Axial-bending coupling vibration of mass eccentric double-beam system with discrete elastic connections

The existence of mass eccentricity will lead to the energy transfer between axial and flexural vibrations of a beam. To study the coupling properties of a double-Timoshenko beam system, a non-uniform coupled double-beam system is modeled in which the upper beam is typical and the lower beam is mass eccentric simulated by a non-uniform two-layer Timoshenko beam. By incorporating Hamilton's principle and spectral element method, the axial-bending coupled governing equations of the system are derived and the approach can also be easily used to analyze the influences of the parameters and other coupled beam systems. Both the free and forced vibration results of a double-beam system by this method are consistent with the corresponding finite element model's and thus this method is validated. The coupled properties and their mechanism are revealed. The influences of axial and transverse flexible connection on the coupling properties including free and forced vibration are investigated. A systematic matching principle of reducing the vibration of the coupled system is proposed.