### Abstract

Microcantilever beams are versatile force sensors used for, among others, microaccelerometry, microelectromechanical systems, and surface force measurements, the most prominent application being atomic force microscopic imaging and force spectroscopy. Bending of the cantilever is used for simple force measurements, while changes in the amplitude or frequency of the fundamental resonance are used to detect small interaction forces or brief perturbations. Spring constants needed for quantitative measurements are determined by "reversing" the force measurements, using either Hooke's law or the oscillation of the beam. The equality of the Hookian and the oscillating spring constant is generally assumed; however, consistent differences in experimental results suggest otherwise. In this work, we introduce a theoretical formula to describe the relationship between these two spring constants for an Euler-Bernoulli beam. We show that the two spring constants are not equal, although the percentage difference stays in the range of a single digit. We derive a general formula for the determination of effective spring constants of arbitrary eigenmodes of the cantilever beam. We demonstrate that all overtones can be treated with a linear spring - effective mass approach, where the mass remains the same for higher eigenmodes.

Original language | English |
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Article number | 172101 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 78 |

Issue number | 17 |

DOIs | |

Publication status | Published - Nov 4 2008 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Electronic, Optical and Magnetic Materials

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*78*(17), [172101]. https://doi.org/10.1103/PhysRevB.78.172101

**Spring constant of microcantilevers in fundamental and higher eigenmodes.** / Kokavecz, J.; Mechler, A.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 78, no. 17, 172101. https://doi.org/10.1103/PhysRevB.78.172101

}

TY - JOUR

T1 - Spring constant of microcantilevers in fundamental and higher eigenmodes

AU - Kokavecz, J.

AU - Mechler, A.

PY - 2008/11/4

Y1 - 2008/11/4

N2 - Microcantilever beams are versatile force sensors used for, among others, microaccelerometry, microelectromechanical systems, and surface force measurements, the most prominent application being atomic force microscopic imaging and force spectroscopy. Bending of the cantilever is used for simple force measurements, while changes in the amplitude or frequency of the fundamental resonance are used to detect small interaction forces or brief perturbations. Spring constants needed for quantitative measurements are determined by "reversing" the force measurements, using either Hooke's law or the oscillation of the beam. The equality of the Hookian and the oscillating spring constant is generally assumed; however, consistent differences in experimental results suggest otherwise. In this work, we introduce a theoretical formula to describe the relationship between these two spring constants for an Euler-Bernoulli beam. We show that the two spring constants are not equal, although the percentage difference stays in the range of a single digit. We derive a general formula for the determination of effective spring constants of arbitrary eigenmodes of the cantilever beam. We demonstrate that all overtones can be treated with a linear spring - effective mass approach, where the mass remains the same for higher eigenmodes.

AB - Microcantilever beams are versatile force sensors used for, among others, microaccelerometry, microelectromechanical systems, and surface force measurements, the most prominent application being atomic force microscopic imaging and force spectroscopy. Bending of the cantilever is used for simple force measurements, while changes in the amplitude or frequency of the fundamental resonance are used to detect small interaction forces or brief perturbations. Spring constants needed for quantitative measurements are determined by "reversing" the force measurements, using either Hooke's law or the oscillation of the beam. The equality of the Hookian and the oscillating spring constant is generally assumed; however, consistent differences in experimental results suggest otherwise. In this work, we introduce a theoretical formula to describe the relationship between these two spring constants for an Euler-Bernoulli beam. We show that the two spring constants are not equal, although the percentage difference stays in the range of a single digit. We derive a general formula for the determination of effective spring constants of arbitrary eigenmodes of the cantilever beam. We demonstrate that all overtones can be treated with a linear spring - effective mass approach, where the mass remains the same for higher eigenmodes.

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U2 - 10.1103/PhysRevB.78.172101

DO - 10.1103/PhysRevB.78.172101

M3 - Article

AN - SCOPUS:56349155070

VL - 78

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 17

M1 - 172101

ER -