摘要
采用整体分析和拉普拉斯变换方法，研究了轴向力作用下考虑支承质量时弹性支承多跨均匀连续梁的横向振动，推导出了频率方程和振型函数的解析表达式．所得公式全面、完整，适用于各种中间支承情况和各种轴向力情况．通过实例分析了支承质量和支承弹簧刚度对连续梁固有频率的影响．结果表明，支承质量会降低连续梁的固有频率，但对低阶固有频率的影响很小．特别是当支承质量较小时，完全可以不考虑其对低阶固有频率的影响．连续梁固有频率随着支承弹簧刚度的增大而增大，当弹簧刚度很大时，弹性支承连续梁的固有频率接近于刚性支承连续梁的固有频率．
On considering axial load and support masses,the uniform continuous beam with
elastic multisupport is analyzed as onepiece structure,and its natural transverse vibration is
studied.The frequency equation and the normalmode function of the beam are derived by
Laplace Transform.The formulas are overall and complete,they can by applied to any
continuous beam with all kinds of intermediate supports and acted by axial load.The effects of
the masses and the stiffnesses of the supports on natural frequencies are illustrated by some
examples.It is shown that the frequencies decrease with the increase of the masses,the effect
of the masses on lower frequencies is small,so the masses can by ignored when they are
small.The frequencies increase with the increase of the stiffnesses,and when the stiffnesses
gradually become greater,the frequencies of the beam with elastic supports will approach these
of the beam with rigid supports.
出处
《西安石油学院学报（自然科学版）》
1999年第4期70-72,75,共4页
Journal of Xi'an Petroleum Institute（Natural Science Edition)
关键词
固有频率
弹性支承
轴向载荷
连续梁
振动频率
transverse vibration,natural frequency,elastic
support,axial load,continuous beam,frequency euqation
