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.

scholarly journals A closed-form analytical solution for the valuation of convertible bonds with constant dividend yield

2006 ◽  
Vol 47 (4) ◽  
pp. 477-494 ◽  
Author(s):  
Song-Ping Zhu
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Analytical Formula ◽  
Solution Process ◽  
Closed Form Solution ◽  
Approximate Solutions ◽  
Convertible Bonds ◽  
Form Solution ◽  
Dividend Yield ◽  
Closed Form Analytical Solution

AbstractIn this paper, a closed-form analytical solution for pricing convertible bonds on a single underlying asset with constant dividend yield is presented. A closed-form analytical formula has apparently never been found for American-style convertible bonds (CBs) of finite maturity time although there have been quite a few approximate solutions and numerical approaches proposed. The solution presented here is written in the form of a Taylor's series expansion, which contains infinitely many terms, and thus is completely analytical and in a closed form. Although it is only for the simplest CBs without call or put features, it is nevertheless the first closed-form solution that can be utilised to discuss convertibility analytically. The solution is based on the homotopy analysis method, with which the optimal converting price has been elegantly and temporarily removed in the solution process of each order, and consequently, the solution of a linear problem can be analytically worked out at each order, resulting in a completely analytical solution for the optimal converting price and the CBs' price.

Design and Analysis of Automotive Serpentine Belt Drive Systems for Steady State Performance

1997 ◽  
Vol 119 (2) ◽  
pp. 162-168 ◽  
Author(s):  
R. S. Beikmann ◽  
N. C. Perkins ◽  
A. G. Ulsoy
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Belt Drive ◽  
Automotive Engine ◽  
Theoretical Predictions ◽  
Serpentine Belt ◽  
Drive Systems

Serpentine belt drive systems with spring-loaded tensioners are now widely used in automotive engine accessory drive design. The steady state tension in each belt span is a major factor affecting belt slip and vibration. These tensions are determined by the accessory loads, the accessory drive geometry, and the tensioner properties. This paper focuses on the design parameters that determine how effectively the tensioner maintains a constant tractive belt tension, despite belt stretch due to accessory loads and belt speed. A nonlinear model predicting the operating state of the belt/tensioner system is derived, and solved using (1) numerical, and (2) approximate, closed-form methods. Inspection of the closed-form solution reveals a single design parameter, referred to as the “tensioner constant,” that measures the effectiveness of the tensioner. Tension measurements on an experimental drive system confirm the theoretical predictions.

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.

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.

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.

Application of Artificial Neural Network to Multi-Variables Regression for Estimations of J-Integral for Surface Cracked Pipes

2020 ◽  
Author(s):  
Youn-Young Jang ◽  
Nam-Su Huh ◽  
Ik-Joong Kim ◽  
Cheol-Man Kim ◽  
Young-Pyo Kim
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Closed Form ◽  
Material Properties ◽  
Closed Form Solution ◽  
Form Solution ◽  
J Integral ◽  
Loading Conditions ◽  
Tabular Form ◽  
J Estimation

Abstract Crack assessment for pipe components of a nuclear power plant or oil/gas pipeline is one of the essential procedures to ensure safe operation services. To assess cracked pipes, J-integral has been considered as a theoretically robust and useful elastic-plastic fracture parameter, so that the estimations of J-integral for various pipe geometries, material properties and loading conditions are highly needed. For this reason, many engineering predictive solutions for J-estimations based on finite element (FE) analyses have been developed. Generally, many engineering predictive solutions have been suggested as a tabular-form or closed-form. Among them, the closed-form solution is more preferred than a tabular-form solution for its convenience when many lots of interpolation are required to use it. However, the accuracy of the closed-form solution tends to be significantly reduced as the number of design parameters increases. Moreover, since there is no strict rule to define the form of functions as well, the accuracy of the closed-form solution is inevitably dependent on the rule of thumb. Therefore, it is highly required to suggest a new approach for J-estimation of cracked pipes with various geometries, material properties and loading conditions. In this paper, we propose an efficient approach based on a machine learning technique to estimate J-integral for surface cracked pipes with various geometric sizes and material properties under axial displacement loading condition. Firstly, parametric FE analysis studies were systematically performed to produce the coefficients representing the engineering J-estimation for the corresponding cracked pipe. Secondly, artificial neural network (ANN) models based on deep multilayer perceptron technique were trained based on FE results. The five input neurons (pipe geometries and material properties) and the two output neurons (the coefficients representing the engineering J-estimation) were considered. Lastly, the accuracy of the trained ANN model was studied by comparing to that of the closed-form solution from multi-variable regressions.

Closed-Form Steady-State Response Solution of the Twin Rotor Damper and Experimental Validation

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Richard Bäumer ◽  
Uwe Starossek
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Parameters ◽  
Control Force ◽  
Steady State Response ◽  
Active Mass ◽  
State Response ◽  
Twin Rotor

In previous research, the twin rotor damper (TRD), an active mass damper, was presented including control algorithms for monofrequent vibrations. In a preferred mode of operation, the continuous rotation mode, two eccentric masses rotate in opposite directions about two parallel axes with a mostly constant angular velocity. The resulting control force is harmonic. Within this paper, the steady-state response of a single-degree-of-freedom (SDOF) oscillator subjected to a harmonic excitation force with and without the TRD is studied. A closed-form solution is presented and validated experimentally. It is shown that the TRD provides damping to the SDOF oscillator until a certain frequency ratio is reached. The provided damping is not only dependent on the design parameters of the TRD but also depends on the steady-state vibration amplitude. The solution serves as a powerful design tool for dimensioning the TRD. The analytical closed-form solution is applicable for other active mass dampers.

An analytical solution for jointed tunnel linings in elastic soil or rock

2008 ◽  
Vol 45 (11) ◽  
pp. 1572-1593 ◽  
Author(s):  
Hany El Naggar ◽  
Sean D. Hinchberger
Keyword(s):  
Finite Element ◽  
Analytical Solution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Segmental Lining ◽  
Sophisticated Method ◽  
Walled Cylinder ◽  
Elastic Soil

This paper presents a closed-form solution for tunnel linings that can be idealized as an inner jointed segmental lining and an outer thick-walled cylinder embedded in a homogeneous infinite elastic soil or rock. Solutions for moment and thrust have been derived for cases involving slip and no slip at the lining–ground and lining–lining interfaces. In addition, the closed-form solution is verified by comparing it with finite element results where it is shown to agree well with this more sophisticated method of analysis.

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