A-posteriori error estimator/corrector for natural frequencies of thin plate vibration problems

Abstract From the finite element theory, a discretized finite element system approaches a continuous system if the finite element size approaches zero. Based on this fact, an asymptotic formula, which describes the asymptotic behaviour of the predicted natural frequency of a system from the finite element analysis, is presented in this paper. Since the proposed asymptotic formula expresses a relationship between the natural frequency and wave number of a thin plate system, it can be viewed as an a-posteriori error estimator/corrector and used to correct the error of the predicted natural frequency of the system from the finite element analysis. Owing to the use of some assumptions and a non-conforming thin plate bending element in the process of deriving the asymptotic formula, the corresponding error estimator/ corrector can only result in a considerable, but not perfect, improvement on the predicted natural frequency from the finite element analysis when the thin plate is of finite size. An example has been given to show the possible application of the error estimator/corrector to the finite element analysis of thin plate vibration problems.