Characterization of a Dual Nonlinear Helmholtz Resonator

Abstract

Resonant elements can generate small amounts of energy that make them pertinent for feeding miniaturized accelerometers with the energy needed. Suitable oscillator candidates are Helmholtz resonators, which have been, for a long time, analyzed and designed within the context of linear vibration. This study focuses on extracting nonlinear characteristics of a dual Helmholtz resonator (HR), with a neck-cavity–neck-cavity configuration, mounted on an acoustic waveguide with harmonically oscillating pressure. The mathematical model used for describing the resonator embraces inherent nonlinear air stiffness and the damping nonlinearity of hydrodynamic origin. Numerical solutions for the resonator’s nonlinear oscillations are obtained. Bifurcation diagrams are produced, indicating that the dual HR behaves in a deterministic fashion within the engineering practical limits. Phase portraits are drawn for the system, showing a quasi-periodic motion. Frequency response curves (FRC) are found to shift to the left at the lower resonant frequency indicating a softening behavior. FRC keep generally symmetric curves at the higher resonant frequency indicating a mostly linear behavior.

Keywords

• dual Helmholtz resonator
• lumped-parameter analysis
• nonlinear oscillations
• bifurcation
• phase portrait
• hardening and softening