Abstract
The differential 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.
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