Free vibration of a toroidal shell with elliptical cross-section.

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  • だ円断面を有する環状殻の自由振動
  • ダエン ダンメン オ ユウスル カンジョウ カク ノ ジユウ シンドウ

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Abstract

An analysis is presented for the free vibration of a toroidal shell with elliptical cross-section as an example of a non-circular cross-section. For this purpose, the governing equations of vibration of toroidal shells are written as a coupled set of first order differential equations by the use of the transfer matrix of the shell. Once the transfer matrix has been determined by the numerical integration of the transfer matrix equation, the frequency equations are derived in terms of the elements of the matrix. The method is applied to toroidal shells with elliptical cross-section and the natural frequencies and the mode shapes of vibration are calculated numerically, and the effects of the cross-section of the shell on the vibration are studied.

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