Wilberforce pendulum: modelling linearly damped coupled oscillations of a spring-mass system

2021 ◽  
Author(s):  
Robert Frederik Diaz Uy ◽  
Chenghao Yuan ◽  
Zhengshan Chai ◽  
Justin Khor
Keyword(s):  
Experimental Data ◽  
Angular Displacement ◽  
Beat Frequency ◽  
Vertical Displacement ◽  
Quantitative Model ◽  
Moment Of Inertia ◽  
Lagrangian Formalism ◽  
Mass System ◽  
Coupled Oscillations ◽  
Theoretical Predictions

Abstract The Wilberforce pendulum is a coupled spring-mass system, where a mass with adjustable moment of inertia is suspended from a helical spring. Energy is converted between the translational and torsional modes, and this energy conversion is most clearly observed at resonance, which occurs when the damped natural frequencies of the two oscillation modes are equal. A theoretical model—with energy losses due to viscous damping accounted for—was formulated using the Lagrangian formalism to predict the pendulum mass’ trajectory. Theoretical predictions were compared with experimental data, showing good agreement. Fourier analysis of both theoretical predictions and experimental data further corroborate the validity of our quantitative model. The dependence of oscillation features like beat frequency and maximum conversion amplitude on relevant parameters such as the initial vertical displacement, initial angular displacement and moment of inertia was also investigated and experimentally verified.

Dehydration of Fractal Particles of Iron (III) and Aluminum Hydroxides

1995 ◽  
Vol 407 ◽  
Author(s):  
A. A. Vertegel ◽  
S. V. Kalinin ◽  
N. N. Oleynikov ◽  
Yu. D. Tretyakov
Keyword(s):  
Experimental Data ◽  
Fractal Dimension ◽  
Metal Atom ◽  
Quantitative Model ◽  
Kinetic Behavior ◽  
Dehydration Rate ◽  
Aluminum Hydroxides ◽  
Theoretical Predictions ◽  
Fractal Particles ◽  
Good Agreement

ABSTRACTThe kinetic behavior of Fe(OH)3 and AI(OH)3 powders during thermal dehydration is investigated. It has been shown that the dehydration rate is governed by the value of fractal dimension of the sample without any respect to the nature of metal atom in hydroxide. The quantitative model for dehydration of fractal particles with particular value of fractal dimension is suggested. Theoretical predictions are in a good agreement with experimental data.

scholarly journals An Additive Model to Predict the Rheological and Mechanical Properties of Polypropylene Blends Made by Virgin and Reprocessed Components

Recycling ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 2
Author(s):  
Francesco Paolo La Mantia ◽  
Maria Chiara Mistretta ◽  
Vincenzo Titone
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Additive Model ◽  
Industrial Process ◽  
Theoretical Predictions ◽  
Experimental Values ◽  
Polypropylene Blends ◽  
Polypropylene Sample

In this work, an additive model for the prediction of the rheological and mechanical properties of monopolymer blends made by virgin and reprocessed components is proposed. A polypropylene sample has been reprocessed more times in an extruder and monopolymer blends have been prepared by simulating an industrial process. The scraps are exposed to regrinding and are melt reprocessed before mixing with the virgin polymer. The reprocessed polymer is, then, subjected to some thermomechanical degradation. Rheological and mechanical experimental data have been compared with the theoretical predictions. The results obtained showed that the values of this simple additive model are a very good fit for the experimental values of both rheological and mechanical properties.

A Technique for the Laboratory Determination of Recirculation in Single Needle Dialysis

1993 ◽  
Vol 16 (2) ◽  
pp. 63-70 ◽  
Author(s):  
N.A. Hoenich ◽  
P.T. Smirthwaite ◽  
C. Woffindin ◽  
P. Lancaster ◽  
T.H. Frost ◽  
...  
Keyword(s):  
Experimental Data ◽  
Flow Rate ◽  
Experimental Results ◽  
New Technique ◽  
Treatment Efficiency ◽  
Single Lumen ◽  
Theoretical Predictions ◽  
Lumen Catheter ◽  
A New Technique

Recirculation is an important factor in single needle dialysis and, if high, can compromise treatment efficiency. To provide information regarding recirculation characteristics of access devices used in single needle dialysis, we have developed a new technique to characterise recirculation and have used this to measure the recirculation of a Terumo 15G fistula needle and a VasCath SC2300 single lumen catheter. The experimentally obtained results agreed well with those established clinically (8.5 ± 2.4% and 18.4 ± 3.4%). The experimental results have also demonstrated a dependence on access type, pump speeds and fistula flow rate. A comparison of experimental data with theoretical predictions showed that the latter exceeded those measured with the largest contribution being due to the experimental fistula.

The liquid blister test

2008 ◽  
Vol 464 (2099) ◽  
pp. 2887-2906 ◽  
Author(s):  
Julien Chopin ◽  
Dominic Vella ◽  
Arezki Boudaoud
Keyword(s):  
Surface Tension ◽  
Surface Energy ◽  
Vertical Displacement ◽  
Quantitative Agreement ◽  
Elastic Plates ◽  
Blister Test ◽  
Thin Liquid Layer ◽  
Theoretical Predictions ◽  
Thin Elastic Plates ◽  
Adhesive Forces

We consider a thin elastic sheet adhering to a stiff substrate by means of the surface tension of a thin liquid layer. Debonding is initiated by imposing a vertical displacement at the centre of the sheet and leads to the formation of a delaminated region or ‘blister’. This experiment reveals that the perimeter of the blister takes one of three different forms depending on the vertical displacement imposed. As this displacement is increased, we observe first circular, then undulating and finally triangular blisters. We obtain theoretical predictions for the observed features of each of these three families of blisters. The theory is built upon the Föppl–von Kármán equations for thin elastic plates and accounts for the surface energy of the liquid. We find good quantitative agreement between our theoretical predictions and experimental results, demonstrating that all three families are governed by different balances between elastic and capillary forces. Our results may bear on micrometric tapered devices and other systems, where elastic and adhesive forces are in competition.

The electro-deposition of silver on stationary and rotating glassy carbon discs

1977 ◽  
Vol 55 (23) ◽  
pp. 4037-4044 ◽  
Author(s):  
Remigio Germano Barradas ◽  
Stephen Fletcher ◽  
Sandor Szabo
Keyword(s):  
Experimental Data ◽  
Mass Transport ◽  
Glassy Carbon ◽  
Quantitative Model ◽  
Nucleation And Growth ◽  
Experimental Conditions ◽  
Electro Deposition ◽  
Transport Effects ◽  
Mass Transport Effects

The deposition of silver onto glassy carbon is described. The solution consisted of 10−2 M AgClO4 in 1.0 M HClO4. Experiments reveal the difficulties in trying to separate nucleation and growth phenomena from mass transport effects. A simple semi-quantitative model is proposed to explain the experimental data. It is also shown that the deposition reaction is not completely reversible under certain experimental conditions.

scholarly journals Bioinspired aerofoil adaptations: the next steps for theoretical models

2019 ◽  
Vol 377 (2159) ◽  
pp. 20190070 ◽  
Author(s):  
Lorna J. Ayton
Keyword(s):  
Experimental Data ◽  
Theoretical Models ◽  
Theoretical Modelling ◽  
Experimental Measurements ◽  
Far Field ◽  
Acoustic Analogy ◽  
Trailing Edge ◽  
Trailing Edge Noise ◽  
Theoretical Predictions ◽  
Field Noise

The extended introduction in this paper reviews the theoretical modelling of leading- and trailing-edge noise, various bioinspired aerofoil adaptations to both the leading and trailing edges of blades, and how these adaptations aid in the reduction of aerofoil–turbulence interaction noise. Attention is given to the agreement between current theoretical predictions and experimental measurements, in particular, for turbulent interactions at the trailing edge of an aerofoil. Where there is a poor agreement between theoretical models and experimental data the features neglected from the theoretical models are discussed. Notably, it is known that theoretical predictions for porous trailing-edge adaptations do not agree well with experimental measurements. Previous works propose the reason for this: theoretical models do not account for surface roughness due to the porous material and thus omit a key noise source. The remainder of this paper, therefore, presents an analytical model, based upon the acoustic analogy, to predict the far-field noise due to a rough surface at the trailing edge of an aerofoil. Unlike previous roughness noise models which focus on roughness over an infinite wall, the model presented here includes diffraction by a sharp edge. The new results are seen to be in better agreement with experimental data than previous models which neglect diffraction by an edge. This new model could then be used to improve theoretical predictions for far-field noise generated by turbulent interactions with a (rough) porous trailing edge. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.

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