辛解框架下矩形夹芯板的新基准自由振动解

IF 3.5 3区 材料科学 Q1 ENGINEERING, MECHANICAL
Chao Zhou, Zhuofan Ni, Xinran Zheng, Bo Wang, Rui Li
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引用次数: 1

摘要

本文首次尝试在辛解框架内得到一些新的矩形夹层板自由振动解析解,这些解析解在常规解析解框架内难以求解。蜂窝芯和桁架芯夹层板首先作为等效厚板处理。然后在哈密顿系统内建立控制对偶方程。然后,将原问题转化为两个子问题,利用变量分离和辛特征展开得到子问题的解析解。叠加得到最终的自由振动解析解,新出现的系数根据原问题与叠加之间的等价性确定。本文所提出的辛叠加法固有频率解和模态振型解分别通过数值结果和图形结果进行了定量显示,并通过与经典解、实验结果或精化有限元模型数值解的一致性得到了很好的验证。除了提供可作为基准的新结果外,还分析了尺寸参数对夹芯板固有频率的影响。由于所开发的方法放弃了任何试解的假设,并遵循严格的推导来产生新的解析解,因此它为解决更复杂的夹层板和壳的问题提供了机会。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On new benchmark free vibration solutions of rectangular sandwich panels within the symplectic solution framework
In this paper, the first attempt is made to obtain some new analytic free vibration solutions of rectangular sandwich panels within the symplectic solution framework, which are difficult to tackle within the conventional analytic solution framework. The sandwich panels with honeycomb and truss cores are first treated as equivalent thick plates. The governing dual equation is then established within the Hamiltonian system. Subsequently, the original problem is converted into two subproblems whose analytic solutions are acquired by applying the variable separation and symplectic eigen expansion. The superposition yields the final analytic free vibration solution, with the emerging coefficients determined according to the equivalence between the original problem and the superposition. The natural frequency and mode shape solutions by the present symplectic superposition method are quantitatively shown via numerical and graphical results, respectively, and are all well validated by consistency with classical solutions, experimental results, or the numerical solutions by the refined finite element modeling. Besides providing the new results that can serve as benchmarks, the effects of the size parameters on the natural frequencies of the sandwich panels are also analyzed. Since the developed method gives up the assumption of any trial solutions and follows a rigorous derivation to yield new analytic solutions, it provides opportunities for solving more intricate problems of sandwich panels and shells.
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来源期刊
Journal of Sandwich Structures & Materials
Journal of Sandwich Structures & Materials 工程技术-材料科学:表征与测试
CiteScore
9.60
自引率
2.60%
发文量
49
审稿时长
7 months
期刊介绍: The Journal of Sandwich Structures and Materials is an international peer reviewed journal that provides a means of communication to fellow engineers and scientists by providing an archival record of developments in the science, technology, and professional practices of sandwich construction throughout the world. This journal is a member of the Committee on Publication Ethics (COPE).
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