Research Papers

Targeted Energy Transfer From One Acoustical Mode to an Helmholtz Resonator With Nonlinear Behavior

[+] Author and Article Information
Emmanuel Gourdon

Univ Lyon, ENTPE,
rue Maurice Audin,
Vaulx-en-Velin F-69518, France
e-mail: emmanuel.gourdon@entpe.fr

Alireza Ture Savadkoohi

Univ Lyon, ENTPE,
rue Maurice Audin,
Vaulx-en-Velin F-69518, France
e-mail: alireza.turesavadkoohi@entpe.fr

Valentin Alamo Vargas

Univ Lyon, ENTPE,
rue Maurice Audin,
Vaulx-en-Velin F-69518, France
e-mail: valentin.alamovargas@entpe.fr

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 21, 2017; final manuscript received April 5, 2018; published online May 7, 2018. Assoc. Editor: Maurizio Porfiri.

J. Vib. Acoust 140(6), 061005 (May 07, 2018) (8 pages) Paper No: VIB-17-1550; doi: 10.1115/1.4039960 History: Received December 21, 2017; Revised April 05, 2018

Targeted energy transfer from one acoustical mode to a Helmholtz resonator (HR) with nonlinear behaviors is studied. For the HR, nonlinear restoring forces and nonlinear damping are taken into account. A time multiple scale method around a 1:1 resonance is used to detect slow invariant manifold (SIM) of the system, its equilibrium and singular points. Analytical predictions are compared with those which are obtained by direct numerical integration of system equations. Experimental verifications are performed and presented for free and forced vibrating system.

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Grahic Jump Location
Fig. 1

Scheme of the straight neck HR

Grahic Jump Location
Fig. 2

Scheme of the coupled acoustic system with a HR

Grahic Jump Location
Fig. 3

(a) N1 versus N2 analytical (-) and numerical (-) for initial conditions (τ = 0) U1=U2=0,(dU1/dτ)=(dU2/dτ)=1×10−5 and (b) numerical N1 with HR (-), N1 without HR (-)

Grahic Jump Location
Fig. 4

(a) N1 versus N2 analytical (-) and numerical (-) for initials conditions (τ = 0) U1=U2=0, (dU1/dτ)=1×10−5, (dU2/dτ)=5×10−5 and (b) Numerical N1 with HR (-) and N1 without HR (-)

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Fig. 5

Experimental setup

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Fig. 6

N1 versus τ with HR (-) and N1 without HR versus τ (-) for three cases: (a) 144 dB, (b) 150 dB, and (c) 153.5 dB

Grahic Jump Location
Fig. 7

Pressure amplitude in the middle of the small diameter tube versus frequency in forced regime for system with HR (with a cavity of Lcav = 26.5 mm) (-) and without HR (-) for three cases: (a) 138 dB, (b) 150 dB, and (c) 157.5 dB

Grahic Jump Location
Fig. 8

Pressure amplitude in the middle of the small diameter tube in forced regime for system without HR (-) and with HR (-) at three cases: (a) 138 dB, (b) 150 dB, and (c) 157.5 dB



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