加筋复合材料层合板的自由振动特性与优化

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摘要该研究运用层合板理论对纵横双向加筋复合材料层合板的自由振动问题进行了理论研究。基于Kirchhoff-Love假设和复合材料结构力学，推导了层合板的本构方程，运用热力学第二定律和瑞利-里兹法建立了四边简支加筋层合板自由振动固有频率的特征方程。通过编写MATLAB软件程序，分析了加筋数目和加筋横截面几何参数的改变对加筋层合板固有频率的影响，所得的理论解与ABAQUS软件有限元结果非常吻合，验证了理论解的正确性。根据参数分析所得的结果，提出了层合板加强筋的优化方案。该研究方法避免了求解平衡微分方程时必须考虑的各个加强筋与层合板之间的耦合作用，大大简化了繁琐的推导过程，节省了计算量，更为主要的是，该方法可以准确地分析当层合板被由不同材料制作、具有不同横截面几何形状、不等间距排放的加强筋增强后的自由振动特性，为航空航天先进复合材料的结构设计和力学分析提供有力的技术支持。

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	梁浩锋
	夏飞
	金福松
	石陈玉
	薛江红

关键词 ：层合结构, 加强结构, 自由振动, 能量法, 板壳理论

Abstract：The free vibration of composite laminates reinforced by longitudinal and transverse ribs was analysed.Constitutive equations were derived based on Kirchhoff-Love assumptions and according to the structural mechanics of composite materials.Using the second law of thermodynamics and Ritz method, a characteristic equation was established to calculate the natural frequency of free vibration of simply supported composite laminates reinforced by longitudinal and transverse ribs.By developing MATLAB program, the influence of rib, including its number and the geometric parameters of its cross section, on the natural frequency of composite laminates was analyzed.According to the parametric study, a further optimization scheme of ribs was put forward so as to acquire the best strength-to-weight ratio.The analytical solutions obtained herein were compared with the finite element results of ABAQUS analysis and it is found they are in good agreement with the latter, thereby demonstrating the correctness of the theoretical approach.The theoretical approach proposed avoids the solving of the coupling relationship between the ribs and the composite laminate which must be considered in solving equilibrium equations.More importantly, this approach can be effectively applied to evaluate the free vibration characteristics of laminates reinforced by ribs made of different materials with different cross-section geometry and unequal spacing placement.

Key words： laminated structure stiffened structure free vibration energy method theory of plates and shells

收稿日期: 2020-04-23 出版日期: 2021-09-28

引用本文:

梁浩锋，夏飞，金福松，石陈玉，薛江红. 加筋复合材料层合板的自由振动特性与优化[J]. 振动与冲击, 2021, 40(18): 190-196.
LIANG Haofeng,XIA Fei,JIN Fusong,SHI Chenyu,XUE Jianghong. Free vibration of rib-reinforced composite laminates and its optimization. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(18): 190-196.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I18/190

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