio of the conservative and nonconservative components of the loading. Depending on the value of this parameter, instability is found to occur for compressive loadings by divergence (static buckling), flutter, or by both (at different loads) with multiple stable and unstable ranges of the load. In the latter case either type of instability may be the first to occur with increasing load. For a range of the parameter, divergence (only) is found to occur for tensile loads. Regardless of the non-conservativeness of the system, the critical loads for divergence can always be determined by the (static) Euler method. The critical loads for flutter (occurring only in nonconservative systems) can be determined, of course, by the kinetic method alone.

On-Board Detection of Derailed Wheel and Wheel Defects

2007 ◽  
Author(s):  
Som P. Singh ◽  
Srinivas Chitti ◽  
S. K. Punwani ◽  
Monique F. Stewart
Keyword(s):  
Ride Quality ◽  
Monitoring Systems ◽  
Vertical Acceleration ◽  
Linear Elastic ◽  
Bearing Defects ◽  
Elastic Systems ◽  
Wheel Model ◽  
Board Monitoring ◽  
Wheel Flat ◽  
Railroad Safety

To improve railroad safety and efficiency, the Office of Research and Development of the Federal Railroad Administration (FRA) is running a project to develop and demonstrate an On-Board Monitoring Systems Concept (OBMSC) for freight trains. The project scope includes onboard detection of hot bearings, bearing defects, vehicle, ride quality, wheel tread defects, and derailed wheels. This paper presents an analytical model to detect derailed wheel conditions. In the model, an idealized wheelset with associated sprung and unsprung vehicle masses running on crossties is simulated using LS-Dyna software. Track structure (i.e., ties) ballast/subgrade, and soil are represented as linear elastic systems. This paper identifies wheelset vertical acceleration magnitude and associated frequencies for a derailed wheel for empty and loaded car conditions at various operating speeds. The research shows that the predicted wheelset acceleration magnitude for a derailed wheel overlap with those resulting from wheel tread defects, such as wheel flat, shells, and built-up tread. To differentiate between a derailed wheel and wheels with tread defects, a set of criteria is formulated based on amplitude and frequency ranges. Based on the analytical results from the derailed wheel model and field-tested results of revenue service wheels with tread defects, it is established that the OBMSC bearing adapter acceleration (BAA) can be used to detect a derailed wheel and conditions communicated to the train crew or other appropriate parties.

Stability and Accuracy for Nonlinear Systems

2005 ◽  
Author(s):  
Shuenn-Yih Chang
Keyword(s):  
Nonlinear Systems ◽  
Stability Limit ◽  
Stable Method ◽  
Numerical Accuracy ◽  
Unconditionally Stable ◽  
Numerical Examples ◽  
Linear Elastic ◽  
Elastic Systems ◽  
Degree Of Convergence ◽  
Stability And Accuracy

Stability and accuracy of the Newmark method for solving nonlinear systems are analytically evaluated. It is proved that an unconditionally stable method for linear elastic systems is also unconditionally stable for nonlinear systems and a conditionally stable method for linear elastic systems remains conditionally stable for nonlinear systems except that the upper stability limit might vary with the step degree of nonlinearity and step degree of convergence. It is also found that numerical accuracy in the solution of nonlinear systems is highly related to the step degree of nonlinearity and the step degree of convergence although its general properties are similar to those of linear elastic systems. Analytical results are confirmed with numerical examples.

scholarly journals Vibration analysis of nonlinear and linear elastic systems

2021 ◽  
Vol 47 (4) ◽  
pp. 141-150
Author(s):  
A. S. Lichkovakha ◽  
B. A. Shemshura ◽  
S. A. Kuznetsov
Keyword(s):  
Elastic System ◽  
Elastic Characteristic ◽  
Progressive Change ◽  
Vehicle Suspensions ◽  
Linear Elastic ◽  
Eccentric Compression ◽  
Elastic Systems ◽  
Elastic Mechanism ◽  
High Flexibility ◽  
Elastic Elements

Objective. In this study, the task is to establish the theoretical prerequisites for the operability of a regressive-progressive elastic mechanism by comparing the amplitude-frequency characteristics and phase trajectories with a linear elastic system of comparable stiffness in a static equilibrium position.Methods. The article presents a comparative dynamic analysis of vibrations of elastic systems with linear rigidity and regressive-progressive characteristics obtained as a result of the use of elastic elements in the form of high flexibility rods with longitudinal eccentric compression. Such elastic elements in various design variants have been tested and patented as damping elements for use in the construction of vibration dampers for construction structures and vehicle suspensions, and have experimentally shown their effectiveness in damping vibrations.Results. The regressiveprogressive elastic characteristic obtained by the elliptic parameters method and using the ANSIS calculation complex is used in the dynamics equations in an approximated form, which expands the capabilities of the method. It is shown that increasing the energy intensity of a curvilinear system reduces the vibration amplitude.Conclusion. The regressive-progressive change of the stiffness of curvilinear elastic systems can be achieved using an elastic element with eccentric longitudinal compression; the regression plot of elastic properties is achieved due to eccentric compression; the progressive plot – through the use of a guide or other design solutions. The implementation of this characteristic allows using such elastic mechanisms in systems where the accumulation of potential energy occurs with a smaller compression stroke for the same perturbation than for linear systems.

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