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

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  • Jun-Yi Sun

    (School of Civil Engineering, Chongqing University, Chongqing 400045, China
    Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, 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
    Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China)

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.

Suggested Citation

  • Jun-Yi Sun & Ning Li & Xiao-Ting He, 2023. "An Improved Mathematical Theory for Designing Membrane Deflection-Based Rain Gauges," Mathematics, MDPI, vol. 11(16), pages 1-32, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3438-:d:1212652
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    References listed on IDEAS

    as
    1. Yong-Sheng Lian & Jun-Yi Sun & Zhi-Hang Zhao & Xiao-Ting He & Zhou-Lian Zheng, 2020. "A Revisit of the Boundary Value Problem for Föppl–Hencky Membranes: Improvement of Geometric Equations," Mathematics, MDPI, vol. 8(4), pages 1-15, April.
    2. Xue Li & Jun-Yi Sun & Xiao-Chen Lu & Zhi-Xin Yang & Xiao-Ting He, 2021. "Steady Fluid–Structure Coupling Interface of Circular Membrane under Liquid Weight Loading: Closed-Form Solution for Differential-Integral Equations," Mathematics, MDPI, vol. 9(10), pages 1-24, May.
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