Dynamics of self-driven microcantilevers

Abstract

The small amplitude thermal vibrations of the microcantilever of an atomic force microscope can be enhanced via a delayed feedback system. This is verified experimentally for a triangular cantilever, and modeled theoretically as a boundary value problem resulting in a second order functional differential equation for the temporal behavior of the cantilever. The eigenvalues of the resulting delay differential equation describing the transverse vibrations of the cantilever are calculated and analyzed. These values are compared with the corresponding resonant frequencies predicted by a point mass model and with the experimentally observed values.

An experimental investigation of analog delay generation for dynamic control of microsensors and atomic force microscopy

“…All three parameters show periodical variations with varied delays/phase shifts. This is in agreement with the reported theoretical simulations [17]. The resonant frequency of the cantilever fluctuated between 58,946 and 59,437 Hz when different delays were applied to the system.…”

“…In a similar experiment, Muralidharan et al examined the conditions under which the small amplitude of thermal vibrations of cantilevers typically used for atomic force microscopy and sensor applications can be enhanced through a feedback mechanism [15]. In a mathematical model, it was then shown that for certain values of two parameters, a time delay t and a gain factor G, such amplification is feasible [16,17]. In these studies, ''Brownian noise'' or ''thermal vibration'' of microcantilever sensors was amplified and controlled through a delayed-feedback system, where the delay was acquired through a phase shifter.…”

Mass-change sensitivity of piezoelectric-excited millimeter-sized cantilever (PEMC) sensors: Model and experiments

“…Micron-sized cantilevers are pursued based on the idea that the smaller the sensor mass is, higher is its mass sensitivity, which has been shown theoretically by several investigators [9][10][11][12][13]. While such sensors exhibit excellent sensitivity in gas phase, their response in liquid environment is over-damped, rendering them unusable in the dynamic mode [3,[14][15][16]. Although method to alleviate damping of microcantilevers in liquid has been reported [16], very few papers using such techniques have been published.…”

“…While such sensors exhibit excellent sensitivity in gas phase, their response in liquid environment is over-damped, rendering them unusable in the dynamic mode [3,[14][15][16]. Although method to alleviate damping of microcantilevers in liquid has been reported [16], very few papers using such techniques have been published. On the other hand, the motion of millimeter-sized cantilever sensors in liquid is in the high Reynolds number domain (>10 5 ) that viscous damping is relatively small [17].…”

Analytical modelling of a pipe with flowing medium subjected to an impulse load

“…In the case of an accident, these pipes are often subjected to a dynamic or impulse loading [1]. On the other end of the length scale, in the last few years, micro-pipes caring liquid or gas have been gaining popularity in various sensor technologies, which involves some dynamic measurements [2]. Therefore, there is now a growing interest in studying the transient response of pipes with flowing media caused by dynamic loading [1e4].…”