Instrument Society of America, 20 Randall St., Apt. 5G, Providence, Rhode Island 02904, USA.
Ultramicroscopy. 2010 Jan;110(2):126-9. doi: 10.1016/j.ultramic.2009.10.009. Epub 2009 Oct 23.
In previous work we showed that the kinetostatic method is very effective in computing the increase in value of the spring constants of an AFM free (with or without added mass) and supported rectangular cantilever for higher mode oscillations relative to their values for natural vibration. We have considered in all previous cases that added mass is a concentrated one. However, the additional mass may be an extended one particularly in the case of a V-shaped cantilever. In this article we consider the influence of the constituent beam's (leg's) mutual skew and the altered position of the nodal points in the case when the attached extended triangular (trapezoid) mass of the V-shaped cantilever has a significant moment of rotational inertia and a center of this mass gravity located beyond the constituent beam end. We show that considering these effects in using the kinetostatic model yields results for the ratios of the spring constants at higher modes of oscillation and their values at the first frequency natural vibration for a V-shaped cantilever which are in good agreement with the thermomechanical noise amplitudes obtained by other researchers. This should prove helpful for the proper calibration of V-shaped cantilevers whose application with higher modes oscillation provides increased measurement sensitivity.
在之前的工作中，我们表明，对于更高阶振动，相对于自然振动的固有频率，动平衡法在计算 AFM 自由（带或不带附加质量）和支撑矩形悬臂的弹簧常数的增加值方面非常有效。在所有之前的案例中，我们都假设附加质量是集中的。然而，附加质量可能是扩展的，特别是在 V 形悬臂的情况下。在本文中，我们考虑了当 V 形悬臂的附加扩展三角形（梯形）质量具有显著的转动惯量和质量重心位于组成梁末端之外时，组成梁（腿）相互倾斜以及节点位置改变的情况对振动的影响。我们表明，在使用动平衡模型时考虑这些影响，会得到 V 形悬臂在更高阶振动模式下的弹簧常数比与第一频率固有振动的比值，与其他研究人员通过热机械噪声幅度获得的结果非常吻合。这对于正确校准 V 形悬臂非常有帮助，其在更高阶振动模式下的应用提供了更高的测量灵敏度。
