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.

中文翻译：

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具有耦合应力的尺寸相关轴对称接触振动分析


本文在力偶应力理论的框架内研究了刚性球形压头和具有迟滞阻尼的半空间之间的接触振动。首先，采用积分最小二乘法确定静态接触压力。随后，通过摄动技术获得动态接触压力，并利用汉克尔变换获得动态接触位移。最后，在振动力足够小的假设下，采用近似动态位移边界条件，获得了接收力并推导了动态接触刚度。参数研究旨在阐明特征材料长度、泊松比、剪切模量和内摩擦对相互接收和动态接触刚度的影响。所得结果表明，尺寸效应对动态接触刚度和倒数承受力的峰值有显着影响。此外，目前的工作为将接触共振显微镜技术应用于微结构材料提供了有用的理论框架。