Modeling and Experimental Investigation of a Helmholtz Resonator With a Flexible Plate

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Shahin S. Nudehi ◽  
G. Scott Duncan ◽  
Umar Farooq
Keyword(s):  
Experimental Investigation ◽  
Transmission Loss ◽  
Helmholtz Resonator ◽  
Single Frequency ◽  
Flexible Plate ◽  
Resonant Frequencies ◽  
Response Characteristics ◽  
Receptance Coupling ◽  
Frequency Response Characteristics ◽  
Plate Assembly

A Helmholtz resonator with a uniform, flexible end plate is studied in this work. This work shows that the flexible plate modifies the frequency response characteristics of the resonator, providing multiple distinct resonant frequencies instead of a single resonant frequency. Therefore, acoustical transmission loss will increase at each of the multiple resonant frequencies of the resonator and plate assembly versus at a single frequency for the unmodified Helmholtz resonator. By using receptance coupling as the modeling approach, the receptance of the Helmholtz resonator and flexible plate assembly is predicted by coupling receptance models of an unmodified Helmholtz resonator and a clamped plate. Finally, the predicted receptance of the Helmholtz resonator and flexible plate assembly is compared against experimental results.

scholarly journals Tailoring Plate Thickness of a Helmholtz Resonator for Improved Sound Attenuation

2016 ◽  
Author(s):  
Mohammad Kurdi ◽  
Shahin Nudehi ◽  
Gregory Scott Duncan
Keyword(s):  
Transmission Loss ◽  
Plate Thickness ◽  
Helmholtz Resonator ◽  
Element Model ◽  
Flexible Plate ◽  
End Plate ◽  
Receptance Coupling ◽  
Coupling Techniques ◽  
Gradient Based ◽  
Optimization Search

A Helmholtz resonator with flexible plate attenuates noise in exhaust ducts, and the transmission loss function quantifies the amount of filtered noise at a desired frequency. In this work the transmission loss is maximized (optimized) by allowing the resonator end plate thickness to vary for two cases: 1) a non-optimized baseline resonator, and 2) a resonator with a uniform flexible endplate that was previously optimized for transmission loss and resonator size. To accomplish this, receptance coupling techniques were used to couple a finite element model of a varying thickness resonator end plate to a mass-spring-damper model of the vibrating air mass in the resonator. Sequential quadratic programming was employed to complete a gradient based optimization search. By allowing the end plate thickness to vary, the transmission loss of the non-optimized baseline resonator was improved significantly, 28 percent. However, the transmission loss of the previously optimized resonator for transmission loss and resonator size showed minimal improvement.

Transfer Functions for Helical Springs

1969 ◽  
Vol 91 (4) ◽  
pp. 1011-1016 ◽  
Author(s):  
B. L. Johnson ◽  
E. E. Stewart
Keyword(s):  
Experimental Data ◽  
Experimental Investigation ◽  
Steady State ◽  
Transfer Functions ◽  
Helical Springs ◽  
Response Characteristics ◽  
Transmitted Force ◽  
Vibratory Motion ◽  
Frequency Response Characteristics ◽  
Displacement Force

This study reports the results of an analytical and experimental investigation of helical springs subjected to vibratory motion. Transfer functions are presented for both displacement and transmitted force as outputs with force as the input. Steady-state sinusoidal Magnitude Ratio (displacement—force) and Transmittance Ratio (force—force) are plotted along with substantiating experimental data. It is shown that an actual spring displays frequency response characteristics over most of the frequency spectrum that would render its function useless in many cases.

Optimal Design of a Helmholtz Resonator With a Flexible End Plate

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Mohammad H. Kurdi ◽  
G. Scott Duncan ◽  
Shahin S. Nudehi
Keyword(s):  
Transmission Loss ◽  
Helmholtz Resonator ◽  
Design Parameters ◽  
Flexible Plate ◽  
Frequency Range ◽  
End Plate ◽  
Pareto Curve ◽  
Resonator Design ◽  
Optimization Formulation ◽  
Design Solutions

This paper describes a design process that produces a small volume Helmholtz resonator capable of achieving high transmission loss across a desired frequency range. A multiobjective optimization formulation was used to design a Helmholtz resonator with a flexible end plate. The optimization formulation generated a Pareto curve of design solutions that quantify the trade-off between the optimization goals: minimum resonator volume and maximum transmission loss across a specified frequency range. The optimization problem was formulated and solved in the following manner. First, a mathematical formulation for the transmission loss of the Helmholtz resonator with a flexible plate was completed based on the resonator design parameters. Then, the weighted transmission loss across a specified frequency range and a minimum resonator volume were defined as optimization objectives. Finally, the Pareto curve of optimum design solutions was calculated using a gradient-based approach via the ɛ-constraint method. The optimization results allow the designer to select resonator design parameters that meet the requirements for both transmission loss and resonator volume. To validate the optimization results, two optimal Helmholtz resonators were manufactured and experimentally confirmed.

scholarly journals Numerical studies of transmission loss performances of asymmetric Helmholtz resonators in the presence of a grazing flow

2018 ◽  
Vol 38 (2) ◽  
pp. 244-254 ◽  
Author(s):  
Zhengli Lu ◽  
Weichen Pan ◽  
Yiheng Guan
Keyword(s):  
Mach Number ◽  
Gas Turbines ◽  
Stokes Equations ◽  
Transmission Loss ◽  
Helmholtz Resonator ◽  
Transmission Losses ◽  
Resonant Frequencies ◽  
Helmholtz Resonators ◽  
Grazing Flow ◽  
Maximum Transmission

As a typical noise-attenuating device, Helmholtz resonators are widely implemented in aero-engines and gas turbines to decrease the transmission of acoustic noise. However, an asymmetric Helmholtz resonator could be designed and implemented due to the limited space available in the engines. To examine and optimize the noise-attenuating performances of the asymmetric resonator, comparison studies are performed. For this, a two-dimensional frequency-domain model of a cylindrical duct with a grazing flow is developed. An asymmetric Helmholtz resonator is attached as a side branch. The model containing the linearized Navier–Stokes equations is validated first by comparing the predicted results with the experimental ones available in the literature. Further validation is conducted by comparing the results of an asymmetric resonator with the analytical ones available in the literature. The effects of (1) neck offset distance from the center of the resonator cavity denoted by [Formula: see text] and (2) the grazing flow Mach number [Formula: see text] are evaluated. It is shown that as the grazing flow Mach number is increased, the resonant frequencies and the maximum transmission losses are dramatically varied for a given [Formula: see text]. As [Formula: see text] is increased from 0 to 0.5 and [Formula: see text], the resonant frequencies and the maximum transmission losses are increased. However, when [Formula: see text] is lower than 0.07, i.e. [Formula: see text], the transmission loss performances are almost unchanged with [Formula: see text] increased. The optimum design of the asymmetric resonator is shown to give rise to the resonant frequency being shifted by 10% and 2–5 dB more transmission loss at higher Mach number. Finally, visualization of vortex shedding formed at the neck of the asymmetric resonator confirms that acoustical energy is transformed into kinetic energy and absorbed by the surrounding air. This study opens up a numerical design approach to optimize an asymmetric resonator.

scholarly journals Tailoring Plate Thickness of a Helmholtz Resonator for Improved Sound Attenuation

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Mohammad Kurdi ◽  
Shahin Nudehi ◽  
Gregory Scott Duncan
Keyword(s):  
Transmission Loss ◽  
Plate Thickness ◽  
Helmholtz Resonator ◽  
Element Model ◽  
End Plate ◽  
Receptance Coupling ◽  
Coupling Techniques ◽  
Minimal Improvement ◽  
Gradient Based ◽  
Optimization Search

In this work, the transmission loss of a Helmholtz resonator is maximized (optimized) by allowing the resonator end plate thickness to vary for two cases: (1) a nonoptimized baseline resonator and (2) a resonator with a uniform flexible endplate that was previously optimized for transmission loss and resonator size. To accomplish this, receptance coupling techniques were used to couple a finite element model of a varying thickness resonator end plate to a mass-spring-damper model of the vibrating air mass in the resonator. Sequential quadratic programming was employed to complete a gradient-based optimization search. By allowing the end plate thickness to vary, the transmission loss of the nonoptimized baseline resonator was improved significantly, 28%. However, the transmission loss of the previously optimized resonator for transmission loss and resonator size showed minimal improvement.

Optimal Design of a Helmholtz Resonator With a Flexible End Plate

2012 ◽  
Author(s):  
Mohammad H. Kurdi ◽  
G. Scott Duncan ◽  
Shahin S. Nudehi
Keyword(s):  
Transmission Loss ◽  
Mathematical Formulation ◽  
Helmholtz Resonator ◽  
Design Parameters ◽  
Flexible Plate ◽  
Frequency Range ◽  
End Plate ◽  
Pareto Curve ◽  
Optimization Formulation ◽  
Design Solutions

A multi-objective optimization formulation to design a Helmholtz resonator with a flexible end plate is studied. The optimization formulation generates a Pareto curve of design solutions that quantify the trade-off between the optimization goals: minimum resonator volume and maximum transmission loss across a specified frequency range. The optimization problem is formulated and solved in the following manner. First, a mathematical formulation for the transmission loss of the Helmholtz resonator with a flexible plate is completed based on the design parameters. Then, the weighted transmission loss across a specified frequency range and a minimum resonator volume are defined as optimization objectives. Finally, the Pareto curve of optimum design solutions is calculated using a gradient-based approach via the ε-constraint method. The optimization results allow the designer to select resonator design parameters that meet the requirements for both transmission loss and resonator volume. To validate the optimization results, one optimal Helmholtz resonator is manufactured and experimentally confirmed.

Analysis of frequency response characteristics of polymer ultrasonic transducers

1992 ◽  
Vol 25 (3) ◽  
pp. 155
Author(s):  
H. Ohigashi ◽  
T. Itoh ◽  
K. Kimura ◽  
T. Nakanishi ◽  
M. Suzuki
Keyword(s):  
Frequency Response ◽  
Ultrasonic Transducers ◽  
Response Characteristics ◽  
Frequency Response Characteristics
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