Conformal analysis of fundamental frequency of vibration of elastic clamped plates

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Abstract

To calculate the fundamental frequency of vibration of special-shaped and elastic clamped plates, the conformal mapping theory is adopted to separate the interpolating points of a complicated boundary into odd and even sequences, both of which can be mutually iterated, so that the conformal mapping function between the complicated region and the unit dish region is established. Trigonometric interpolation and convergence along the normal direction methods are provided, and the complex coefficients of the conformal mapping function are calculated. Galerkin method is used to obtain the solution of fundamental frequency in the vibrating differential function of the complicated vibrating region. Finally, taking ellipse elastic clamped plates as an example, the effects on fundamental frequency coefficient caused by eccentric ratio e and area size are analyzed.

Keywords

vibration, fundamental frequency, mode, conformal mapping, trigonometric interpolation method, elastic clamped plates

CHANGE HISTORY

A Correction to this paper has been published:
https://doi.org

The Retraction Note was updated to reflect reception of statements of disagreement from all authors.

This article has been retracted.Please see the Retraction Notice for more detail:
https://doi.org