Adaptive finite element analysis of free vibration problems with frequency error control alone as the objective

SUN Haohan1,2,YUAN Si3

Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (4) : 106-115.

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PDF(1978 KB)
Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (4) : 106-115.

Adaptive finite element analysis of free vibration problems with frequency error control alone as the objective

  • SUN Haohan1,2,YUAN Si3
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Abstract

Adaptive finite element analysis of free vibration problems based on element energy projection (EEP) method has been proved to be reliable and efficient, where the errors of frequencies and modes are simultaneously controlled. In practical applications, the error evaluation of frequencies can sometimes be more required than the error distribution of modes. The paper proposes an approach to calculate the super-convergent frequencies, and then sets up the transformation relation between the global frequency error and the local mode error, so that the former is used to control the termination of the adaptive algorithm on the whole and the latter is used to drive mesh refinement locally. As a result, an adaptive finite element analysis of free vibration problem with frequency error control alone as the objective is established. The method is verified by its application to second order Sturm-Liouville problem and free vibration problem of elastic membrane.

Key words

free vibration / finite element method (FEM) / super-convergence / adaptive analysis / element energy projection (EEP)

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SUN Haohan1,2,YUAN Si3. Adaptive finite element analysis of free vibration problems with frequency error control alone as the objective[J]. Journal of Vibration and Shock, 2023, 42(4): 106-115

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