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Characterization of a Dual Nonlinear Helmholtz Resonator
Maher O Al-Turk1, Sajid Ali2, Muhammad A Hawwa1
1Department of Mechanical Engineering & IRC for Advanced Materials, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia.
Micromachines
|November 24, 2022
Summary
This study explores the nonlinear behavior of dual Helmholtz resonators (HRs) for energy harvesting. Findings show deterministic motion and softening behavior, crucial for powering miniaturized devices.
Area of Science:
- Acoustics
- Nonlinear Dynamics
- Energy Harvesting
Background:
- Helmholtz resonators (HRs) are traditionally analyzed for linear vibrations.
- Miniaturized accelerometers require small amounts of energy for operation.
- Extracting energy from ambient vibrations is a key challenge in micro-device design.
Purpose of the Study:
- To investigate the nonlinear characteristics of a dual Helmholtz resonator (HR).
- To model and analyze the energy harvesting potential of HRs under harmonic pressure.
- To understand the dynamic behavior of HRs beyond linear approximations.
Main Methods:
- Developed a mathematical model incorporating nonlinear air stiffness and hydrodynamic damping.
- Obtained numerical solutions for the resonator's nonlinear oscillations.
- Generated bifurcation diagrams and phase portraits to analyze system dynamics.
- Calculated frequency response curves (FRCs) to identify resonance behaviors.
Main Results:
- The dual HR exhibits deterministic behavior within practical engineering limits.
- Numerical simulations reveal quasi-periodic motion in the resonator.
- Frequency response curves show a leftward shift at lower frequencies, indicating softening behavior.
- Higher resonant frequencies display mostly linear behavior with symmetric FRCs.
Conclusions:
- Dual Helmholtz resonators demonstrate complex nonlinear dynamics.
- The identified nonlinear characteristics, including softening, are relevant for energy harvesting applications.
- Understanding these nonlinearities is essential for optimizing HRs in miniaturized energy harvesting systems.
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