Conformal analysis of fundamental frequency of vibration of elastic clamped plates |
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Authors: | Qi Hongyuan and Zhu Hengjun |
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Affiliation: | (1) School of Mechanical and Electric Control Engineering, Beijing Jiaotong University, Beijing, 100044, China |
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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.
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Translated from Engineering Mechanics, 2006, 23(10): 73–76 译自: 工程力学] |
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Keywords: | vibration fundamental frequency mode conformal mapping trigonometric interpolation method elastic clamped plates |
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