考虑随从力作用的运动粘弹性板的动力稳定性

从二维粘弹性微分型本构关系出发,建立了运动Kelvin-Voigt粘弹性矩形薄板受切向均布随从力作用下的运动微分方程,采用归一化幂级数法,导出了四边简支运动粘弹性板在随从力作用下的复特征方程。分析了系统的前三阶复频率与量纲一运动速度、量纲一延滞时间及量纲一随从力的变化关系。计算结果表明:量纲一延滞时间、量纲一运动速度和量纲一随从力对运动非保守粘弹性板的动力稳定性有着显著的影响。

DYNAMIC STABILITY OF MOVING VISCOELASTIC PLATE SUBJECTED TO FOLLOWER FORCE

Based on two dimensional viscoelastic differential constitutive relationships,the differential equation of motion of a moving viscoelastic plate constituted by Kelvin-Voigt model under the action of uniformly distributed tangential follower forces is established,and the complex characteristic equation for the moving viscoelastic plate with four edges simply supported and subjected to follower forces is derived by the normalized power series method.The variation relationship between the first three complex frequencies of the system and the dimensionless moving speed,delay time as well as follower force is analyzed.The numerical results show that the dimensionless delay time,moving speed and follower force have remarkable effects on dynamic behaviors and stability of the moving non-conservative viscoelastic plate.