213 / 2019-08-29 21:41:18

Forced vibration analysis of blade after selective laser shock processing based on the theory of functionally graded beam

计算流体力学、多场耦合、生物力学、动力学等 > 动力学相关

Abstract: Improving the characteristic of vibration response is an important way to extend the service life of engine blades. At present, for the laser shock processing (LSP) technology that has been successfully applied to enhance the service life of blades, most of the relevant studies mainly focus on revealing its internal strengthening mechanism related to residual compressive stress, grain refinement and high-density dislocations in the material of the local strengthened zone through experiments and simulations, and still lack the researches about the vibration response of blade after LSP treatment. The main purpose of this work is to theoretically explore the effect of the selective LSP on the forced vibration response based on the functionally graded Timoshenko beam theory. Firstly, a TC4 titanium alloy blade after the selective LSP treatment is simplified into a rotating diamond-shaped cantilever beam model with the gradient distributions of both elastic modulus and residual compressive stress induced by microstructure evolution and plastic deformation at the local strengthened zone, and further regarded as an axially loaded pre-stressed functionally graded stepped beam with finite uniform segments. Based on functionally graded beam and axially loaded Timoshenko beam theory, the pre-stress is transformed into an additional excitation load by an integral technique, and thus an analytical solution for this type of segment is obtained. Then, in order to avoid the complex calculation process of additional integration constants, a simple semi-analytical solution for forced vibration of rotating pre-stressed functionally graded beam with arbitrary cross-section is presented by using the continuity conditions of deflection and rotation angle, and the effects of strengthened zone, thickness of strengthened layer and single-sided/double-sided impact on the response characteristic of forced vibration are discussed, respectively. The results show that the selective LSP can effectively suppress the response of vibration deflection. As the distance from the strengthened zone to the tip of blade decreases, the response level of blade first decreases and then rises. And the appropriate expansion of strengthened zone is beneficial to enhance the suppression effect on the blade response. In addition, the stiffness of strengthened zone increases with the increasing strengthened layer thickness, which results in the improvement of strengthening effect. Compared with the single-sided impact, the double-sided impact can cause deeper strengthened layer, and the corresponding suppression effect on the blade response is also more significant.