Free vibration of arches considering axial load effects
Veletsos, Anestis S.
Master of Science
An analysis of the in-plane, free vibration of uniform, circular arches is made considering the effects of both the axial load and the rotatory inertia in the arch. Both hinged- and fixed-ended arches are considered. From a study of numerical solutions, it is concluded that the axial load significantly decreases the natural frequencies of the predominantly inextensional modes, but may increase the frequencies of the extensional modes, especially of the higher extensional modes. The conditions of occurrence of each case are explained, and for several cases, simple approximate formulas are presented with the aid of which the natural frequencies of such systems may be estimated readily. In the course of this investigation, a study has also been made of the buckling load of the arch considering the extensibility of the arch axis. The buckling loads of fixed- or hinged-ended arches with 9° angle of opening are presented as a function of the slenderness ratio. The work reported herein is complementary to earlier studies carried out at Rice University on this subject. In the other studies, the effects of the axial load were not considered.