Journal of Central South University of Technology

, Volume 14, Issue 5, pp 708–712

# Mapping analysis of vibrating fundamental frequency for simple-supported elastic rectangle-plates with concentrated mass

• Qi Hong-yuan  (齐红元)
• Wang Shuang-xin  (王爽心)
• Zhu Heng-jun  (朱衡君)
Article

## Abstract

By conformal mapping theory, a trigonometric interpolation method between odd and even sequences in rectangle boundary region was provided, and the conformal mapping function of rectangle-plate with arc radius between complicated region and unite dish region was carried out. Aiming at calculating the vibrating fundamental frequency of special-shaped, elastic simple-supported rectangle-plates, in the in-plane state of constant stress, the vibration function of this complicated plate was depicted by unit dish region. The coefficient of fundamental frequency was calculated. Whilst, taking simple-supported elastic rectangle-plates with arc radius as an example, the effects on fundamental frequency caused by the concentrated mass and position, the ratio of the length to width of rectangle, as well as the coefficient of constant in-plane stress were analyzed respectively.

## Key words

conformal mapping elastic simple-supported plates vibration fundamental frequency mode method of trigonometric interpolation

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© Central South University Press, Sole distributor outside Mainland China: Springer 2007

## Authors and Affiliations

• Qi Hong-yuan  (齐红元)
• 1
Email author
• Wang Shuang-xin  (王爽心)
• 1
• Zhu Heng-jun  (朱衡君)
• 1
1. 1.School of Mechanical and Electric Control EngineeringBeijing Jiaotong UniversityBeijingChina