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.
Perturbation Analysis of a Nonlinear Resonator
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 20, 2009; final manuscript received January 23, 2012; published online June 14, 2012. Assoc. Editor: Al Ferri.
- Views Icon Views
- Share Icon Share
- Cite Icon Cite
- Search Site
Nudehi, S. S., and Farooq, U. (June 14, 2012). "Perturbation Analysis of a Nonlinear Resonator." ASME. J. Comput. Nonlinear Dynam. January 2013; 8(1): 011001. https://doi.org/10.1115/1.4005998
Download citation file:
- Ris (Zotero)
- Reference Manager