Resonance regulation on a hydraulic pipe via boundary excitations

Resonance of a hydraulic pipe is the standing wave brought by the excitation in fact. This provides a new idea of vibration control of the hydraulic pipe, which means the resonance can be regulated by combination of excitations. Inspired by this opinion, the current work studies the multi-modal resonance regulation of a hydraulic pipe by multiple boundary excitations for the first time. The system considers the pump installed at the pipe's end as the fixed boundary with a displacement excitation. To minimize the multi-modal resonance, a force excitation and a moment excitation are acted on the right end. These three excitations have different phase angles and different amplitudes. But they have the same frequency to avoid combination resonance or even beat phenomenon and chaos. Combined responses subject to these three excitations are derived via the analytical method, and verified by a numerical simulation method. To find out the regulating mechanism, nonlinearities of the system are neglected for calculating the exact analytical solution first. The discussion clarifies that, the phase angle of the moment excitation has the same effect on different modal resonances. It is an advantage for the multi-modal resonance reduction. On the contrary, the phase angle of the force excitation has different effects on different modal resonances. By optimizing phase angles and amplitudes of excitations, both the first-two resonances are reduced by 50% comparing with the system suffered to the displacement excitation only. The optimized conclusion is also real for the nonlinear system. The potential energy and dissipation work are reduced by over 70% for the first-two resonances. This work proposes a potential boundary control technique for the hydraulic pipe system. Multi-modal resonance control can be realized by adjusting the phase angle or the amplitude of boundary excitations.