1007.0813 (Saragosa Silvano)

Mathematical model of Lame Problem for Simplified Elastic Theory applied
to Controlled-Clearance Pressure Balances    [PDF]

Saragosa Silvano

This paper is based on the original work of the master degree thesis [1] and
also represents a revision of the models and their correlations with the
analytical solutions given by other authors in previous publications from 2003
to 2007. All the publications from 2003 to 2007 about simplified analytical
methods applied to controlled-clearance pressure balances are not original
works (with some errors) based on the thesis[1]. The analysis described in this
paper begins with the mathematical model of thick-walled cylinder applied to
the Mechanical theory of elastic equilibrium [5] for the formulation of the so
called Simplified Elastic Theory which represents an analytical approach for
the study of pressure balances. This analysis is known as the Lame problem. The
solution of the The Lame Problem is used to determine the pressure distortion
coefficient for the controlled-clearance pressure balances. This analysis
includes the case of pressure balances with the cylinder made up of two
materials (used for high pressure measurements) and completes the literature of
the simplified analytical methods applied to the pressures balances. With two
new formulae (eqs. 25-31) it is possible to directly evaluate the jacket
pressure distortion coefficient nj of controlled-clearance pressure balances
with the cylinder made up of both single material and two materials.

View original: http://arxiv.org/abs/1007.0813