This paper aims to investigate the free coupled flexural-torsional vibrations of a double piezoactive micro-cantilever probe. The probe consists of two identical Euler-Bernoulli microcantilevers with piezoelectric layers on top. The microcantilevers are connected by a rigid tip connection at their free ends. The probe in this study vibrates in two distinct modes: flexural mode or coupled flexural-torsional mode. The flexural mode refers to in-phase flexural vibrations of the two microcantilevers resulting in translation of the tip connection, while the coupled flexural-torsional mode refers to the coupled flexural-torsional vibrations of the microcantilevers resulting in the rotation of the tip connection. The latter is the main interest of this research. The governing equations of motion and boundary conditions are developed. Two uncoupled equations are realized for each microcantilever: one corresponding to the flexural vibrations and the other one corresponding to the torsional vibrations of the microcantilevers. The characteristic equations for both the flexural and the coupled flexural-torsional vibration modes are derived. The natural frequencies and the mode shapes are determined utilizing the orthogonality condition. Moreover, numerical and experimental investigations show that the coupled flexural-torsional fundamental frequency of the probe is dependent on the dimensional parameters including the length of the microcantilevers and the length of the tip connection.A macroscale structure for experimental validation is utilized. The first two natural frequencies of the flexural mode and the coupled flexural-torsional mode for each configurations of the structure are found. To that end, various length values for beams including 307.4, 343, 393.8, 444.6, and 495.4 mm are used. For each of these length values, the following tip connection length values are utilized: 50.8, 76.2, 101.6, 127, and 152.4 mm. Therefore, there is a total of 25 configurations for the structure. Similarly, the natural frequency corresponding to the coupled flexural-torsional vibrations of the beams, resulting in rotating modes of the tip connection, is calculated. The first two natural frequencies found for each mode of vibration for various configurations of the structure are shown in Tables 1 and 2.The coupled flexural-torsional fundamental frequency of the structure was shown to decrease with an increase in either the length of the cantilevers or the length of the tip connection. The experimental data verifies this trend that was found numerically. The experimentally found values for the coupled flexural-torsional fundamental frequencies are shown to be within 2 percent (average error) of the numerically found values.

Flexural-Torsional Free Vibration Analysis of a Piezoactive Double-Beam Afm Probe

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

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