Resonant frequency of an adjustable Helmholtz resonator in a hydraulic system

Kela, Lari

doi:10.1007/s00419-008-0279-5

Cited by 40 publications

(17 citation statements)

References 32 publications

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“…For Long Beach Harbor, the Helmholtz model approximates the frequency of tidal resonance to within 1% (Miles and Lee 1975). The frequency of resonance is approximated well for not too extreme dimension ratios, as investigated by Kela (2009). For Helmholtz resonator basins whose hypsometry, i.e., its available ("wetted") surface area A, varies as a function of depth z, Maas (1997) derived the following nonlinear oscillator equation in terms of excess volume V(t) as a function of time t…”

Section: Theoretical Backgroundmentioning

confidence: 97%

Amplified exchange rate by tidal forcing of a piecewise-linear Helmholtz bay

Boer

Maas

2011

Ocean Dynamics

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Sea-level and current measurements have been performed in the Mok Bay, a tidal embayment in the Dutch Wadden Sea, situated on the island of Texel, the Netherlands. Characteristic for this estuary is its nonuniform hypsometry. Oscillations in both water level and inflow of the estuary were observed, with characteristic frequencies of 31 and 48 cycles per day. The significant change in basin shape between low and high water is the cause for the existence of these two frequencies of resonance. Due to its semi-enclosed nature, the basin could at both tidal phases be characterized as a Helmholtz resonator, albeit of different dimensions. Depth measurements were performed to find these characteristic dimensions of the estuary, allowing the determination of its theoretical Helmholtz frequencies. These estimates match to within 10% with the observed frequencies, and this deviation can partly be explained. Although sea level oscillations at these frequencies have small amplitude (of order 1 cm), the accompanying oscillatory flow at the entrance is of similar magnitude as the tidal flow. The water level measurements (spanning only 8 days of data) were therefore modeled using a piecewise-uniform hypsometry that approximates the real hypsometric curve well. The simplified semi-analytical piecewise-linear viscous Helmholtz model captures the observed combination of tidal and eigenoscillations well. However, despite its simplicity, this model is able to display nonlinear behav- ior for certain parameter values. This is because of the intrinsic nonlinearity that accompanies the matching of the low and high water phases. In the setting studied here, bifurcations up to period 13 were found. This nonlinear type of response may be of importance in facilitating an extra exchange of sediments and nutrients between the Bay and the sea.

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Section: Theoretical Backgroundmentioning

confidence: 97%

Amplified exchange rate by tidal forcing of a piecewise-linear Helmholtz bay

Boer

Maas

2011

Ocean Dynamics

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“…Vael, López et al (2004) designed a compact Helmholtz resonator with a resonance frequency of 3490 Hz to combat an internal resonance in their floating cup pump design. Kela (2008) and Kela and Vähäoja (2009) have also studied the use of Helmholtz resonators, specifically with the controllability of variable-volume devices. Mikota and Manhartsgruber (2001) and Mikota and Reiter (2003) developed a type of compact, hybrid vibration absorber to be applied to hydraulic systems -essentially a tuned vibration absorber using a hydraulic volume as a spring.…”

Section: Introductionmentioning

confidence: 98%

Compact Helmholtz Resonators for Hydraulic Systems

Earnhart¹,

Cunefare²

2012

International Journal of Fluid Power

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Noise is an ongoing concern in the fluid power industry. A great deal of research has been invested in reducing flow pulsations in hydraulic systems, from design modifications to adding noise control components. The physical principles of noise reduction are the same as for air, however, the much higher sound speed of hydraulic fluid makes creating compact noise control devices difficult. This paper introduces a Helmholtz resonator design that uses a compliant, voided urethane lining to increase the apparent volume of the device. The addition of the lining permits much smaller physical sizes for the same resonance frequency. Specifically, the design presented here has a total volume of 0.31 L and generates 20 dB of transmission loss at a resonance frequency of 37 Hz when the hydraulic system is pressurized at 2.07 MPa. At this pressure, it has a total volume that is two orders of magnitude smaller than a similar, unlined device of the same resonance frequency. Experimental data is presented that demonstrates the performance of the device. An analytical model was developed and least-squares fit to the experimental data to extract the complex bulk modulus of the liner material at hydrostatic pressures from 2.07 -4.83 MPa, which is the range of available test pressures. This work is anticipated to lead to devices and liner materials designed for higher pressures.

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“…To control and attenuate vibrations, developed techniques have two main approaches by focusing on materials and structures. To achieve active vibration control, various systems such as dynamic absorbers [Hunt and Nissen, 1982], tuned dampers [Sun et al, 1995], and Helmholtz resonators [Kela, 2009] have been used to attenuate vibration and impact. However, these systems are generally effective only at a narrow target frequency.…”

Section: Introductionmentioning

confidence: 99%

Sandwich-Structured Woodpile Metamaterials for Impact Mitigation

Hwang

Lee

Yang

et al. 2018

Int. J. Appl. Mechanics

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The objective of this study was to investigate 3D woodpile metamaterials for mitigating impact-induced vibrations by leveraging their local resonant and nonlinear contact characteristics. For experimental demonstrations, we designed, fabricated and tested prototypes of sandwich-structured woodpile metamaterials consisting of two plates, slender cylindrical rods and fasteners. We experimentally and numerically obtained impact responses of sandwich-structured woodpile metamaterials under various geometries and boundary conditions. We found that sandwich-structured woodpile metamaterials could efficiently manipulate and attenuate the impact vibrations due to their local bending motions and nonlinear contact between members. In addition, sandwich-structured woodpile metamaterials could have high damping as well as high stiffness by controlling the rod spacing. The findings from this study suggest sandwich-structured woodpile metamaterials can be used as structural components for impact-induced vibration mitigation.

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Resonant frequency of an adjustable Helmholtz resonator in a hydraulic system

Cited by 40 publications

References 32 publications

Amplified exchange rate by tidal forcing of a piecewise-linear Helmholtz bay

Amplified exchange rate by tidal forcing of a piecewise-linear Helmholtz bay

Compact Helmholtz Resonators for Hydraulic Systems

Sandwich-Structured Woodpile Metamaterials for Impact Mitigation

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