Free Vibrations and Buckling Loads of Columns with Multiple Elastic Springs

여러 개의 스프링으로 탄성지지된 기둥의 자유진동 및 좌굴하중

  • Published : 2000.12.01

Abstract

Numerical methods for calculating both the natural frequencies and buckling loads of columns with the multiple elastic springs are developed. In order to derive the governing equations of such columns, each elastic spring is modeled as a discrete elastic foundation with the finite longitudinal length. By using this model, the differential equations governing both the free vibrations and buckled shapes, respectively, of such columns are derided. These differential equations are solved numerically. The Runge- Kutta method is used to integrate the differential equations, and the determinant search method combined with Regula-Falsi method is used to determine the eingenvalues. namely natural frequencies and buckling loads. In the numerical examples, the clamped-clamped. clamped-hinged, hinged-clamped and hinged-hinged end constraints are considered. Extensive numerical results including the frequency parameters, mode shapes of free vibrations and buckling load parameters are presented in the non-dimensional forms.

이 논문은 여러 개의 스프링으로 탄성지지된 기둥의 고유진동수와 좌굴하중에 산정에 관한 연구이다. 하나의 스프링을 폭이 매우 좁은 탄성지반으로 모형화하고, 이 모형을 이용하여 기둥의 자유진동과 좌굴된 기둥의 탄성곡선을 지배하는 미분방정식을 유도하였다. 이 미분방정식들을 Runge-Kutta법과 행열값 탐사법을 이용하여 미분방정식의 고유치 즉 고유진동수와 좌굴하중을 산정하였다. 수치해석 예에서는 고정-고정, 고정-회전, 회전-고정 및 회전-회전의 단부조건을 고려하였다. 수치해석의 결과로 기둥 변수들과 고유진동수 및 좌굴하중 사이의 관계를 고찰하고, 스프링으로 지지된 지지되지 않은 기둥의 진동형을 비교하였다.

Keywords

References

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