This article reports on the analysis of the vibration modes (central eigenfrequencies) observed on a dry steel sphere clamped between two planes, under static compression and subjected to an acoustic excitation. The experimental technique is based on the analysis of the ultrasonic resonance spectrum (RUS); compression or transverse excitations are used. Two types of vibrations are observed. The first occurring in the low frequency range corresponds to modes of movement conditioned by the contacts; the second corresponds to the internal, toroidal and spheroidal deformation modes. In this article we limit our research to the modes observed in the low frequency regime and our objective is to study the influence of the static force on the position of the peaks observed in the frequency spectra. In the case of a longitudinal excitation, only one mode is observed; the transverse excitation makes it possible to detect two modes. The experimental results are compared to theoretical calculations based on theoretical models of Hertz and Hertz-Mindlin, on a development of the JKR model based on adhesion due to Van der Waals forces. In this work, the mechanical coefficients are considered to be independent of time and we do not study the phenomena of hysteresis of these coefficients.

本文报告了对夹在两个平面之间的干钢球上观察到的振动模式（中心特征频率）的分析，在静态压缩和声激励下。实验技术基于对超声共振谱（RUS）的分析；使用压缩或横向激励。观察到两种类型的振动。第一个出现在低频范围内，对应于接触条件下的运动模式；第二个对应于内部、环形和球形变形模式。在本文中，我们将研究限制在低频范围内观察到的模式，我们的目标是研究静力对频谱中观察到的峰值位置的影响。在纵向激励的情况下，只观察到一种模式；横向激励可以检测两种模式。将实验结果与基于 Hertz 和 Hertz-Mindlin 理论模型的理论计算进行比较，基于基于范德华力粘附的 JKR 模型的发展。在这项工作中，机械系数被认为与时间无关，我们不研究这些系数的滞后现象。