Nonlinear softening and hardening behavior in Helmholtz resonators for nonlinear regimes
Résumé
The governing equation of a Helmholtz resonator considering nonlinear
terms of restoring and damping forces is studied. The system is treated by a time
multi-scales method and the softening and hardening behaviors of such resonators are
detected as functions of amplitudes. Analytically detected responses of the system are
compared with obtained results via direct numerical integration of its equation, with
continuation and also with experimental results.