体外预应力梁动力特性分析的一种新方法

A new method for analyzing dynamic behavior of externally prestressed beam

提出了两个假设:在第1自振频率计算中,体外筋预拉力增量产生的弯矩图等效为梁第1振型的比例图,忽略了体外筋对其他自振频率的效应。这两个假设改进了文献[5]中的体外筋预拉力增量与梁跨中位移成正比的假设。建立了体外预应力梁的动力平衡方程,解得梁的振型和自振频率。与文献[5]中的分析方法相比,由于假设更为合理,计算结果也更准确,与数值解吻合良好。计算结果表明:文献[5]方法低估了体外筋对第1自振频率的效应;随着体外筋面积和偏心距的增加,梁的自振频率也随之增加。

Two assumptions are made that in 1st natural frequency calculation,the bending moment diagram caused by the tension increment of external tendon is equivalent to the diagram proportional to the first vibration mode,and the effect of external tendon on the other natural frenquencies is neglected.These assumptions modify the assumption in reference [5],that is,tension increment of external tendon is proportional to the deflection at mid-span of beam.The dynamic equilibrium of the externally prestressed beam is established and the vibration modes and natural frequencies of the beam are obtained.Comparing with the analytical method in reference [5],the assumptions are more rational,therefore the results are more accurate,and conform well with the numerical results.The calculation results show： the effect of external tendon on 1st natural frequency is underestimated by the method in reference [5]： when the area and the eccentricity of external tendon are increased,the vibration frequency of the beam increases.