Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams

Skrzypacz, Piotr; Nurakhmetov, Daulet; Wei, Dongming

doi:10.1007/s10409-019-00912-8

Cited by 14 publications

(5 citation statements)

References 25 publications

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“…In our work, we determine the effective mass of the micro-cantilever based on Hollomons power law stressstrain equation for both modes. The effective mass for the micro-cantilever power-law beam of mass m is approximated as follows [26] Here, the strain hardening component n is equal to 1 for linear elastic material of the micro-cantilever. Therefore, effective mass of the micro-cantilever is introduced in equation (B.…”

Section: Discussionmentioning

confidence: 99%

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Theoretical study on the sensitivity of dynamic acoustic force measurement through monomodal and bimodal excitations of rectangular micro-cantilever

Yilmaz¹,

Şahin²,

Topal³

2021

Eng. Res. Express

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We present a detailed analysis on measurement sensitivity of dynamic acoustic forces via numerical simulation of the micro-cantilever responses. The rectangular micro-cantilever is regarded as a point mass in the dynamic model of forced and damped harmonic oscillator. We use single- and bimodal-frequency excitation schemes for actuation of the micro-cantilever in the presence of dynamic acoustic forces. In bimodal-frequency excitation scheme, the micro-cantilever is excited at its first two eigenmode frequencies simultaneously as opposed to single-frequency excitation. First, we numerically obtain micro-cantilever deflections by solving the equations of Motions (EOMs) constructed for the first two eigenmodes. Then, we determine oscillation amplitude and phase shift as a function of acoustic force strength within different frequency regions. Moreover, we relate amplitude and phase shift to virial and energy dissipation in order to explore the interaction between flexural modes in multifrequency excitation. The simulation results point out that bimodal-frequency excitation improves the measurement sensitivity of dynamic acoustic forces at particular frequencies. Herein, simultaneous application of driving forces enables higher sensitivities of observables and energy quantities as acoustic force frequencies become around the eigenmode frequencies. For our case, we obtain the highest phase shift (∼178°) for the acoustic force strength of 100 pN at the frequency of around 307.2 kHz. Therefore, this method can be easily adapted to improve measurement sensitivity of dynamic acoustic forces in a wider frequency window.

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Section: Discussionmentioning

confidence: 99%

“…The effective mass of the micro-cantilever m e is determined using the expression (equation ( 14)) as introduced in [26]. The mass density ρ of the micro-cantilever is equal to 2320kg m −3 as in [24].…”

Section: Numerical Simulationmentioning

confidence: 99%

Theoretical study on the sensitivity of dynamic acoustic force measurement through monomodal and bimodal excitations of rectangular micro-cantilever

Yilmaz¹,

Şahin²,

Topal³

2021

Eng. Res. Express

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“…The relevant dimensional parameters of the microcantilever possessing a rectangular shape with a length (l) of 225 µm, width (w) of 40 µm, thickness (b) of 1.8 µm and mass density (ρ) of 2320 kg m 13 are taken from [25]. The effective mass of the micro-cantilever is calculated by using the expression (equation ( 13)) as in [29].…”

Section: Numerical Calculationmentioning

confidence: 99%

Exploring the static acoustic force sensitivity using AFM micro-cantilever under single- and bimodal-frequency excitation

Yilmaz

Şahin

Topal

2021

Meas. Sci. Technol.

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We present here a numerical calculation for sensitivity comparison of single-and bimodal-excitation of micro-cantilever (owing rectangular shape) on the measurement of static acoustic force. We model the micro-cantilever as a point mass in our simulations similar to forced harmonic oscillator with damping. In bimodal operation, the micro-cantilever is excited at its first two flexural modes. Results of amplitude and phase shift obtained through bimodal-frequency excitation are compared with the ones obtained using single-frequency excitation scheme. Oscillation observables are calculated in both excitation schemes with respect to magnitudes of excitation forces at fundamental and second eigenmode. Influence of driving force for micro-cantilever actuation on amplitude and phase shift is explored so that optimum excitation parameters can be provided for highest observable sensitivity. Moreover, we relate our findings with virial and energy dissipation to understand the physics behind observed dynamics. Our results clearly indicates that phase sensitivity at the fundamental eigenmode to static acoustic force could be enhanced using multi-frequency excitation scheme. In addition, results of virial and dissipated power at second eigenmode point out the existence of interaction of flexural modes in the presence of static acoustic force in bimodal-frequency excitation scheme. Therefore, our approach can be used to increase sensitivity of dynamically excited micro-cantilever for measuring ultra-low (pN) acoustic forces.

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“…The mass density of the micro-cantilever, made of silicon material, is equal to 2320 3 . The effective mass of the microcantilever is determined using the following expression as in (Skrzypacz, Nurakhmetov, & Wei, 2019).…”

Section: Numerical Simulationmentioning

confidence: 99%

Çok Modlu Tahrik Şemalarının Kullanıldığı Dinamik Akustik Kuvvet Ölçümünde Eğilme Özmodlarındaki Genlik Tepkileri

Yilmaz¹,

Topal²

2021

European Journal of Science and Technology

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In this paper, we present a computational investigation to study amplitude sensitivities to acoustic forces in a wide frequency range. We utilize bimodal, trimodal, and tetramodal excitation schemes for the actuation of the Atomic Force Microscopy (AFM) micro-cantilever in the presence of dynamic acoustic forces. In multimodal operations, the micro-cantilever is driven by applying external excitation forces at eigenmode angular frequencies. The Equation of Motion (EOM) is constructed in the consideration of the driven and damped harmonic oscillator as a model and solved numerically to obtain the deflections of the micro-cantilever at flexural eigenmodes. In this current work, time-domain responses of the micro-cantilever to acoustic forces are introduced for different excitation schemes so that free oscillations are compared with the oscillations of the driven micro-cantilever undergoing acoustic forces. Then, we evaluate the results of amplitude responses at the first four eigenmodes with respect to acoustic force frequencies for diverse force strengths. For our case, we obtain the amplitude response at the fourth eigenmode of around 0.303 nm for the force strength of 2900 pN at the frequency of 1740 kHz. This result proves that acoustic forces at megahertz frequencies are measured by using resonant AFM micro-cantilever under tetramodal operation. Therefore, multimodal excitation schemes can be applied to enhance the amplitude sensitivities to dynamic acoustic forces.

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Generalized stiffness and effective mass coefficients for power-law Euler–Bernoulli beams

Cited by 14 publications

References 25 publications

Theoretical study on the sensitivity of dynamic acoustic force measurement through monomodal and bimodal excitations of rectangular micro-cantilever

Theoretical study on the sensitivity of dynamic acoustic force measurement through monomodal and bimodal excitations of rectangular micro-cantilever

Exploring the static acoustic force sensitivity using AFM micro-cantilever under single- and bimodal-frequency excitation

Çok Modlu Tahrik Şemalarının Kullanıldığı Dinamik Akustik Kuvvet Ölçümünde Eğilme Özmodlarındaki Genlik Tepkileri

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