An Efficient Technique for the Approximate Analysis of Vibro-Impact

1983 ◽  
Vol 105 (3) ◽  
pp. 332-336 ◽  
Author(s):  
R. K. Miller ◽  
B. Fatemi
Keyword(s):  
Approximate Solution ◽  
Substantial Reduction ◽  
Solution Procedure ◽  
Computational Effort ◽  
Mean Square ◽  
Base Excitation ◽  
Weighted Mean ◽  
Linearization Technique ◽  
Adjacent Structures ◽  
Impact Problems

An approximate solution procedure is presented for a class of steady vibro-impact problems consisting of adjacent structures separated by a gap and subjected to harmonic base excitation. The procedure is based on a weighted mean-square linearization technique, and is capable of substantial reduction of computational effort over that required for an exact numerical simulation. As an illustration of the general approach, a detailed analysis of an example problem is presented, together with a comparison of results with an exact solution. It is shown for the example problem that the level of accuracy of the approximate solution is adequate for many applications.

On the Approximate Solution of Nonclassically Damped Linear Systems

1993 ◽  
Vol 60 (3) ◽  
pp. 695-701 ◽  
Author(s):  
J. H. Hwang ◽  
F. Ma
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Error Bound ◽  
Large Scale ◽  
Substantial Reduction ◽  
Approximation Error ◽  
Computational Effort ◽  
Common Procedure ◽  
Damping Matrix ◽  
Modal Damping

A common procedure in the solution of a nonclassically damped linear system is to neglect the off-diagonal elements of the associated modal damping matrix. For a large-scale system, substantial reduction in computational effort is achieved by this method of decoupling the system. In the present paper, the error introduced by disregarding the off-diagonal elements is evaluated, and a quadrature formula for the approximation error is derived. A tight error bound is then obtained. In addition, an effective scheme to improve the accuracy of the approximate solution is outlined.

Indikatoren schulischen Wohlbefindens bei gesunden und chronisch kranken Kindern: Psychometrische Prüfung und Validierung adaptierter FEESS-Skalen

2020 ◽  
Vol 34 (3-4) ◽  
pp. 201-219
Author(s):  
Kathleen Schnick-Vollmer ◽  
Christiane Diefenbach ◽  
Christine Gräf ◽  
Dorle Hoffmann ◽  
Isabell Hoffmann ◽  
...  
Keyword(s):  
Item Response ◽  
Mean Square ◽  
Weighted Mean ◽  
Externe Validität ◽  
Chronisch Kranke

Zusammenfassung. Das schulbezogene Wohlbefinden (SBWB) ist eine wichtige Voraussetzung für schulischen Erfolg. Trotzdem existieren – insbesondere mit Blick auf die Erfassung des SBWB von Erstklässlern – im deutschsprachigen Raum nur vereinzelt Studien. Dies lässt sich möglicherweise durch das Fehlen geeigneter Instrumente begründen. Dies gilt auch und insbesondere dann, wenn der Gesundheitszustand der Kinder berücksichtigt werden soll. Das Ziel der vorliegenden Arbeit besteht in der Validierung des adaptierten Fragebogens zur Erfassung von emotionalen und sozialen Schulerfahrungen (FEESS 1 – 2; Rauer & Schuck, 2004 ) mit Fokus auf die Eignung des Instruments für chronisch kranke und gesunde Kinder. Dafür wird zunächst das Konstrukt Wohlbefinden (WB) resp. SBWB definiert und in einschlägige Theorien – die Selbstbestimmungstheorie nach Deci und Ryan (1985) und das Erwartung-mal-Wert-Modell nach Wigfield und Eccles (2000) – eingebettet. Die Bedeutung der verwendeten FEESS-Skalen und ihr Zusammenhang zum schulischen Erfolg werden aufgezeigt. 1491 Kinder wurden zu ihrer Lernfreude (LF), sozialen Integration (SI) und zu ihrem schulbezogenen Fähigkeitsselbstkonzept (SK) befragt. Die Erfassung des Gesundheitszustands wurde über Elternfragebögen und Schuleingangsuntersuchungen eruiert. Zudem wurden die Eltern zur gesundheitsbezogenen Lebensqualität (LQ) ihrer Kinder mit Hilfe eines Fragebogens zur Erfassung der Lebensqualität von Kindern (KINDL; Bullinger, Mackensen & Kirchberger, 1994 ) befragt. Die psychometrische Qualität der adaptierten FEESS-Skalen wurde für beide Gruppen (erkrankt / gesund) auf Skalen- und Itemebene untersucht. Hierzu kamen sowohl klassische Verfahren als auch Verfahren der Item-Response-Theorie zum Einsatz. Die Ergebnisse untermauern die Validität des Konstruktes SBWB und stützen die Annahme der Dreidimensionalität (LF, SI, SK). Alle drei Skalen zeigen eine zufriedenstellende bis sehr gute Reliabilität. Die Items zeigen sehr gute MNSQ-Werte (weighted mean-square; gewichtete Abweichungsquadrate) und geeignete Trennschärfen. Die externe Validität, für deren Berechnung der Zusammenhang zwischen den Angaben der Kinder und den Angaben der Eltern zur gesundheitsbezogenen LQ untersucht wurde, konnte noch nicht ausreichend nachgewiesen werden. Bis auf diese Einschränkung kann mit Hilfe der adaptierten FEESS-Skalen im nächsten Schritt das SBWB von gesunden und erkrankten Kindern verglichen werden, um mögliche Chancenungleichheiten auszugleichen.

Analysis of Linear Nonconservative Vibrations

1995 ◽  
Vol 62 (3) ◽  
pp. 685-691 ◽  
Author(s):  
F. Ma ◽  
T. K. Caughey
Keyword(s):  
Modal Analysis ◽  
Equations Of Motion ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Equivalence Transformations ◽  
State Space Approach ◽  
Nonconservative System ◽  
First Order ◽  
Physical Insight ◽  
Space Approach

The coefficients of a linear nonconservative system are arbitrary matrices lacking the usual properties of symmetry and definiteness. Classical modal analysis is extended in this paper so as to apply to systems with nonsymmetric coefficients. The extension utilizes equivalence transformations and does not require conversion of the equations of motion to first-order forms. Compared with the state-space approach, the generalized modal analysis can offer substantial reduction in computational effort and ample physical insight.

Exact analysis of the bending of wide beams by a modified elastica approach

2011 ◽  
Vol 225 (11) ◽  
pp. 2759-2764 ◽  
Author(s):  
L F Campanile ◽  
R Jähne ◽  
A Hasse
Keyword(s):  
Finite Element ◽  
Substantial Reduction ◽  
Short Review ◽  
Computational Effort ◽  
Two Dimensional ◽  
Finite Element Calculations ◽  
Dimensional Finite Element ◽  
Wide Beams ◽  
Insight Into ◽  
Selection Of

Classical beam models do not account for partial restraint of anticlastic bending and are therefore inherently inaccurate. This article proposes a modification of the exact Bernoulli–Euler equation which allows for an exact prediction of the beam's deflection without the need of two-dimensional finite element calculations. This approach offers a substantial reduction in the computational effort, especially when coupled with a fast-solving schema like the circle-arc method. Besides the description of the new method and its validation, this article offers an insight into the somewhat disregarded topic of anticlastic bending by a short review of the published theories and a selection of representative numerical results.

Thermal Analysis of the Hot Dip-Coating Process

1993 ◽  
Vol 115 (2) ◽  
pp. 453-460 ◽  
Author(s):  
Hui Zhang ◽  
M. Karim Moallemi ◽  
Sunil Kumar
Keyword(s):  
Experimental Data ◽  
Thermal Analysis ◽  
Approximate Solution ◽  
Dip Coating ◽  
Solution Procedure ◽  
Heat Diffusion ◽  
Coating Process ◽  
Parametric Effects ◽  
Simplifying Assumptions ◽  
Axial Heat

In this study a thermal analysis is performed on the hot dip-coating process where solidification of metal occurs on a bar moving through a finite molten bath. A continuum model is considered that accounts for important transport mechanisms such as axial heat diffusion, buoyancy, and shear-induced melt motion in the bath. A numerical solution procedure is developed, and its predictions are compared with those of an analytical approximate solution, as well as available experimental data. The predictions of the numerical scheme are in good agreement with the experimental data. The results of the approximate solution, however, exhibit significant disagreement with the data, which is attributed to the simplifying assumptions used in its development. Parametric effects of the bath geometry, and initial and boundary temperatures and solid velocity, as characterized by the Reynolds number, Grashof number, and Stefan numbers, are presented.

Approximate Solution of Nonclassically Damped Systems

1991 ◽  
Author(s):  
F. Ma ◽  
J. H. Hwang
Keyword(s):  
Approximate Solution ◽  
Large Scale ◽  
Computational Effort ◽  
Frequency Separation ◽  
Common Procedure ◽  
Damping Matrix ◽  
Complex Modes ◽  
Modal Coupling ◽  
Order Of Magnitude ◽  
Damped Systems

Abstract In analyzing a nonclassically damped linear system, one common procedure is to neglect those damping terms which are nonclassical, and retain the classical ones. This approach is termed the method of approximate decoupling. For large-scale systems, the computational effort at adopting approximate decoupling is at least an order of magnitude smaller than the method of complex modes. In this paper, the error introduced by approximate decoupling is evaluated. A tight error bound, which can be computed with relative ease, is given for this method of approximate solution. The role that modal coupling plays in the control of error is clarified. If the normalized damping matrix is strongly diagonally dominant, it is shown that adequate frequency separation is not necessary to ensure small errors.

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