Vibration suppression of a geometrically nonlinear beam with boundary inertial nonlinear energy sinks

As a simplified model of structures of many kinds, the Euler Bernoulli beam has proved useful for studying vibration suppression. In order to meet engineering design requirements, inertial nonlinear energy sinks (I-NESs) can be installed on the boundaries of an elastic beam to suppress its vibration. The geometric nonlinearity of the elastic beam is here considered. Based on Hamilton's principle, the dynamic governing equations of an elastic beam are established. The steady-state response of nonlinear vibration is obtained by the harmonic balance method and verified by numerical calculation. It is found that the geometric nonlinearity of the beam principally affects the first-order main resonance and reduces the response amplitude. An uncoupled system and the coupled I-NES system both show strong nonlinear hardening characteristics. I-NES achieves good vibration suppression. Finally, the optimal range of parameters for different damping is discussed. The results show that the vibration reduction effect of an optimized inertial nonlinear energy sink can reach 90%.