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Natural frequency

About: Natural frequency is a research topic. Over the lifetime, 9382 publications have been published within this topic receiving 109544 citations.


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Journal ArticleDOI
TL;DR: In this paper, a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method was used to obtain the natural frequencies of rectangular plates. But the results for lower modes were not as good as those obtained by other methods.

469 citations

Journal ArticleDOI
12 Nov 1998-Nature
TL;DR: In this article, the authors report parametrically excited torsional oscillations in a single-crystal silicon microelectromechanical system, which can provide a unique testing ground for dynamical phenomena that are difficult to detect in macroscopic systems.
Abstract: The Mathieu equation1 governs the forced motion of a swing2, the stability of ships3 and columns4, Faraday surface wave patterns on water5,6, the dynamics of electrons in Penning traps7, and the behaviour of parametric amplifiers based on electronic8 or superconducting devices9. Theory predicts that parametric resonances occur near drive frequencies of 2ω0/n, where ω0 is the system's natural frequency and n is an integer ⩾1. But in macroscopic systems, only the first instability region can typically be observed, because of damping and the exponential narrowing10 of the regions with increasing n. Here we report parametrically excited torsional oscillations in a single-crystal silicon microelectromechanical system. Five instability regions can be measured, due to the low damping, stability and precise frequency control achievable in this system. The centre frequencies of the instability regions agree with theoretical predictions. We propose an application that uses parametric excitation to reduce the parasitic signal in capacitive sensing with microelectromechanical systems. Our results suggest that microelectromechanical systems can provide a unique testing ground for dynamical phenomena that are difficult to detect in macroscopic systems.

449 citations

Journal ArticleDOI
TL;DR: In this paper, a second-order, linear, damped system with self-excited wake-oscillators is proposed to model the aerodynamic lift force and the instantaneous value of a fluctuating lift coefficient, whose characteristics are derived from existing experimental data.
Abstract: The main feature is the representation of fluctuating lift behavior in terms of a proposed wake-oscillator. The primary purpose of the paper is to demonstrate the potential of the wake-oscillator concept for future studies. The elastically mounted cylinder is modeled as a second-order, linear, damped system. The aerodynamic lift force is proportional to the instantaneous value of a fluctuating lift coefficient. The instantaneous lift coefficient is derived from the response of a proposed lift-oscillator, whose characteristics are deduced from existing experimental data. This oscillator is self-excited, its natural frequency is proportional to wind speed, and it is subjected to a coupling term proportional to the transverse cylinder velocity.

413 citations

Journal ArticleDOI
TL;DR: In this article, the benefits of using a non-linear stiffness in an energy harvesting device comprising a mass-spring-damper system are investigated based on the principle of conservation of energy.
Abstract: The benefits of using a non-linear stiffness in an energy harvesting device comprising a mass–spring–damper system are investigated. Analysis based on the principle of conservation of energy reveals a fundamental limit of the effectiveness of any non-linear device over a tuned linear device for such an application. Two types of non-linear stiffness are considered. The first system has a non-linear bi-stable snap-through mechanism. This mechanism has the effect of steepening the displacement response of the mass as a function of time, resulting in a higher velocity for a given input excitation. Numerical results show that more power is harvested by the mechanism if the excitation frequency is much less than the natural frequency. The other non-linear system studied has a hardening spring, which has the effect of shifting the resonance frequency. Numerical and analytical studies show that the device with a hardening spring has a larger bandwidth over which the power can be harvested due to the shift in the resonance frequency.

396 citations

Journal ArticleDOI
TL;DR: In this paper, a study of the dynamics and fluid forcing on an elastically mounted rigid cylinder, constrained to oscillate transversely to a free stream, is presented, with very low damping and with a low specific mass that is around 1% of the value used in the classic study of Feng (1968).

352 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023343
2022896
2021447
2020421
2019396
2018482