Van der Pol type self-excited micro-cantilever probe of atomic force microscopy

Abstract

We pr （ ，pose a van der Po1 − type self − excited cantilever beam わy positive velocity feedback and nonli 【 〕 ear feedback ． Self − excited oscillation keeps the resonant condition indeper 】dent of the mQdulation of system p 乱 rameters and the resonance chaTacteristic o 正 self − excited oscillation is suitable to raalize aut 〔 ， ． resonance machines such as AFM micro − cautilever proble ． Because the arnp 巨tude of self − excited oscMation grows w 圭 th tirl ユe ， a special control method i8 required for the amplitude controL To this end ， we propose the application of the nonlineur dynamics of van der Pol osci11ator ． Making ug． e of thc characteristic of a stacked − typc piezoelectricactuator ， we demeilstrate that the alnplitude control ｛ユ f a czntilevcr beam by using only integril controller without d正 f〔 erential controller ． We show the equati ⊂ 旧 of motiDn il ユ whlch the nonhnear effect is taken jnto account alld the averaged equation 、 vhich is derived by applying the method of mul 七 iple scales ． The bifurcation d壬 agram is theorctically descrlbed， Then ， it isclarihcd that the amplitude of the cantilever beam can be controlled by setting the nonlinear feedback guin ． Furthermore ， a van der Po 卜 type self excited 〔 ： antilever beam is rea ！ 正 zed by using a simple apParatus and the validity of amplitude cDntrol method

On Nonlinear Response Near-Half Natural Frequency of Electrostatically Actuated Microresonators

“…Their equation was developed by¯rst assuming that the fringe correction factor function could be described in the same form as the MeijsÀFokkema correction (6). They then numerically computed the capacitance per unit length of a thick and narrow beam for di®erent values of width and thickness.…”

Amplitude Control in a van der Pol-Type Self-Excited AFM Microcantilever

“…To achieve such a sufficiently small and steady vibration amplitude of the cantilever used in this study, we produced a microcantilever with vibration characteristics that are equivalent to van der Pol-type self-excited oscillation using linear feedback and nonlinear feedback (6) (7) . Van der Pol-type self-excited oscillation is well known to have steady state vibration with finite amplitude because of its nonlinearity (8) .…”

“…The condition in which Φ 3 can have a solution (solvability condition) is obtainable using Φ 1 (7) .…”

Self-excited coupled-microcantilevers for mass sensing

“…Self-excited coupled-microcantilevers for mass sensing Daichi Endo, 1 Hiroshi Yabuno, 1,a) Keiichi Higashino, 2 Yasuyuki Yamamoto, 3 and Sohei Matsumoto 4 1 Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba Science City 305-8573, Japan This paper reports ultrasensitive mass detection based on the relative change in the amplitude ratio of the first mode oscillation using self-excited coupled microcantilevers. The method proposed and demonstrated using the macrocantilevers in the previous study can measure eigenstate shifts caused by objects with high accuracy without being affected by the viscous damping effect of measurement environments.…”

“…In order to overcome these difficulties in the detection of the natural frequency, a method using self-excited oscillation produced through the velocity feedback of a cantilever has been utilized. 1,13,14 On the other hand, it is known that the method based on the eigenstate shift in coupled cantilevers 15 has better accuracy compared to based on the conventional natural frequency shift. 16,17 The eigenstate has been identified from the magnitude ratio of the resonance peak of the frequency response curve in the coupled cantilevers under the external or forced excitation.…”