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.

中文翻译：

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基于铁木辛柯梁理论的选择性激光冲击加工后叶片受迫振动分析

摘要 本文的主要目的是基于功能梯度（FG）铁木辛柯梁理论，从理论上探讨选择性激光冲击处理（LSP）对叶片受迫振动响应的影响。考虑到弹性模量梯度分布、预应力和变截面导致直接求解的复杂性，将选择性LSP后的实际叶片简化为一系列均匀的段。通过积分技术将预应力转化为附加激励载荷，从而得到该类型管片的解析解。然后，为了避免求解额外的积分常数，利用变形的连续性条件，以及加强位置、加强层厚度和单面/双面的影响，给出了任意截面旋转预应力FG梁受迫振动的简单半解析解。分别讨论了侧面冲击模式对振动响应幅值的影响。结果表明，选择性LSP可以通过扩大强化区、加深强化层和采用双面冲击来有效抑制振动挠度。