初应力拱侧向振动的固有频率

在初应力位形上附加变形场论的框架下,引入自然坐标系,采用平截面假设,建立对数值方法和解析方法十分有用的、初应力曲拱位移变分方程。给出了平面曲拱在平面初始变形状态下附加变形变分方程,将拱的初始内力嵌入其中。根据所得的方程,讨论了面内载荷对圆截面初应力圆弧形拱侧向振动固有频率的影响,给出了侧向振动固有频率与初载荷的解析关系。结果表明,面内初始载荷的存在减小了侧向挠曲的固有频率;减少的数值与用频率方法诊断构件缺陷通常可得到的灵敏度属同量级。

NATURAL FREQUENCIES OF INITIALLY STRESSED ARCHES IN LATERAL VIBRATION

Under the natural coordinate system of arch axis, a variational formulation equation is established for arches with initial stress. The axial force, bending moment and shear force of plane arches in plane deformation that produced by initial loads are taken into account. An analytical relation between initial loads and the natural frequencies is presented, which shows that the natural frequencies in lateral vibration are reduced because of initial loads. The reduction of frequencies is of the same quantitative order as the sensitivity of frequency method in damage identification in structures.