不同初始应力及变形对梁自振频率的影响

Effect of initial stresses and deformations on the natural frequencies of beams

应用Hamilton原理,建立了同时考虑初始荷载产生的弯曲和轴向变形影响时梁的控制微分方程,利用Galerkin方法推导出了考虑两种初始变形影响时简支梁自振频率的解析表达式,讨论了初始荷载大小、梁自身刚度及约束情况等不同参数对这两种初始变形对梁动力反应影响的敏感度,采用产生相同变形能的方式,定量地比较了各种边界条件下两种初始变形对梁自振频率的影响。

Based on the Hamilton principle,the governing differential equations were established for beams,considering the effects of both axial and flexural deformations induced by initial load and the analytical expression for the natural frequencies of a simply-supported beam under these effects was derived by the Galerkin method.A discussion on the analytical expression demonstrates the susceptivity of the two types of effects to the magnitude of initial load,beam stiffness and restraint conditions.Under the same amount of deformation energy produced,the effects of the two types of initial deformations on the natural frequencies of beams with various boundary conditions were compared quantitatively.