A variational formulation for vibration analysis of curved beams with arbitrary eccentric concentrated elements

In this paper, a modified variational method is developed to study the free and forced vibration of curved beams subjected to different boundary conditions. An arbitrary number of eccentric concentrated elements (ECEs) attached to the beams are taken into account. A modified variational principle and least-square weighted residual method are employed to impose the continuity constraints on the internal interfaces and the boundaries of the curved beam. The shear and inertial (or radial-tangential-rotational coupling) effects are incorporated into the system kinetic and potential functional using the generalized shell theory. To test the efficiency and accuracy of the present method, both free and force vibrations of the curved beams are examined under various boundary conditions including non-classical boundary conditions. Good agreement is observed between the results obtained by the present method and those from finite element program ANSYS. Corresponding curved beams with non-eccentric concentrated elements are also developed to investigate the effects of the ECEs on the vibration behaviors of the curved beams.