Isochronous Beams by an Inclined Roller Support

The paper addresses the problem of isochronous beams, namely those that oscillate with a frequency that is independent of the amplitude also in the nonlinear regime. The mechanism adopted to obtain this goal is that of having, as a boundary condition, a roller that can slide on a given path. A geometrically exact Euler–Bernoulli formulation is considered, and the nonlinear analysis is done by the multiple time scale method, that is applied directly to the partial differential equations governing the motion without an a priori spatial reduction. The analytical expression of the backbone curve is obtained, up to the third-order, and its dependence on the roller path is addressed. Conditions for having a straight backbone curve, i.e., the isochronous beam, are determined explicitly. As a by-product of the main result, the free and forced nonlinear oscillations of a beam with an inclined support sliding on an arbitrary path have been investigated.