On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

1978 ◽  
Vol 100 (3) ◽  
pp. 442-444 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Performance Characteristics ◽  
Gas Bearing ◽  
Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

scholarly journals A New Closed-Form Solution of the Side Abutment Pressure Distribution of Roadway

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Liang Cheng ◽  
Yidong Zhang
Keyword(s):  
Plastic Zone ◽  
Pressure Distribution ◽  
Closed Form ◽  
Abutment Pressure ◽  
Closed Form Solution ◽  
Evaluation Process ◽  
Friction Angle ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Roadway Stability

Instability of coal wall is one of the hot-button and difficult issues in the study of coal mine ground control. The shallow side coal of roadway in the coal measures is usually weak and consequently easy to bring about failure. Hence, the side abutment pressure redistributes and dramatically influences the roadway stability. Since the previous closed-form solutions of the side abutment pressure do not take into account all the necessary parameters which include the properties of the coal and the interface between coal and roof/floor, the roadway height, and the support strength, a mechanical model is established based on the equilibrium of the plastic zone, and a new closed-form solution is derived in this paper. Moreover, a numerical investigation is conducted to validate the accuracy of the closed-form solution. The numerical results of the side abutment pressure distribution are in good agreement with the closed-form solution. Afterwards, a parametric analysis of the width of the plastic zone is carried out, and the results show that the width of the plastic zone is nearly negatively linearly correlated with the friction angle and the cohesion of the coal, the interfacial cohesion, and the support strength. By contrast, it is positively linearly correlated with the roadway height and negatively exponentially correlated with the interfacial friction angle. The results obtained in the present study could be useful for the evaluation process of roadway stability.

A New Accurate Closed-Form Analytical Solution for Junction Temperature of High-Powered Devices

2014 ◽  
Vol 136 (1) ◽  
Author(s):  
J. H. L. Ling ◽  
A. A. O. Tay
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Material Properties ◽  
Heat Dissipation ◽  
Field Effect Transistors ◽  
Closed Form Solution ◽  
Form Solution ◽  
Junction Temperature ◽  
Design Parameters ◽  
Closed Form Analytical Solution

The peak junction temperature has a profound effect on the operational lifetime and performance of high powered microwave devices. Although numerical analysis can help to estimate the peak junction temperature, it can be computationally expensive and time consuming when investigating the effect of the device geometry and material properties on the performance of the device. On the other hand, a closed-form analytical method will allow similar studies to be done easily and quickly. Although some previous analytical solutions have been proposed, the solutions either require over-long computational times or are not so accurate. In this paper, an accurate closed-form analytical solution for the junction temperature of power amplifier field effect transistors (FETs) or monolithic microwave integrated circuits (MMICs) is presented. Its derivation is based on the Green's function integral method on a point heat source developed through the method of images. Unlike most previous works, the location of the heat dissipation region is assumed to be embedded under the gate. Since it is a closed-form solution, the junction temperature as well as the temperature distribution around the gate can be easily calculated. Consequently, the effect of various design parameters and material properties affecting the junction temperature of the device can be easily investigated. This work is also applicable to multifinger devices by employing superposition techniques and has been shown to agree well with both numerical and experimental results.

Determination of a closed-form solution for the multidimensional transport equation using a fractional derivative

2002 ◽  
Vol 29 (10) ◽  
pp. 1141-1150 ◽  
Author(s):  
Jorge Zabadal ◽  
Marco Túllio Vilhena ◽  
Cynthia Feijó Segatto ◽  
Rúben Panta Pazos
Keyword(s):  
Fractional Derivative ◽  
Transport Equation ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution

scholarly journals Use of a Strongly Nonlinear Gambier Equation for the Construction of Exact Closed Form Solutions of Nonlinear ODEs

2007 ◽  
Vol 2007 ◽  
pp. 1-25
Author(s):  
M. P. Markakis
Keyword(s):  
Closed Form ◽  
Initial Conditions ◽  
Closed Form Solution ◽  
Form Solution ◽  
Nonlinear Odes ◽  
Analytical Technique ◽  
Closed Form Solutions ◽  
Strongly Nonlinear ◽  
Parameter Values

We establish an analytical method leading to a more general form of the exact solution of a nonlinear ODE of the second order due to Gambier. The treatment is based on the introduction and determination of a new function, by means of which the solution of the original equation is expressed. This treatment is applied to another nonlinear equation, subjected to the same general class as that of Gambier, by constructing step by step an appropriate analytical technique. The developed procedure yields a general exact closed form solution of this equation, valid for specific values of the parameters involved and containing two arbitrary (free) parameters evaluated by the relevant initial conditions. We finally verify this technique by applying it to two specific sets of parameter values of the equation under consideration.

Determination of Closed Form Solution for Acceptance Sampling Using ANN

2005 ◽  
Vol 11 (1) ◽  
pp. 43-61 ◽  
Author(s):  
D. Vasudevan ◽  
V. Selladurai ◽  
P. Nagaraj
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Acceptance Sampling

Elastomer Seal With Frictional Contact: Analytical Solution

2013 ◽  
Author(s):  
Moosa S. M. Al-Kharusi ◽  
Sayyad Zahid Qamar ◽  
Tasneem Pervez ◽  
Maaz Akhtar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Numerical Models ◽  
Fluid Pressure ◽  
Closed Form Solution ◽  
Field Conditions ◽  
Design Parameters ◽  
Sealing Pressure ◽  
Elastomer Seal

Main motivation for this work is the need for performance evaluation of swelling (and inert) elastomer seals used in petroleum applications. Closed-form (analytical) solutions are derived for sealing pressure distribution along the elastomer seal as a function of material properties of the elastomer, seal geometry and dimensions, seal compression, and differential fluid pressure acting on the seal ends. Seal performance is also modeled and simulated numerically. Good agreement between analytical and numerical results gives confidence that the analytical solution can be used for reliable prediction of sealing behavior of the elastomer. Detailed investigation is then carried out to find out the effect of variation in seal design parameters on seal performance. For both analytical and numerical models, properties of the seal material at various stages of swelling are needed. Therefore, a series of experiments were also designed and conducted to study the effect of swelling on mechanical properties (E, G, K, and ν) of the sealing material. One major finding is that sealing pressure distribution along the seal is not constant but varies nonlinearly depending on seal parameters and loading conditions, with maximum sealing pressure occurring at the center of the seal length. Longer seals are not necessarily better; after a certain seal length, sealing pressure reaches a steady value for a given set of field conditions. As expected, higher seal compression gives higher sealing pressure. Seal compression can be increased either by tubular expansion or by selecting an elastomer that swells more, or a combination of the two. Experimental evaluation of swelling-elastomer seal performance can be very costly, and is not even possible in many cases. Numerical simulations, if validated, can be more convenient, but computational effort and cost can be high as simulations have to be run for each set of conditions. Analytical approach presented here not only gives an elegant closed-form solution, but can give reasonably accurate and much faster prediction of elastomer performance under various actual oil and gas field conditions.

Formulation of surface temperature for laser evaporative pulse heating: The time exponentially decaying pulse case

2002 ◽  
Vol 216 (3) ◽  
pp. 289-299 ◽  
Author(s):  
B S Yilbas ◽  
M Kalyon
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Solid Substrate ◽  
Form Solution ◽  
Solution Temperature ◽  
Heating Process ◽  
Pulse Parameter ◽  
Pulse Profile ◽  
Transform Method

Modelling of the laser heating process is fruitful, since it enhances the understanding of the physical processes involved and minimizes the experimental cost. In the present study, an analytical solution for the temperature distribution inside the solid substrate is obtained using a Laplace transform method. A time exponentially decaying laser pulse profile is introduced in the analysis. The phase change process and recession velocity are accommodated to account for the evaporation at the surface. The closed-form solution obtained is compared with the analytical solution obtained previously for a conduction limited heating case. It is found that the closed-form solution obtained from the present study reduces to a previously obtained analytical solution when the pulse parameter, β∗, is set to zero in the closed-form solution. Temperature predictions from simulations agree well with the results obtained from the closed-form solution.

Determination of Eigenstresses from Curvature Data

1992 ◽  
Vol 276 ◽  
Author(s):  
Mauro Ferrari ◽  
Marie Weber
Keyword(s):  
Structural Analysis ◽  
Closed Form ◽  
Mechanical Systems ◽  
Closed Form Solution ◽  
Form Solution ◽  
Curvature Measurements

ABSTRACTCurvature measurements are generally employed in conjunction with elementary structural analysis to estimate deposition stresses in miniaturized electro-mechanical systems. In this paper the validity of this procedure is discussed by presenting a closed form solution for a bilayer subject to nonuniform intrinsic straining, and comparing the exact stress-curvature relations with the oft-used formulae of Stoney and Brenner-Senderoff.

Sign in / Sign up

Export Citation Format

Share Document