平板力学史 : 平板理論への挑戦とその背景

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This paper presents the history of development and background on plate theories. The German physicist, Chladni discovered the various modes of free vibrations for plates by his experiments to form regular patterns with distributed powder. The French Academy invited applications for a price essay dealing with the mathematical theory of plate vibrations substantiated by experimental verification of the theoretical results in 1809. The French mathematician, Sophie Germain obtained a differential equation for vibration of plates using the calculus of variations, and she won the prize in 1816. Poisson and Navier also attempted to solve the vibration of plates with limited boundary conditions. The German physicist, G.R.Kirchhoff developed the first complete theory of plate bending in 1850. Love applied Kirchhoff's work to thick plates. W. Ritz proposed Ritz method in 1908 to analyze vibration plates. After that, many numerical methods such as the finite element method have been developed to analyze plate problems.
大同工業大学の論文