Size-dependent axisymmetric contact vibration analysis with couple stress

Xin Lv, Liao Liang Ke*, Sami El-Borgi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper investigates the contact vibration between a rigid spherical indenter and a half-space with hysteretic damping within the framework of the couple stress theory. Firstly, the static contact pressure is determined by using the integral least square approach. Subsequently, the dynamic contact pressure is obtained through the perturbation technology, and the dynamic contact displacement is obtained by employing the Hankel transform. Finally, the receptance is obtained and the dynamic contact stiffness is deduced by adopting approximate dynamic displacement boundary conditions under the assumption of a sufficiently small oscillation force. Parametric studies are presented to clarify the effects of the characteristic material length, Poisson's ratio, shear modulus, and internal friction on the reciprocal receptance and dynamic contact stiffness. The results obtained reveal that the size effect has a pronounced effect on the peak values of the dynamic contact stiffness and reciprocal receptance. Furthermore, the present work provides a useful theoretical framework for applying contact resonance microscopy techniques to micro-structured materials.

Original languageEnglish
Pages (from-to)286-309
Number of pages24
JournalApplied Mathematical Modelling
Volume133
DOIs
Publication statusPublished - Sept 2024
Externally publishedYes

Keywords

  • Contact vibration
  • Couple stress
  • Hankel transform
  • Perturbation method

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