Influence of Boundary Impedance of 3D Cavity on Targeted Energy Transfer between a Damped Acoustic Mode and a Nonlinear Membrane Absorber
Abstract
:1. Introduction
2. Description of the System
3. Acoustic Damping Coefficient
4. Experimental and Numerical Forced Responses of the System
- (1)
- In the low excitation amplitude range, such as , the acoustic displacement amplitude has a single resonance peak at the resonance frequency, and the response amplitude of increases with the increase in the excitation amplitude.
- (2)
- In the medium excitation amplitude range, such as , the forced response produces a plateau with an amplitude of about m within a certain frequency range, and the resonance peak is suppressed and disappears, where the regime of responses of the system is SMR. This range starts with the appearance of the plateau and ends with the appearance of another new resonance peak. As the forcing excitation amplitude increases, the energy triggers the working threshold of the membrane NES in a wider frequency band near the resonance frequency, and the frequency range of the plateau gradually increases.
- (3)
- In the high excitation amplitude range, such as , the forced response has a new resonance peak below the original resonance frequency, which is higher than the resonance peak under the low forcing excitation. In addition, the plateau of the forced response appearing near the resonance frequency under the forcing excitation with medium amplitude begins to disappear. As the forcing excitation amplitude increases, the second resonance peak increases further, and the plateau of the forced response near the resonance frequency basically disappears.
5. Influence of the Wall Impedance for the TET
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Symbol | Unit | Description |
Corresponding normal mode in direction | ||
Nm/s | Acoustic damping | |
m/s | Sound wave velocity | |
MPa | Modulus of the membrane | |
N | External force amplitude | |
Hz | First resonance frequency without pre-stress of the membrane | |
Hz | First resonance frequency with pre-stress of the membrane | |
m | Thickness of the membrane | |
N/m | Modal stiffness of the system | |
Wave number of the mode | ||
N/m | Linear stiffness of the membrane | |
Nonlinear stiffness of the membrane | ||
m | Length of the cavity | |
m | Width of the cavity | |
m | Height of the cavity | |
Normal modes | ||
kg | Modal mass of the system | |
kg | Mass of the membrane | |
Boundary normal vector | ||
Pa | Acoustic pressure | |
Pa | Acoustic pressure of a damped mode | |
Quality factor | ||
m | Transversal displacement amplitude of the membrane center | |
m | Position vector | |
m | Radius of the membrane | |
Surface of the cavity | ||
Surface of the membrane | ||
Surface of the cavity without the surface of the membrane | ||
s | Time | |
m | Acoustic displacement amplitude | |
m | Position of the membrane center | |
Acoustic impedance | ||
Sound absorption coefficient | ||
Sound absorption coefficient of the cavity | ||
Sound absorption coefficient of each wall of the cavity | ||
Specific impedance ratio | ||
Specific impedance ratio of each wall of the cavity | ||
Test function | ||
Coefficients | ||
Damping of the membrane | ||
Poisson ratio of the membrane | ||
Density of the membrane | ||
Air density | ||
Damped mode shape of the cavity | ||
Internal volume of the cavity | ||
rad/s | Normal angular frequency |
Appendix B
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0.00011 m | |||
0.001 s | 0.04 m | ||
0.47 | 1.58 MPa |
α | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 |
Q | 132.68 | 66.34 | 43.98 | 33.03 | 30.27 | 21.99 |
β | 0.0025 | 0.005 | 0.0075 | 0.01 | 0.0125 | 0.015 |
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Shao, J.; Luo, Q.; Zeng, T.; Wu, X. Influence of Boundary Impedance of 3D Cavity on Targeted Energy Transfer between a Damped Acoustic Mode and a Nonlinear Membrane Absorber. Machines 2022, 10, 841. https://doi.org/10.3390/machines10100841
Shao J, Luo Q, Zeng T, Wu X. Influence of Boundary Impedance of 3D Cavity on Targeted Energy Transfer between a Damped Acoustic Mode and a Nonlinear Membrane Absorber. Machines. 2022; 10(10):841. https://doi.org/10.3390/machines10100841
Chicago/Turabian StyleShao, Jianwang, Qimeng Luo, Tao Zeng, and Xian Wu. 2022. "Influence of Boundary Impedance of 3D Cavity on Targeted Energy Transfer between a Damped Acoustic Mode and a Nonlinear Membrane Absorber" Machines 10, no. 10: 841. https://doi.org/10.3390/machines10100841