Conformal analysis of fundamental frequency of vibration of simple-supported elastic ellipse-plates with concentrated substance

Abstract

Aimed at calculating the fundamental frequency of vibration of special-shaped, simple-supported elastic plates, Conformal Mapping theory is applied, and the mathematical method of trigonometric interpolation with interpolation points mutual iterative between odd and even sequences in boundary region is provided, as well as the conformal mapping function which can be described by real number region between complicated region and unit dish region is carried out. Furthermore, in the in-plane state of constant stress, vibrating function is completed by unit dish region method for simple-supported elastic plates with concentrated substance of complicated vibrating region, and the coefficient of fundamental frequency of the plate is analyzed. Meanwhile, taking simple-supported elastic ellipseplates as an example, the effects on fundamental frequency caused by eccentric ratio, the coefficient of constant inplane stress, as well as the concentrated substance mass and positions are analyzed respectively.

Keywords

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