Forced vibration analysis of blade after selective laser shock processing based on Timoshenko’s beam theory

Abstract

The main purpose of this paper is to theoretically explore the effect of selective laser shock processing (LSP) on the forced vibration response of blade based on the functionally graded (FG) Timoshenko’s beam theory. Considering the complexity of direct solution caused by gradient distribution of elastic modulus, pre-stress, and variable cross-section, the actual blade after selective LSP is simplified into a series of uniform segments. The pre-stress is transformed into an additional excitation load by an integral technique, and thus an analytical solution for this type of segment can be obtained. Then, in order to avoid solving the additional integration constants, a simple semi-analytical solution for the forced vibration of rotating pre-stressed FG beam with arbitrary cross-section is presented by using the continuity condition of deformation, and the effects of strengthened position, thickness of strengthened layer and single-sided/double-sided shock mode on the amplitude of vibration response are discussed, respectively. The results show that the selective LSP can effectively suppress the vibration deflection by enlarging the strengthened zone, deepening the strengthened layer and employing the double-sided shock.