针对复杂边界条件下金属空心球复合材料点阵夹芯梁振动机理不清晰的问题，基于点阵芯层均质等效假设，采用改进傅里叶级数法和Rayleigh-Ritz法，建立了任意边界条件下金属空心球复合材料点阵夹芯梁自由振动特性分析的理论模型。引入2种不同类型的约束弹簧来模拟点阵夹芯梁两端的弹性边界条件；采用APDL自编程方式计算出随机分布金属空心球复合材料的等效参数。通过与数值仿真及现有文献对比，验证了理论模型的正确性。在此基础上，研究了杆径、倾角、填充率等系统参数对结构振动特性的影响规律。研究结果表明：弹性边界会降低结构固有频率，导致结构固有频率以质量控制为主；增加金属空心球的占比，会降低点阵夹芯梁的固有频率。
To solve the problem that the vibration mechanism of metal hollow sphere composite lattice sandwich beam is unclear under complex boundary conditions, Based on the hypothesis of homogeneous equivalence of lattice core layer, a theoretical model of free vibration characteristics analysis of metal hollow sphere composite lattice sandwich beam under arbitrary boundary conditions was established by using improved Fourier series method and Rayleigh-Ritz method. Two different types of constraint springs are introduced to simulate the elastic boundary conditions at both ends of lattice sandwich beams. The equivalent parameters of randomly distributed metal hollow sphere composites are calculated by APDL self-programming method. Compared with numerical simulation and existing literature, the theoretical model was verified to be correct. On this basis, the influence of system parameters such as rod diameter, inclination angle and filling rate on structural vibration characteristics is studied. The results show that the elastic boundary will reduce the natural frequency of the structure, which will lead to the quality control. Increasing the proportion of metal hollow spheres will reduce the natural frequency of lattice sandwich beams.
2025,47(18): 12-17 收稿日期：2024-10-8
DOI：10.3404/j.issn.1672-7649.2025.18.003
分类号：U661.44
基金项目：山东省重点研发计划（重大创新工程）（2022CXGC020509）；装备预先研究应用创新项目（62602010322）；国防基础科研计划项目（KY10100230078）；烟台市科技创新发展计划校地融合项目（2023XDRH018）
作者简介：王文群（1995 – ），男，硕士，工程师，研究方向为船舶结构力学
参考文献：
[1] HWU C B, CHANG W C, GAI H S. Vibration suppression of composite sandwich beams[J]. Journal of Sound and Vibration, 2004, 272(1-2): 1-20.
[2] 娄佳, 马力, 吴林志. 复合材料四面体点阵夹芯梁的自由振动分析[J]. 固体力学学报, 2011, 32(4): 339-345.
[3] LOU J, WANG B, MA L, et al. Free Vibration analysis of simply supported sandwich beams with lattice truss core[J]. Materials Science and Engineering: B, 2012, 177(19): 1712-1716.
[4] LI F M, LYU X X. Active vibration control of lattice sandwich beams using the piezoelectric actuator/sensor pairs[J]. Composites Part B-engineering, 2014, 67: 571-578.
[5] ZHAO Z, WEN S R, LI F M. Vibration analysis of multi-span lattice sandwich beams using the assumed mode method[J]. Composite Structures, 2018, 185: 716-727.
[6] SONG Z, LI F M. Aeroelastic analysis and active flutter control of nonlinear lattice sandwich beams[J]. Nonlinear Dynamics, 2014, 76: 57-68.
[7] SONG Z G, LI F M. Flutter and buckling characteristics and active control of sandwich panels with triangular lattice core in supersonic airflow[J]. Composites: Part B, 2017, 108: 334-344.
[8] CHEN J E, ZHANG W, SUN M, et al. Free vibration analysis of composite sandwich plates with different truss cores[J]. Mechanics of Advanced Materials and Structures, 2018, 25(9): 701-713.
[9] XU G D, ZENG, T, CHENG S, et al. Free vibration of composite sandwich beam with graded corrugated lattice core[J]. Composite Structures, 2019, 229: 111466.
[10] JIN Y Q, LU Y Y, YANG D, et al. An analytical method for vibration analysis of multi-span Timoshenko beams under arbitrary boundary conditions[J]. Archive of Applied Mechanics, 2024, 94: 529-553.
[11] JIN Y Q, LUO X W, LIU H X, et al. An accurate solution method for vibration analysis of multi-span lattice sandwich beams under arbitrary boundary conditions[J]. Thin-Walled Structures, 2022, 175: 109214.
