Topic

# Natural frequency

About: Natural frequency is a(n) research topic. Over the lifetime, 9382 publication(s) have been published within this topic receiving 109544 citation(s).

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01 Jan 1979-

1,971 citations

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Abstract: Future MEMS devices will harvest energy from their environment. One can envisage an autonomous condition monitoring vibration sensor being powered by that same vibration, and transmitting data over a wireless link; inaccessible or hostile environments are obvious areas of application. The base excitation of an elastically mounted magnetic seismic mass moving past a coil, considered previously by several authors, is analysed in detail. The amplitude of the seismic mass is limited in any practical device and this, together with the magnitude and frequency of the excitation define the maximum power that can be extracted from the environment. The overall damping coefficient (part of which is mechanical) is associated with the harvesting and dissipation of energy and also the transfer of energy from the vibrating base into the system. It is shown that net energy flow from the base through the damper is positive (negative) for ω > ω n ( ω ω n ) , but is zero when ω = ω n . The mechanical part of the damper cannot contribute more power than it dissipates and is neutral, at best, when ω / ω n → ∞ . Maximum power is delivered to an electrical load when its resistance is equal to the sum of the coil internal resistance and the electrical analogue of the mechanical damping coefficient, which differs from what has been claimed. A highly damped system has the advantage of harvesting energy over a wider band of excitation frequencies on either side of the natural frequency, is smaller, but will harvest marginally less power. One possible strategy for variable amplitude excitation is proposed.

760 citations

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Abstract: Vibration energy harvesting is an attractive technique for potential powering of wireless sensors and low power devices. While the technique can be employed to harvest energy from vibrations and vibrating structures, a general requirement independent of the energy transfer mechanism is that the vibration energy harvesting device operate in resonance at the excitation frequency. Most energy harvesting devices developed to date are single resonance frequency based, and while recent efforts have been made to broaden the frequency range of energy harvesting devices, what is lacking is a robust tunable energy harvesting technique. In this paper, the design and testing of a resonance frequency tunable energy harvesting device using a magnetic force technique is presented. This technique enabled resonance tuning to ±20% of the untuned resonant frequency. In particular, this magnetic-based approach enables either an increase or decrease in the tuned resonant frequency. A piezoelectric cantilever beam with a natural frequency of 26 Hz is used as the energy harvesting cantilever, which is successfully tuned over a frequency range of 22‐32 Hz to enable a continuous power output 240‐280 μW over the entire frequency range tested. A theoretical model using variable damping is presented, whose results agree closely with the experimental results. The magnetic force applied for resonance frequency tuning and its effect on damping and load resistance have been experimentally determined. (Some figures in this article are in colour only in the electronic version)

589 citations

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Abstract: The dynamic problems of Bernoulli–Euler beams are solved analytically on the basis of modified couple stress theory. The governing equations of equilibrium, initial conditions and boundary conditions are obtained by a combination of the basic equations of modified couple stress theory and Hamilton’s principle. Two boundary value problems (one for simply supported beam and another for cantilever beam) are solved and the size effect on the beam’s natural frequencies for two kinds of boundary conditions are assessed. It is found that the natural frequencies of the beams predicted by the new model are size-dependent. The difference between the natural frequencies predicted by the newly established model and classical beam model is very significant when the ratio of characteristic sizes to internal material length scale parameter is approximately equal to one, but is diminishing with the increase of the ratio.

524 citations

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Virginia Tech

^{1}Abstract: We present a nonlinear model of electrically actuated microbeams accounting for the electrostatic forcing of the air gap capacitor, the restoring force of the microbeam and the axial load applied to the microbeam The boundary-value problem describing the static deflection of the microbeam under the electrostatic force due to a dc polarization voltage is solved numerically The eigenvalue problem describing the vibration of the microbeam around its statically deflected position is solved numerically for the natural frequencies and mode shapes Comparison of results generated by our model to the experimental results shows excellent agreement, thus verifying the model Our results show that failure to account for mid-plane stretching in the microbeam restoring force leads to an underestimation of the stability limits It also shows that the ratio of the width of the air gap to the microbeam thickness can be tuned to extend the domain of the linear relationship between the dc polarization voltage and the fundamental natural frequency This fact and the ability of the nonlinear model to accurately predict the natural frequencies for any dc polarization voltage allow designers to use a wider range of dc polarization voltages in resonators

453 citations