Conformal analysis of fundamental frequency of vibration of elastic clamped plates

2007年第2卷第4期

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《机械工程前沿（英文）》 >> 2007年第2卷第4期 doi: 10.1007/s11465-007-0073-z

Conformal analysis of fundamental frequency of vibration of elastic clamped plates

School of Mechanical and Electric Control Engineering, Beijing Jiaotong University, Beijing 100044, China;

发布日期： 2007-12-05

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摘要

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 and area size are analyzed.

关键词

direction ; theory ; vibration ; odd ; complicated boundary