A note on in-plane vibrations of arch-type structures of non-uniform cross-section: The case of linearly varying thickness

This study deals with the determination of the first two natural frequencies of vibration of symmetric circular arches with linearly varying thickness carrying concentrated masses. Two situations are taken into account: (a) hinged arches; (b) clamped arches. The displacement amplitude is approximated by means of polynomial co-ordinate functions which include an optimization, exponential parameter γ. The frequency equation is generated by means of the Ritz method and the eigenvalues are then optimized with respect to the parameter γ.