Improving the Accuracy of Geometric Interpolation for Determining Fundamental Frequency of Parallelogram Plates Vibration

The paper considers a method of geometric interpolation of basic solutions for two-dimensional problems in the theory of elasticity and structural mechanics, particularly as applied to mechanical engineering. The scope of the study is the vibrations of thin elastic parallelogram plates of constant thickness. To determine the fundamental frequency of vibration it is suggested to use an interpolation method with a newly introduced geometric characteristic of plates which is a ratio of inner conformal radius to outer conformal radius. Taken from the theory of conformal mapping, the conformal radii of domains are obtained by mapping the plates onto the interior and exterior of a unit circle. The studies have shown that the use of the suggested ratio ​​gives up to twice more accurate results of the geometric interpolation. The paper presents the basic terms and formulas of the method with comparative analysis of the curve diagrams using a shape factor and a conformal radii ratio.