Effects of Inline Rotating Component on Piping System Dynamic Characteristics

2003 ◽  
Author(s):  
Zakaria N. Ibrahim
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
System Dynamic ◽  
Piping System ◽  
Problem Solution ◽  
Rotating Shaft ◽  
Eigen Value ◽  
Quick Assessment

Piping system dynamic characteristics are determined utilizing the classical Eigen-Value problem solution. Systems with integrated inline rotating components would experience some changes in these characteristics. The intensity of these changes depends on the relative magnitudes of their rotational momentums. Pseudo single degree of freedom ‘SDOF’, systems that include gyroscopic momentum of a rotating shaft are formulated and are subjected to seismic base excitations. The comparative responses of these SDOF are investigated. The gyroscopic inertia significantly alters their predicted seismic responses. For multi-degree of freedom system, simplified methodology is formulated to provide quick assessment of including the gyroscopic effects of the rotating components. The lumped parameters of the inline-rotating component within the piping system require the velocity degrees of freedom to be included in the analysis. This results in the non-classical Eigen-Value problem type of formulation. The latter is simplified utilizing the classical Eigen-Value solution conventionally termed as normal modes extraction. The normal modes synthesis reduces the number of degrees of freedom for the non-classical Eigen-Value problem to a manageable level. The concept of mode shape utilization coefficient ‘MSUC’, is introduced to provide quick assessment of the system. The gyroscopic inertia does not dominate the system dynamic characteristics. Low to moderate rotational momentums, typically installed by the industry, slightly affect the piping system dynamic characteristics. This justifies the industry practice of ignoring the rotational momentums within the piping systems routine analysis. It is also found that very high rotational momentums are artificially required to dramatically change the system dynamic characteristics.

A guide to classical flutter

1988 ◽  
Vol 92 (919) ◽  
pp. 339-355 ◽  
Author(s):  
L. T. Niblett
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Structural Coupling ◽  
Two Degrees Of Freedom ◽  
Single Degree ◽  
Lifting Surface ◽  
Classical Flutter ◽  
Comprehensive Study

Summary First essentials of classical flutter are demonstrated by a comprehensive study of the behaviour of a lifting surface with two degrees of freedom under the action of airforces limited to those in phase with displacement. Structural coupling between the coordinates is eliminated by taking the normal modes to be the deflection coordinates, and this results in conditions for stability with particularly concise forms. It is shown that the flutter stability can be seen to be very much a matter of the relative amplitudes of heave and pitch in the normal modes. In-quadrature airforces are then introduced and it is shown that they have little effect when the flutter is severe. They are of more importance in the milder forms of flutter, the extreme of which are shown to be little different from instabilities in a single degree of freedom.

scholarly journals Nonlinear Normal Modes of a Rotating Shaft Based on the Invariant Manifold Method

2004 ◽  
Vol 10 (4) ◽  
pp. 319-335 ◽  
Author(s):  
Mathias Legrand ◽  
Dongying Jiang ◽  
Christophe Pierre ◽  
Steven W. Shaw
Keyword(s):  
Invariant Manifold ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Rotating Shaft ◽  
Nonlinear Mode ◽  
Large Amplitude Motions ◽  
Nonlinear Normal ◽  
The Individual

The nonlinear normal mode methodology is generalized to the study of a rotating shaft supported by two short journal bearings. For rotating shafts, nonlinearities are generated by forces arising from the supporting hydraulic bearings. In this study, the rotating shaft is represented by a linear beam, while a simplified bearing model is employed so that the nonlinear supporting forces can be expressed analytically. The equations of motion of the coupled shaft-bearings system are constructed using the Craig–Bampton method of component mode synthesis, producing a model with as few as six degrees of freedom (d.o.f.). Using an invariant manifold approach, the individual nonlinear normal modes of the shaft-bearings system are then constructed, yielding a single-d.o.f. reduced-order model for each nonlinear mode. This requires a generalized formulation for the manifolds, since the system features damping as well as gyroscopic and nonconservative circulatory terms. The nonlinear modes are calculated numerically using a nonlinear Galerkin method that is able to capture large amplitude motions. The shaft response from the nonlinear mode model is shown to match extremely well the simulations from the reference Craig–Bampton model.

scholarly journals Modal testing and modelling the dynamic characteristics of a plate with bolted joints

2021 ◽  
Vol 15 (4) ◽  
pp. 8555-8564
Author(s):  
A.R. Bahari ◽  
M. A. Yunus ◽  
M.N. Abdul Rani ◽  
A.A. Prakasam
Keyword(s):  
Thin Plate ◽  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Bolted Joints ◽  
Modal Testing ◽  
Mode Shapes ◽  
Fe Model ◽  
Six Degrees Of Freedom ◽  
Alternative Approach

Modelling the dynamic characteristics of the bolted joints in a complex assembled structure with a high accuracy is very challenging due to the assumptions and uncertainties in the input data of the FE model. In this paper, the identification of the dynamic characteristics of the bolted joints structure using the CBUSH element connector is proposed. Modal testing and normal modes analysis are conducted on a thin plate assembled structure with bolted joints. In the simulation work, the CBUSH element connector is employed and the stiffness coefficient for six degrees of freedom is computed based on four flexibility formulae. The predicted natural frequencies and their corresponding mode shapes are compared against the results of the experimental work. A good agreement of the FE model is achieved by using the coefficient of stiffness as represented in the Swift flexibility formula. The study justifies that the dynamic characteristics of the bolt joints could be accurately modelled by using the CBUSH element connector. The obtained findings provided an alternative approach to modelling the dynamic characteristics of a thin plate assembled structure with bolted joints.

Triatomic molecules

2018 ◽  
Author(s):  
John H. D. Eland ◽  
Raimund Feifel
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Electronic States ◽  
Triatomic Molecules ◽  
Doubly Charged Ions ◽  
Spectral Bands ◽  
Valence Electrons ◽  
Doubly Charged ◽  
Charged Ions ◽  
Double Ionisation

Double ionisation of the triatomic molecules presented in this chapter shows an added degree of complexity. Besides potentially having many more electrons, they have three vibrational degrees of freedom (three normal modes) instead of the single one in a diatomic molecule. For asymmetric and bent triatomic molecules multiple modes can be excited, so the spectral bands may be congested in all forms of electronic spectra, including double ionisation. Double photoionisation spectra of H2O, H2S, HCN, CO2, N2O, OCS, CS2, BrCN, ICN, HgCl2, NO2, and SO2 are presented with analysis to identify the electronic states of the doubly charged ions. The order of the molecules in this chapter is set first by the number of valence electrons, then by the molecular weight.

scholarly journals Design and Calibration of a Hall Effect System for Measurement of Six-Degree-of-Freedom Motion within a Stacked Column

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3740
Author(s):  
Olafur Oddbjornsson ◽  
Panos Kloukinas ◽  
Tansu Gokce ◽  
Kate Bourne ◽  
Tony Horseman ◽  
...  
Keyword(s):  
Hall Effect ◽  
Degrees Of Freedom ◽  
Reactor Core ◽  
Degree Of Freedom ◽  
Life Extension ◽  
Scale Model ◽  
Design Development ◽  
Seismic Safety ◽  
Six Degrees Of Freedom ◽  
Six Degree Of Freedom

This paper presents the design, development and evaluation of a unique non-contact instrumentation system that can accurately measure the interface displacement between two rigid components in six degrees of freedom. The system was developed to allow measurement of the relative displacements between interfaces within a stacked column of brick-like components, with an accuracy of 0.05 mm and 0.1 degrees. The columns comprised up to 14 components, with each component being a scale model of a graphite brick within an Advanced Gas-cooled Reactor core. A set of 585 of these columns makes up the Multi Layer Array, which was designed to investigate the response of the reactor core to seismic inputs, with excitation levels up to 1 g from 0 to 100 Hz. The nature of the application required a compact and robust design capable of accurately recording fully coupled motion in all six degrees of freedom during dynamic testing. The novel design implemented 12 Hall effect sensors with a calibration procedure based on system identification techniques. The measurement uncertainty was ±0.050 mm for displacement and ±0.052 degrees for rotation, and the system can tolerate loss of data from two sensors with the uncertainly increasing to only 0.061 mm in translation and 0.088 degrees in rotation. The system has been deployed in a research programme that has enabled EDF to present seismic safety cases to the Office for Nuclear Regulation, resulting in life extension approvals for several reactors. The measurement system developed could be readily applied to other situations where the imposed level of stress at the interface causes negligible material strain, and accurate non-contact six-degree-of-freedom interface measurement is required.

The thermodynamics of intracrystalline sorption I. Models of the sorbed state

1956 ◽  
Vol 234 (1196) ◽  
pp. 24-34 ◽  
Keyword(s):  
Mobile Phase ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Translational Degree ◽  
Sorbate Concentration ◽  
The Ideal

Three basic models of the intracrystalline sorbed state are discussed: a localized phase, a mobile phase possessing two translational degrees of freedom, and a mobile phase with one translational degree of freedom. The isotherm and entropy of each of these models have been investigated for the ideal phase, and where possible the influence of sorbate-sorbate interactions has been considered. Expressions for the molal and differential entropies of each model are given as a function of sorbate concentration. The method of comparing theoretical isotherms and entropies with experimental observations is outlined.

Research on Simulation Customers Participate Type in Open Innovation

2014 ◽  
Vol 926-930 ◽  
pp. 2054-2057
Author(s):  
Jun Hui He
Keyword(s):  
Open Innovation ◽  
Degrees Of Freedom ◽  
New Products ◽  
Innovation Process ◽  
Degree Of Freedom ◽  
Three Dimensions ◽  
Dynamic Evolution ◽  
Evolution Simulation ◽  
High Degree

This paper proposed customers to participate typology based on three dimensions, which are the customers’ autonomy in the process, the nature of the firm‐customer collaboration, and the stage of the innovation process. Then proposed customers to participate in the type of open innovation framework. Through the static comparative and dynamic evolution simulation found: customers tend to be open to participate in the development of new products pre innovation, the tendency to begin to choose the low participation of degrees of freedom, and ultimately tend to opt for a high degree of freedom to participate.

Analysis of Five-Degree-of-Freedom Robot Arms

1983 ◽  
Vol 105 (1) ◽  
pp. 23-27 ◽  
Author(s):  
K. Sugimoto ◽  
J. Duffy
Keyword(s):  
Arc Welding ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Industrial Robot ◽  
Degree Of Freedom ◽  
Numerical Example ◽  
Robot Arms ◽  
Special Cases ◽  
Computer Controlled ◽  
Five Axes

Many kinds of robot arms with five degrees of freedom are widely used in industry for arc welding, spray painting, assembling etc. It is necessary to be able to compute joint displacements when such devices are computer controlled. A solution to this problem is presented and the analysis is illustrated by a numerical example using the most common industrial robot with five axes. Further, special cases are discussed using screw theory.

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