### Free Vibration Of Simply Supported Beam Subjected To Axial Force

*Journal of University of Babylon*

2012, Volume 20, Issue 1, Pages 301-314

2012, Volume 20, Issue 1, Pages 301-314

#### Abstract

This paper presents a theoretical investigation of the free transverse vibrations of a uniform beam that is simply supported at both ends subjected to a static axial force. The beam is considered to have different shapes of cross section (Rectangle section, Box section, I-section and T-section) with the same value of area for all and at different values of second moments of area. The problem is modeled and solved analytically. based on the analytical solution. The effect of static axial force (tension or compression) on the characteristics of vibration ( natural frequency and mode shape) are studied. It was concluded that increasing the tensile axial force causes an increase in the natural frequency while increasing the compressive force resulting in decreasing the natural frequency. It is found that the beam of rectangular cross section have natural frequency lower than the other types of cross sections for the same applied force, while the beam of T-section has the higher value of natural frequency compared with other types. The beam of rectangle section losses its stability by buckling with compression force less than the other types. The beams of the same shape of cross section and the same value of the area have lower value of natural frequency at which have smaller value of second moment of area.

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