An Improved Mathematical Theory for Designing Membrane Deflection-Based Rain Gauges

Jun-Yi Sun (), Ning Li and Xiao-Ting He
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Jun-Yi Sun: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Ning Li: School of Civil Engineering, Chongqing University, Chongqing 400045, China
Xiao-Ting He: School of Civil Engineering, Chongqing University, Chongqing 400045, China

Mathematics, 2023, vol. 11, issue 16, 1-32

Abstract: This paper is devoted to developing a more refined mathematical theory for designing the previously proposed membrane deflection-based rain gauges. The differential-integral equations governing the large deflection behavior of the membrane are improved by modifying the geometric equations, and more accurate power-series solutions of the large deflection problem are provided, resulting in a new and more refined mathematical theory for designing such rain gauges. Examples are presented to illustrate how to analyze the convergence of the power-series solutions and how to numerically calibrate membrane deflection-based linear rain gauges. In addition, some important issues are demonstrated, analyzed, and discussed, such as the superiority of the new mathematical theory over the old one, the reason why the classical geometric equations cause errors, and the influence of changing design parameters on the input–output relationships of rain gauges.

Keywords: conductive membrane; transversely loading; axisymmetric deformation; large deflection; power-series solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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