Free vibration of elastically coupled dual-span curved beams

The free vibration response of dual-span extensional and inextensional circular curved beams constrained by an intermediate elastic support is studied. The elastic constraint consists of a transverse and rotational spring, as well as a tangential spring, which couples the extensional motion of one span with the other. Wave propagation techniques are used to formulate the eigenvalue problem, which result in exact eigensolutions. The effects of the support type and stiffness on the transverse and tangential modes are examined. In addition, the influence of the curvature on the free response of the extensional curved beam is also addressed. For certain support conditions, the extensional and inextensional curved beams have similar behavior. In general, however, the behavior of the system is shown to depend strongly on the type of support, the modeling of the beam as extensional or inextensional, and whether the natural frequencies are above or below the cut-off frequency.