Effect of tip length and normal and lateral contact stiffness on the flexural vibration responses of atomic force microscope cantilevers

Control of MEMS Vibration Modes With Pulsed Digital Oscillators: Part I—Theory

“…The system (9) is subjected to pulsed excitation given by the expressions (14) . Between two sampling instants, the resonator moves freely, and at each sampling event its velocity is instantaneously changed by the applied delta-pulse.…”

“…In gravimetric sensors, the use of higher order modes generally serves to increase the sensitivity to mass changes, whereas it is desired in gyroscopes to avoid the activation of certain resonant modes of the inertial mass [13]. Moreover, the activation of higher vibration modes to increase performance has been also reported in atomic force microscopes [14], [15] and in piezoelectric sensors and actuators [16], where electrodes have been specifically designed to activate certain modes. Thus, depending on the specific application, the selective activation of different spatial vibration modes of a mechanical resonator can be one way to improve performance for a large number of MEMS sensors [17].…”

Size-Dependent Resonant Frequency and Flexural Sensitivity of Atomic Force Microscope Microcantilevers Based on the Modified Strain Gradient Theory

“…Chang et al [12] investigated the effect of normal damping using a set of springs and dashpots and ignoring the influences of the contact position and tip moment of inertia. The influence of tip length and contact stiffness on the flexural vibration response of AFM rectangular cantilevers was studied by Wu et al [13] Lin and Wang [14] developed an analytical model for a cantilever with an eccentric tip. Lee et al [15] predicted the flexural sensitivity of a V-shaped AFM microcantilever including the effects of the cantilever slope and interaction forces.…”

Vibration Responses of Atomic Force Microscope Cantilevers

“…Chang et al (Chang & Chu, 2003) found an analytical solution of flexural vibration responses on tapped AFM cantilevers, and obtained the resonance frequency at arbitrary dimensions and tip radii. Wu et al (Wu, et al, 2004) demonstrated a closed-form expression for the sensitivity of vibration modes using the relationship between the resonant frequency and contact stiffness of the cantilever and the sample. Horng ) developed an analytical solution to deal with the flexural vibration problem of AFM cantilever during a nanomachining process by using the modal superposition method.…”