Bryan's Factor for Truncated Spherical and Conical Shells

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
K. Y. Narasimhan
Keyword(s):  
Closed Form ◽  
Material Properties ◽  
Q Factor ◽  
Conical Shells ◽  
Galerkin Procedure ◽  
Modes Of Vibration

Closed-form expressions are derived for the Bryan's factor of truncated spherical and conical shells through a Galerkin procedure. Results lead to the value obtained by G. H. Bryan for the case of the ring, thereby demonstrating accuracy of the method. It is shown that the Bryan's factor depends only on the shape of the structure and the modes of vibration. The material properties are required to determine the resonating frequency and the Q-factor.

Multiple-Mode Input Shaping Sequences for Reducing Residual Vibrations

1994 ◽  
Author(s):  
B. Whitney Rappole ◽  
Neil C. Singer ◽  
Warren P. Seering
Keyword(s):  
Closed Form ◽  
Management System ◽  
Flexible Structures ◽  
Silicon Wafers ◽  
New Method ◽  
Input Shaping ◽  
Feed Forward ◽  
Multiple Mode ◽  
Modes Of Vibration

Abstract A closed-form method of calculating Input Shaping sequences for two modes of vibration is presented. The new method eliminates the optimization routines previously required to find the same solutions. Input Shaping is a feed forward method of reducing residual vibrations in flexible structures by convolving an Input Shaping sequence with a command profile. The two-mode sequences are installed on a four-axis robot used in the manufacture of silicon wafers — the Cassette Management System. The new sequences are found to significantly improve the performance of the system. In standard throughput tests, speed increases of 15%–25% were obtained on each axis while vibrations were simultaneously reduced by 20%–90%.

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.

A General Expression for the Welding Tendon Force

2021 ◽  
pp. 1-50
Author(s):  
Mitchell R. Grams ◽  
Patricio F. Mendez
Keyword(s):  
Closed Form ◽  
Material Properties ◽  
Closed Form Expression ◽  
Mathematical Treatment ◽  
Correction Factors ◽  
Temperature Dependent ◽  
Form Expression ◽  
Ongoing Research ◽  
Thin Sections ◽  
Tendon Force

Abstract This study presents a novel expression for the tendon force associated with residual stresses produced during welding of large, thin sections. A general engineering equation is presented as the combination of an closed form expression, based on idealized treatment, and correction factors to account for the effects of temperature dependent thermal and mechanical material properties. The closed form expression corresponds to the assumption of constant material properties. A rigorous mathematical treatment is utilized to derive explicit, exact expressions for the temperature dependent correction factors without the need for empirical correlations. The temperature dependent behaviour of materials is captured accurately using four dimensionless groups. The analysis was validated through numerical simulations with common structural grades of low-carbon steel, stainless steel, aluminum and titanium. The idealized treatment resulted in predictions with a mean difference of 18%, which was reduced to 7% by incorporating the correction factors. The remaining error is a systematic overestimate which can be attributed to compliance effects of the finite plate used in the simulations, and is the focus of ongoing research. The utility of applying the novel tendon force equation to problems in fabrication procedure design is demonstrated with an example predicting distortion during manufacturing of hollow structural sections.

Contact Stresses in Cables due to Tension and Torsion

1997 ◽  
Vol 64 (4) ◽  
pp. 935-939 ◽  
Author(s):  
K. Kumar ◽  
J. E. Cochran ◽  
J. A. Cutchins
Keyword(s):  
Closed Form ◽  
Material Properties ◽  
Contact Stresses ◽  
Single Strand ◽  
Fundamental Theory ◽  
Wire Ropes ◽  
Maximum Contact ◽  
Insight Into

The fundamental theory of wire ropes developed by Costello and Phillips is utilized to obtain closed-form expressions for maximum contact stresses in single strand cables with fibrous cores. These should be useful for gaining an insight into the influence of various parameters of the cable as well as the material properties on its strength and hence design.

Analytical modal analysis of thin-film flat lenses

2005 ◽  
Vol 219 (1) ◽  
pp. 55-59 ◽  
Author(s):  
H R Hamidzadeh ◽  
L Moxey
Keyword(s):  
Thin Film ◽  
Analytical Solution ◽  
Dynamic Response ◽  
Modal Analysis ◽  
Closed Form ◽  
Material Properties ◽  
Mathieu Equation ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Closed Form Solutions

The free vibrations of circular and elliptical thin-film lens are investigated. In particular, linear closed-form solutions for free vibrations of these structures were achieved and modal analysis was performed. The vibration response of the thin-film membranes were mathematically modelled using the Mathieu equation. Numerical results for various nodal diameters were computed. For the limited case, when an elliptical lens becomes circular, an excellent comparison was established with the available analytical solution. Experimental analyses were conducted to determine the effects of various parameters, such as material properties, membrane pre-strain rate, and the geometry, on natural frequency and mode shapes of these structures. The comparison verified the adequacy of linear solutions to predict the dynamic response of thin-film lenses.

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