Abstract
A perturbation analysis of a Helmholtz-type resonator with one of the resonator ends replaced by a membrane is studied in this work. A membrane is known to exhibit nonlinear behavior under certain conditions; thus, when attached to a resonator system, it modifies the dynamic characteristics of the original system. This modified resonator system is modeled by coupled nonlinear differential equations and investigated by using the singular perturbation theory. The resonant frequency of the nonlinear resonator in the primary resonance case is analytically obtained using first-order approximate solutions. A good agreement is seen when the frequency response of the first-order approximate system is compared with the numerically simulated results.
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