Vibrational power flow analysis of Timoshenko microbeams with a crack

In this paper, an analytical model based on the modified couple stress theory and Timoshenko beam theory is developed to study the vibrational power flow of a microbeam with a crack. The open edge crack on the microbeam is modeled as a rotational spring, which connects the two segments of the microbeam separated by the crack location. The governing equations of the cracked microbeam are derived from Hamilton's principle. By introducing the differential operator method, the differential equations are transformed into algebraic equations, and the governing equations are decoupled. The wave propagation method is applied to solve the vibrational problem of a cracked microbeam under a transverse harmonic excitation. Both the input power flow and the transmitted power flow in the cracked microbeam are computed and analyzed. The size effect of the cracked microbeam in terms of material length scale is firstly analyzed. Subsequently, the effects of crack depth and crack location on the input and transmitted power flows are investigated. It is found that the existence of crack significantly changes the transmission characteristics of the power flow.