Abstract
A perturbation analysis of a Helmholte 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, and thus when attached to a resonator system modifies the dynamic characteristics of the original system. This modified Helmholtz resonator system modeled by coupled nonlinear differential equations is investigated by using the singular perturbation theory. The resonant frequency of nonlinear resonator in the primary resonance case is analytically obtained by using the first order approximate solutions. A good agreement is seen when the frequency response of first order approximate system is compared with the numerically simulated results.
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