The main objective of the present paper is to study the transverse vibration of the prestressed beams. The differential equation of the transverse vibration of the Euler-Bernoulli beam is developed, in which the initial axial strain in every cross section of the beam is taken into account, so that the initial normal stress is not equal to zero. We have proposed some formulae to determine the natural frequencies of the prestressed beam. | Vietnam Journal of Mechanics, VAST, Vol. 28, No. 3 (2006), pp. 145- i54 ON THE COMPRESSION SOFTENING EFFECT OF PRESTRESSED BEAMS NGUYEN VAN KHANG , NGUYEN PHONG DIEN, NGUYEN THI VAN HUONG Department of Applied Mechani cs, Hanoi University of Technology Abstract. The main objective of the present paper is to study the transverse vibration of the prestressed beams. The differential equation of the transverse vibration of the Euler-Bernoulli beam is developed , in which the initial axial strain in every cross section of the beam is taken into account, so that the initial normal stress is not equal to zero. We have proposed some formulae to determine the natural frequencies of the prestressed beam. The forced transverse vibration of the beam with a moving external force has been considered. From this it follows compression softening effect of prestressed beams. A detailed comparison between the calculating results for the prestressed and the non-prestressed beam is also presented. 1. INTRODUCTION In recent years, the prestressed ferro-concrete beams are usually used in branches of the construction and the road traffic. However, the research on the transverse vibration of the prestressed beams is still not extensively considered in Vietnam, alt hough it is very necessary. The calculation of the stress of these beams is only confined to the evaluation of static stresses using t he experimental formulae. The international literature on t his respect is also little and a systematic study has not been shown. In some publications [1-8], the influence of axial forces or fatigue cracks on the natural frequencies of t he beam, which is pre-compressed by t he axial forces, was investigated. In the last case, the axial forces are usually supposed as constants. The main objective of the present paper is to study in detail the transverse vibration of the prestressed beams. Firstly, the differential equation of the transverse vibration of the Euler-Bernoulli beam is .
