Geometric analysis of the vibration of rubber wiper blade

Tsai Jung Chen, Ying Ji Hong

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

The purpose of this paper is to work out the theoretical aspects of the vibration problem of rubber wiper blade on convex windshield. Over the past 20 years, some 2-dimensional spring-mass models were presented in engineering science to simulate the vibration of rubber wiper blade on windshield. In this paper, we will consider the elasticity perspective on this 3-dimensional vibration problem. Our theoretical analysis suggests that there should exist two classes of vibration frequencies corresponding to "*-exact deformations (Class I)" and "*-closed deformations (Class II)". We prove mathematical theorems on the characterization of deformations of Class I. We also explain how elementary deformations of Class II can be constructed. We then deduce two mathematical formulas, for the vibration problem of rubber wiper blade on convex windshield, from our theoretical analysis. Our theoretical predictions are in almost perfect agreement with experimental data. One of the crucial steps of our analysis is a decomposition theorem motivated by the de Rham Cohomology and the Hodge Theory.

Original languageEnglish
Pages (from-to)491-516
Number of pages26
JournalTaiwanese Journal of Mathematics
Volume25
Issue number3
DOIs
Publication statusPublished - 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics

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