Unified Treatment of the Vibrating Arm. Part II. The Solution When the Restoring Force Is Positive and Also When It Is Expressed as a Power Series in ψ

1957 ◽  
Vol 25 (4) ◽  
pp. 241-248
Author(s):  
Dan McLachlan
Keyword(s):  
Power Series ◽  
Restoring Force

Identification of model-free structural nonlinear restoring forces using partial measurements of structural responses

2016 ◽  
Vol 20 (1) ◽  
pp. 69-80 ◽  
Author(s):  
Y Lei ◽  
SJ Luo ◽  
MY He
Keyword(s):  
Power Series ◽  
Structural Parameters ◽  
Structural System ◽  
Restoring Force ◽  
Model Free ◽  
Nonlinear Structural ◽  
Structural Nonlinearities ◽  
Restoring Forces ◽  
Structural Responses ◽  
Nonlinear Behaviors

Identification of nonlinear structural system is an important but challenging task for structural health monitoring. Due to the complexities of structural nonlinearities, it is hard to establish proper mathematical models for some structural nonlinear behaviors. Moreover, only partial structural responses can be measured in practice; it is essential to conduct identification of nonlinear structural systems using only partial measurements of structural responses. To cope with these issues, an algorithm is proposed in this article for the identification of some model-free structural nonlinear restoring forces using only partial measurements of structural responses. First, an equivalent linear structural system is introduced for the identification of the locations of structural nonlinearities. Then, a model-free structural nonlinear restoring force is approximated by a power series polynomial. The unknown coefficients of the power series polynomials together with other structural parameters are identified by the extended Kalman filter so that the characteristics of the behaviors of the model-free of nonlinear restoring forces can be identified. Some numerical examples including the identification of two nonlinear multi-story shear frames and a planar nonlinear truss with different structural nonlinear restoring forces are used to validate the proposed algorithm.

The Software «MMI–calibration 3.0»

Metrologiya ◽  
2020 ◽  
pp. 16-24
Author(s):  
Alexandr D. Chikmarev
Keyword(s):  
Power Series ◽  
Data Processing ◽  
Statistical Treatment ◽  
Correction Function ◽  
Calibration Function ◽  
Measuring Instrument ◽  
Working Standard ◽  
Calibration Protocol ◽  
Error Probabilities ◽  
Continuous Power

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

Identification of the string boundary conditions using natural frequencies

2016 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
I.M. Utyashev ◽  
A.M. Akhtyamov
Keyword(s):  
Inverse Problems ◽  
Power Series ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Boundary Value ◽  
External Environment ◽  
Direct And Inverse Problems ◽  
Symmetric Potential ◽  
Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

On the Role of Marangoni Effects on the Critical Heat Flux for Pool Boiling of Binary Mixtures

1996 ◽  
Vol 118 (1) ◽  
pp. 103-109 ◽  
Author(s):  
W. R. McGillis ◽  
V. P. Carey
Keyword(s):  
Surface Tension ◽  
Heat Flux ◽  
Binary Mixtures ◽  
Critical Heat Flux ◽  
Full Range ◽  
Pool Boiling ◽  
Marangoni Effect ◽  
Restoring Force ◽  
Marangoni Effects

The Marangoni effect on the critical heat flux (CHF) condition in pool boiling of binary mixtures has been identified and its effect has been quantitatively estimated with a modified model derived from hydrodynamics. The physical process of CHF in binary mixtures, and models used to describe it, are examined in the light of recent experimental evidence, accurate mixture properties, and phase equilibrium revealing a correlation to surface tension gradients and volatility. A correlation is developed from a heuristic model including the additional liquid restoring force caused by surface tension gradients. The CHF condition was determined experimentally for saturated methanol/water, 2-propanol/water, and ethylene glycol/water mixtures, over the full range of concentrations, and compared to the model. The evidence in this study demonstrates that in a mixture with large differences in surface tension, there is an additional hydrodynamic restoring force affecting the CHF condition.

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