点支承对受随从力梁稳定性的影响

Influence of Point Supports on the Stability of Beam Subjected to Follower Force

利用在梁的不同位置增加一定刚度的点支承,来提高随从力作用下梁的稳定性。建立随从力作用下点弹性支承梁的运动微分方程,利用微分求积法得到复特征方程。通过求解复特征方程,得出点支承梁复频率与随从力的变化关系,以及支承刚度对梁失稳形式的影响。计算结果表明,支承位置靠近自由端时,随着支承刚度的增加,梁的失稳形式由颤振转化为屈曲;支承位置靠近固定端时,随着支承刚度的增加,梁的失稳形式保持颤振;当刚性支承距离固定端大约L1=0.4L处,随从力失稳临界值最大,梁的稳定性最高。

To improve the stability of beam subjected to a follower compressive load,point support with certain stiffness is used on different positions.Differential equation of motion is established.By using differential quadrature method,numerical results of the complex characteristic equation are calculated.The change relation between complex frequency and follower force,and the influence of support stiffness on the destabilizing pattern of beam are obtained.The results shows that when the support is close to the free end of beam,with the increase of support stiffness,the destabilizing pattern of beam can change from flutter to buckling;when the support is close to the fixed end of beam,with the increase of support stiffness,the destabilizing pattern will always be flutter;when the rigid support is close to the fixed end at L1=0.4L,the critical value of follower force is up to the maximum.