Natural frequency calculation of elastically connected double-beam system with arbitrary boundary condition

In this paper, the free vibration characteristics of an elastically connected double-beam system (ECDBS) connected by an elastic layer with uniform elastic stiffness under arbitrary boundary conditions have been investigated. Timoshenko beam theory, in which the effects of shear deformation and rotational inertia are considered, is utilized to model the free vibration of the ECDBS, and displacement components can be obtained from the Haar wavelet series and their integral. Hamilton’s principle is applied to construct coupled governing equations, and the virtual spring boundary technique is applied to generalize boundary conditions at four ends of the ECDBS. The convergence and accuracy of the proposed method can be confirmed by comparing the results with those of previous literature. A lot of new features have been identified, such as the frequency characteristics of the ECDBS with different cross sections under arbitrary boundary conditions, which can be provided as reference data for future research.