In-plane vibration of circular arches with variable cross-sections

Free and forced in-plane vibrations of circular arches with variable cross-sections are investigated. Using the Kirchhoff assumptions for thin beams and taking the neutral axis as inextensible, a closed form solution is obtained for circular arches of uniform cross-section. This exact solution is used for circular arches with stepped cross-sections and is applied to obtain an approximate solution for arches with non-uniform cross-sections. For free vibration, an analytic form of frequency equation is obtained by using the general solution expressed in terms of some initial parameters at one end of the arch; while for forced vibration, the system's response is obtained analytically by solving a set of algebraic equations with only three unknowns. Several examples are presented to illustrate the validity and accuracy of the method.NRC publication: Ye