Free vibrations of non-circular arches with non-uniform cross-section

The di€erential equations governing free, in-plane vibrations of linearly elastic non-circular arches with non- uniform cross-section are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are presented for the quadratic, parabolic, catenary and elliptic arches with hinged±hinged, hinged±clamped, and clamped±clamped end constraints. Three general taper types for a rectangular section are considered. Experimental measurements of frequencies and their corresponding mode shapes agree closely with those predicted by theory. 7