Received: 7 January 2019 Revised: 14 May 2019 Accepted: 3 June 2019 DOI: 10.1002/zamm.201900009 REVIEW Review of applications of self-excited oscillations to highly sensitive vibrational sensors Hiroshi Yabuno 1-1-1, Ten-no-dai, Tsukuba, Ibaraki, 305-8573, Japan Correspondence Hiroshi Yabuno, 1-1-1, Ten-no-dai, Tsukuba, Ibaraki, 305-8573, Japan. Email: yabuno@esys.tsukuba.ac.jp Funding information Grant-in-Aid for Scientific Research A, Grant/Award Number: No. 16H02318; Mit- sutoyo Association of Science and Technology Vibrational sensors with resonators are suited for online monitoring because of their fast response and ability to measure instantly and continuously. Also, their miniatur- ization realizes much higher resolution. In this review, we begin by discussing sensor resolution based on the natural frequency shift of the resonator. For mass and stiffness sensing, the detection method for the natural frequency shift by self-excited oscillation is characterized comparing with that by external excitation. Self-excited oscillation automatically compensates for the viscous damping effects of the environment on the resonators, thus ensuring direct and accurate detection of the natural frequency shift. Another application of self-excited oscillation is to viscometers. Instead of detecting the natural frequency shift, this system detects the critical feedback gain to generate self-excited oscillation. This is important for measuring very high viscosity, where the peak of the frequency response curve is ambiguous or does not exist, meaning the Q value cannot be estimated from such curves. Another method, introduced for ultra- sensitive mass sensing, is based on the eigenmode shift in multiple weakly coupled resonators. In this system, the self-excitation compensates for the viscous damping effects to enable direct detection of the eigenmode shift. KEYWORDS atomic force microscope, mass sensor, mode localization, self-excited, oscillation, viscometer MSC (2010) 00-xx 1 INTRODUCTION Self-excited oscillation in dynamical systems has attracted interest for a long time because its resonance mechanism is essen- tially different from that of harmonic resonance under external excitation. [46] While the response frequency of an externally excited resonator equals the excitation frequency regardless of the natural frequency of the resonator, the response frequency of the self-excited resonator actually equals the natural frequency of the resonator when the response amplitude is small. Further- more, while the steady-state amplitude at resonance under external excitation mainly depends on viscous damping, the response amplitude of the self-excited resonator is not determined by viscous damping but by the nonlinearity of the resonator. To main- tain resonance by external excitation when the natural frequency of the resonator varies, the external excitation frequency has to be tuned according to the deviation. However, for a self-excited resonator, positive velocity feedback generates and main- tains the resonance without tuning. Systems that use this characteristic of self-excited resonators are called autoresonant. [4] For example, vibrating machines that perform ultrasonically assisted cutting use autoresonance because the resonance is maintained despite the varying cutting load. [5] Many applications of autoresonance have been developed. [38–40] Highly accurate vibrational Z Angew Math Mech. 2019;e201900009. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 of 13 www.zamm-journal.org https://doi.org/10.1002/zamm.201900009