Type and number of elements effect on the calculation of cantilever beam free natural frequencies using the finite element method

2019 2nd International Conference on Electrical, Communication, Computer, Power and Control Engineering (ICECCPCE) Pub Date : 2019-02-01 DOI:10.1109/ICECCPCE46549.2019.203747

I. J. Hasan

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引用次数: 1

Abstract

The free vibration calculation of a rectangular cross-section cantilever beam will be analyzed in this study. Using the finite element method (FEM), the stiffness and mass matrices were created and solving the behavior equation with a general program suitable for any number of a one-dimension element using (MATLAB) program. For the same condition, but with different numbers and types of elements, the (ANSYS) software will be used to simulate the cantilever beam. The first three natural frequencies and mode shapes are investigated for each case, and the results compared with the exact solution. The results showed that the difference between the exact and numerical results are decreases when the number of elements increases and the one-dimension element used with the (MATLAB) is more efficient for beam, one-dimension element (BEAM188 & BEAM189) gives more efficient results with less number of elements in comparing with the two and three-dimensions element (PLANE183 & SOLID186), two and three-dimensions element (PLANE182 & SOLID185) needs high number of elements to give suitable results.

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有限元法计算悬臂梁自由固有频率时，单元类型和单元数量的影响

本文分析了矩形截面悬臂梁的自由振动计算。采用有限元法建立了结构的刚度矩阵和质量矩阵，并利用MATLAB程序编制了适用于任意数量一维单元的通用程序求解了结构的性能方程。在相同条件下，采用不同单元数量和类型的ANSYS软件对悬臂梁进行模拟。研究了每种情况下的前三个固有频率和振型，并将结果与精确解进行了比较。结果表明，随着单元数的增加，精确计算结果与数值计算结果之间的差异减小，使用(MATLAB)的一维单元对梁的计算效率更高，一维单元(BEAM188和BEAM189)与二维和三维单元(PLANE183和SOLID186)相比，单元数较少，计算效率更高，而二维和三维单元(PLANE182和SOLID185)需要较多的单元数才能得到合适的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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2019 2nd International Conference on Electrical, Communication, Computer, Power and Control Engineering (ICECCPCE)

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