THE INTERFACE PROBLEM IN MODEL SEISMOLOGY

Geophysics ◽  
1968 ◽  
Vol 33 (3) ◽  
pp. 473-480 ◽  
Author(s):  
Fred Schwab ◽  
Robert Burridge
Keyword(s):  
Finite Thickness ◽  
Mathematical Formulation ◽  
Analytical Techniques ◽  
Experimental Results ◽  
Interface Problem ◽  
Bonding Layer ◽  
Contact Interface ◽  
Bonding Agents ◽  
Model Seismology ◽  
Theoretical Results

Many seismic problems involve interfaces. Seismic modeling provides a means of passing from the mathematical formulation to the solution of such problems when suitable analytical techniques are not available. Accurate interface formulations are necessary if modeling is to be as effective as possible in this role. Application of improved techniques has provided more accurate and detailed results than possible in the original work (Toksöz and Schwab, 1964) on model interface formulations. The present investigation was limited to butt‐joined, two‐dimensional models constructed with metallic sheets and epoxy bonding agents. Experimental results were first compared with those predicted by the simplest of “welded‐contact” theories—that which totally ignores the bonding layer. For a layer thickness of 0.007 cm, fair agreement was noted for frequencies below 125 kHz. New theoretical results were then predicted by taking the finite thickness and elastic properties of the bonding layer into consideration. The metal‐epoxy interfaces were assumed “welded‐contacts.” Irrespective of whether the formulation specified a perfectly elastic or an anelastic bonding material, the correlation between predicted and experimental results was quite poor. The disparity was much greater, over the entire frequency range, than that obtained from the formulation which totally ignored the bonding layer. All the welded‐contact interface formulations tested in this investigation were found unsatisfactory for highly accurate work. Based on the technique used to test the welded‐contact assumption, a mathematically accurate description of the interface was developed.

A Comparison of Theoretical and Experimental Results From Spherical Shells With a Single Radially Attached Nozzle

1967 ◽  
Vol 89 (3) ◽  
pp. 333-338 ◽  
Author(s):  
F. J. Witt ◽  
R. C. Gwaltney ◽  
R. L. Maxwell ◽  
R. W. Holland
Keyword(s):  
Spherical Shell ◽  
Internal Pressure ◽  
Experimental Results ◽  
Strain Gages ◽  
Spherical Shells ◽  
Axial Thrust ◽  
Outside Diameter ◽  
Theoretical Results

A series of steel models having single nozzles radially and nonradially attached to a spherical shell is presently being examined by means of strain gages. Parameters being studied are nozzle dimensions, length of internal nozzle protrusions, and angles of attachment. The loads are internal pressure and axial thrust and moment loadings on the nozzle. This paper presents both experimental and theoretical results from six of the configurations having radially attached nozzles for which the sphere dimensions are equal and the outside diameter of the attached nozzle is constant. In some instances the nozzle protrudes through the vessel.

scholarly journals The vibro-impact capsule system in millimetre scale: numerical optimisation and experimental verification

Meccanica ◽  
2020 ◽  
Vol 55 (10) ◽  
pp. 1885-1902
Author(s):  
Yang Liu ◽  
Joseph Páez Chávez ◽  
Jiajia Zhang ◽  
Jiyuan Tian ◽  
Bingyong Guo ◽  
...  
Keyword(s):  
Dynamical System ◽  
Mathematical Formulation ◽  
Path Following ◽  
Piecewise Smooth ◽  
Experimental Results ◽  
Scale Down ◽  
Speed Up ◽  
Small Bowel Endoscopy ◽  
Numerical Optimisation ◽  
Smooth Dynamical System

Abstract The vibro-impact capsule system has been studied extensively in the past decade because of its research challenges as a piecewise-smooth dynamical system and broad applications in engineering and healthcare technologies. This paper reports our team’s first attempt to scale down the prototype of the vibro-impact capsule to millimetre size, which is 26 mm in length and 11 mm in diameter, aiming for small-bowel endoscopy. Firstly, an existing mathematical model of the prototype and its mathematical formulation as a piecewise-smooth dynamical system are reviewed in order to carry out numerical optimisation for the prototype by means of path-following techniques. Our numerical analysis shows that the prototype can achieve a high progression speed up to 14.4 mm/s while avoiding the collision between the inner mass and the capsule which could lead to less propulsive force on the capsule so causing less discomfort on the patient. Secondly, the experimental rig and procedure for testing the prototype are introduced, and some preliminary experimental results are presented. Finally, experimental results are compared with the numerical results to validate the optimisation as well as the feasibility of the vibro-impact technique for the potential of a controllable endoscopic procedure.

Experimental Study on the Failure Criterion for Brittle Materials in Compression

2011 ◽  
Vol 320 ◽  
pp. 259-262
Author(s):  
Xu Ran ◽  
Zhe Ming Zhu ◽  
Hao Tang
Keyword(s):  
Thin Film ◽  
Experimental Study ◽  
Compressive Strength ◽  
Fracture Mechanics ◽  
Failure Criterion ◽  
Brittle Materials ◽  
Experimental Results ◽  
Experiment Study ◽  
Confining Stress ◽  
Theoretical Results

The mechanical behavior of multi-cracks under compression has become a very important project in the field of fracture mechanics and rock mechanics. In this paper, based on the previous theoretical results of the failure criterion for brittle materials under compression, experiment study is implemented. The specimens are square plates and are made of cement, sand and water, and the cracks are made by using a very thin film (0.1 mm). The relations of material compressive strength versus crack spacing and the lateral confining stress are obtained from experimental results. The experimental results agree well with the failure criterion for brittle materials under compression, which indicates that the criterion is effective and applicable.

Unbalance Response of a Dual Rotor System: Theory and Experiment

1993 ◽  
Vol 115 (4) ◽  
pp. 427-435 ◽  
Author(s):  
K. Gupta ◽  
K. D. Gupta ◽  
K. Athre
Keyword(s):  
System Theory ◽  
Transfer Matrix ◽  
Mode Shape ◽  
Reasonable Agreement ◽  
Complex Variables ◽  
Rotor System ◽  
Experimental Results ◽  
Unbalance Response ◽  
Theoretical Results ◽  
Theory And Experiment

A dual rotor rig is developed and is briefly discussed. The rig is capable of simulating dynamically the two spool aeroengine, though it does not physically resemble the actual aeroengine configuration. Critical speeds, mode shape, and unbalance response are determined experimentally. An extended transfer matrix procedure in complex variables is developed for obtaining unbalance response of dual rotor system. Experimental results obtained are compared with theoretical results and are found to be in reasonable agreement.

An Assessment of the Value of Theory in Predicting Gas-Bearing Performance

1961 ◽  
Vol 83 (2) ◽  
pp. 195-200 ◽  
Author(s):  
S. Cooper
Keyword(s):  
Steady State ◽  
Slip Velocity ◽  
Reynolds Equation ◽  
Energy Equation ◽  
Experimental Methods ◽  
Experimental Results ◽  
Theoretical Investigations ◽  
Gas Bearing ◽  
Theoretical Results

The object of the paper is to indicate the value of theoretical investigations of hydrodynamic finite bearings under steady-state conditions. Methods of solution of Reynolds equation by both desk and digital computing, and methods of stabilizing the processes of solution, are described. The nondimensional data available from the solutions are stated. The outcome of an attempted solution of the energy equation is discussed. A comparison between some theoretical and experimental results is shown. Experimental methods employed and some difficulties encountered are discussed. Some theoretical results are given to indicate the effects of the inclusion of slip velocity, stabilizing slots, and a simple case of whirl.

Vibratory Feeding by Nonsinusoidal Vibration—Optimum Wave Form

1985 ◽  
Vol 107 (2) ◽  
pp. 188-195 ◽  
Author(s):  
S. Okabe ◽  
Y. Kamiya ◽  
K. Tsujikado ◽  
Y. Yokoyama
Keyword(s):  
Experimental Results ◽  
Wave Form ◽  
Velocity Wave ◽  
The Mean ◽  
Straight Lines ◽  
Vibratory Conveyor ◽  
Theoretical Results ◽  
Vibratory Feeding

This paper presents the conveying velocity on a vibratory conveyor whose track is vibrated by nonsinusoidal vibration. The velocity wave form of the vibrating track is approximated by six straight lines, and five distortion factors of the wave form are defined. Considering the modes of motion of the particle, the mean conveying velocity is calculated for various conditions. Referring to these results, the optimum wave form is clarified analytically. The theoretical results show that the mean conveying velocity is considerably larger than that of ordinary feeders if the proper conveying conditions are chosen. The theoretical results are confirmed by experimental results.

Pneumatic Mechanism of Gas Cooled or Heated Through a Throttle Orifice

2011 ◽  
Vol 141 ◽  
pp. 408-412 ◽  
Author(s):  
Yao Bao Yin ◽  
Ling Li
Keyword(s):  
Equation Of State ◽  
Total Energy ◽  
Negative Energy ◽  
Experimental Results ◽  
Attractive Force ◽  
Positive Energy ◽  
Real Gas ◽  
Thomson Coefficient ◽  
Theoretical Results ◽  
Conversion Temperature

The mechanism of gas cooled or heated through a pneumatic throttle orifice is analyzed. Supposing the total energy of the gas is constant, if the force between the molecules does positive energy, it makes gas heated; if it does negative energy, it makes gas cooled. The conversion temperature of gas is an evaluation parameter for repulsive or attractive force. It has utilized Joule-Thomson coefficient and real gas equation of state to obtain the characteristics of conversion temperature, and the relationships between the molecules distance and the phenomenon of gas cooled or heated after throttle at normal temperature by the conversion characteristics are achieved. The experimental results agreed well with the theoretical results.

Part II: Steady aerofoil-spoiler characteristics

1987 ◽  
Vol 91 (908) ◽  
pp. 359-366
Keyword(s):  
Separated Flow ◽  
Experimental Results ◽  
Surface Singularity ◽  
Separation Region ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Singularity Method ◽  
Total Head ◽  
Low Speeds ◽  
Theoretical Results

Summary A surface singularity method has been formulated to predict two-dimensional spoiler characteristics at low speeds. Vorticity singularities are placed on the aerofoil surface, on the spoiler surface, on the upper separation streamline from the spoiler tip and on the lower separation streamline from the aerofoil trailing edge. The separation region is closed downstream by two discrete vortices. The flow inside the separation region is assumed to have uniform total head. The downstream extent of the separated wake is an empirical input. The flows both external and internal to the separated regions are solved. Theoretical results have been obtained for a range of spoiler-aerofoil configurations which compare reasonably with experimental results. The model is deficient in that it predicts a higher compression ahead of the spoiler than obtained in practice. Furthermore, there is a minimum spoiler angle below which a solution is not possible; it is thought that this feature is related to the physical observation that at small spoiler angles, the separated flow from the spoiler reattaches on the aerofoil upper surface ahead of the trailing edge.

A Possible Criterion for Cavitation Inception on Hemispherical Headforms

1981 ◽  
Vol 103 (4) ◽  
pp. 577-582
Author(s):  
B. R. Parkin
Keyword(s):  
Mathematical Formulation ◽  
Experimental Results ◽  
Quantitative Criterion ◽  
Cavitation Inception ◽  
Sequence Of Events ◽  
Future Publication

The present paper reviews several pertinent papers about the onset of bubble-ring cavitation on hemispherical headforms in which a laminar bubble is present. From this review, a likely sequence of events for cavitation inception, or desinence, can be discerned. When this sequence is postulated, the observational basis for each event is discussed. Once the physical aspects of the inception process have been noted, a mathematical formulation of key relationships required to establish an inception criterion can be undertaken. From these results, a quantitative criterion for the inception of bubble ring cavitation is stated and we give a discussion which interprets this possible inception criterion for future use. The use of this criterion in a theory of inception and a comparison of analytical and experimental results is left to a future publication.

scholarly journals Conducting Non-Adaptive Experiments in a Live Setting: A Bayesian Approach to Determining Optimal Sample Size

2019 ◽  
Author(s):  
Nandan Sudarsanam ◽  
Ramya Chandran ◽  
Daniel D. Frey
Keyword(s):  
Statistical Learning ◽  
Optimal Allocation ◽  
Analytical Techniques ◽  
Optimal Level ◽  
Base Case ◽  
Allocation Of Resources ◽  
Worst Case ◽  
Optimal Sample Size ◽  
Optimal Sample ◽  
Theoretical Results

Abstract This research studies the use of predetermined experimental plans in a live setting with a finite implementation horizon. In this context, we seek to determine the optimal experimental budget in different environments using a Bayesian framework. We derive theoretical results on the optimal allocation of resources to treatments with the objective of minimizing cumulative regret, a metric commonly used in online statistical learning. Our base case studies a setting with two treatments assuming Gaussian priors for the treatment means and noise distributions. We extend our study through analytical and semi-analytical techniques which explore worst-case bounds and the generalization to k treatments. We determine theoretical limits for the experimental budget across all possible scenarios. The optimal level of experimentation that is recommended by this study varies extensively and depends on the experimental environment as well as the number of available units. This highlights the importance of such an approach which incorporates these factors to determine the budget.

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