Wave Separation and Vibrational Energy Transmission in a Beam with an Internal Hinge

The analytical framework is presented for spatial separation of traveling and standing waves along a uniform beam with a single internal hinge of both a rotational spring and a damper. The mode complexity introduced by the local damping within the hinge, which may represent the passive energy absorption, is deduced to lead to the coexistence of acoustics and vibration of the steady-state response under the left-end harmonic base excitation. In this work, the hinge’s characteristics of the critical stiffness and damping are explored extensively, such that no vibration energy can be reflected backward into the excitation part by passing through the in-span hinge. In this way, the ideal one-way energy transmission and vibration localization are explicitly achieved in the beams of different boundary conditions. Furthermore, the power flow method is applied to illustrate the vibro-acoustic energy transmission and confinement over the beam length, and the vibrational energy dissipation ratio is estimated to describe the structural vibration suppression. Numerical results show that in the structural steady-state response, a great part of the input energy to the system is locally dissipated in the internal viscoelastic joint for the coexistence of traveling and standing waves in the two complementary regions of the beam.