Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope

@article{Sader1998FrequencyRO,
  title={Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope},
  author={John Elie Sader},
  journal={Journal of Applied Physics},
  year={1998},
  volume={84},
  pages={64-76}
}
  • J. Sader
  • Published 19 June 1998
  • Engineering
  • Journal of Applied Physics
The vibrational characteristics of a cantilever beam are well known to strongly depend on the fluid in which the beam is immersed. In this paper, we present a detailed theoretical analysis of the frequency response of a cantilever beam, that is immersed in a viscous fluid and excited by an arbitrary driving force. Due to its practical importance in application to the atomic force microscope (AFM), we consider in detail the special case of a cantilever beam that is excited by a thermal driving… 

Figures from this paper

Frequency response of cantilever beams immersed in viscous fluids near a solid surface with applications to the atomic force microscope

Theoretical models for the frequency response of a cantilever beam immersed in a viscous fluid commonly assume that the fluid is unbounded. Experimental measurements show, however, that proximity to

Torsional frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope

The frequency response of a cantilever beam is strongly dependent on the fluid in which it is immersed. In a companion study, Sader [J. Appl. Phys. 84, 64, (1998)] presented a theoretical model for

Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope: Arbitrary mode order

The frequency response of a cantilever beam is well known to depend strongly on the fluid in which it is immersed. In this article, we present a theoretical model for the frequency response of a

Experimental validation of theoretical models for the frequency response of atomic force microscope cantilever beams immersed in fluids

Detailed measurements of the frequency responses of a series of rectangular atomic force microscope (AFM) cantilever beams, immersed in a range of fluids, have been performed to test the validity and

Resonant frequencies of a rectangular cantilever beam immersed in a fluid

The resonant frequencies of cantilever beams can depend strongly on the fluid in which they are immersed. In this article, we expand on the method of Elmer and Dreier [J. Appl. Phys. 81, 7709 (1997)]

Frequency response of atomic force microscope cantilever driven by fluid

The most widely used dynamic atomic force microscopy technique in fluids is the piezo-drive, where a cantilever is driven by fluid excited by a piezoelectric. The study of the frequency response of

Hydrodynamics of oscillating atomic force microscopy cantilevers in viscous fluids

We present a study of thermal noise of commercially available atomic force microscopy (AFM) cantilevers in air and in water. The purpose of this work is to investigate the oscillation behavior of a

Resonant Response of Rectangular AFM Cantilever in Liquid

Dynamic characteristics of atomic force microscopy (AFM) cantilevers can be influenced by their working media. We perform an experimental study on the resonant responses of rectangular AFM

Dynamic Response of an Electrostatically Actuated Micro-Beam in an Incompressible Viscous Fluid Cavity

This paper studies the dynamic instability of cantilever micro-beam submerged in an incompressible viscous fluid cavity and actuated by electrostatic force. Equivalent squeeze film damping is
...

References

SHOWING 1-10 OF 38 REFERENCES

RESONANCE RESPONSE OF SCANNING FORCE MICROSCOPY CANTILEVERS

A variational method is used to calculate the deflection and the fundamental and harmonic resonance frequencies of commercial V‐shaped and rectangular atomic force microscopy cantilevers. The

Studies of vibrating atomic force microscope cantilevers in liquid

An atomic force microscope (AFM) design providing a focused spot of order 7 μm in diameter was used to analyze the motion of vibrating cantilevers in liquid. Picking an operating frequency for

Vibration of beams immersed in a liquid

Experimental and analytical analysis of a vibrating beam immersed in a fluid and carrying concentrated mass and concentrated rotatory inertia was performed. It was found that mode shapes are not

Method for the calibration of atomic force microscope cantilevers

The determination of the spring constants of atomic force microscope (AFM) cantilevers is of fundamental importance to users of the AFM. In this paper, a fast and nondestructive method for the

Eigenfrequencies of a rectangular atomic force microscope cantilever in a medium

We calculate the eigenfrequencies of a rectangular cantilever of an atomic force microscope immersed in a fluid or a gas. To do so, the problem of combined elastomechanical and hydrodynamical

Distance-dependent noise measurements in scanning force microscopy

The changes in the thermal noise spectrum of a scanning-force-microscope cantilever upon approach of the tip to the sample were used to investigate the interactions between the cantilever and the

Scan speed limit in atomic force microscopy

The scan speed limit of atomic force microscopes has been calculated. It is determined by the spring constant of the cantilever k, its effective mass m, the damping constant D of the cantilever in

Short cantilevers for atomic force microscopy

We have designed and tested a family of silicon nitride cantilevers ranging in length from 23 to 203 μm. For each, we measured the frequency spectrum of thermal motion in air and water. Spring

Resonant frequency of a polyvinylidene flouride piezoelectric bimorph: the effect of surrounding fluid

This work presents experimental and theoretical results on the dynamic behavior of piezoelectric cantilever bimorph in the presence of surrounding air. The bimorph is composed of a pair of

NATURAL FREQUENCIES OF A BODY OF REVOLUTION VIBRATING TRANSVERSELY IN A FLUID

A previously developed procedure, in which the natural frequencies of a body vibrating in a fluid are given by the eigenvalues of the potential energy matrix of an elastic body with respect to the