Modeling and nonlinear modal characteristics of the cable-stayed beam

•Considering the static configuration of the cable and beam, using the piecewise function, the mode shapes of the cable-stayed beam can be obtained precisely.•The nonlinear modal properties of the system have been investigated.•The nonlinear coupling term make a meaningful contribution of the modal properties.

Based on Hamilton's variational principle, the equations of motion of cable-stayed beam can be obtained. Then the in-plane and out-of-plane eigenvalue problems are solved. Using the piecewise function, the mode shapes of the cable-stayed beam can be obtained precisely. We investigate the nonlinear modal properties of the system with the direct approach and discretization approach. The effects of the nonlinear coupling term are also studied. It is worth noting that the coupling term makes a meaningful contribution of the nonlinear characteristics of the modal properties. Following, a discussion about the existence and stability of coupled nonlinear normal modes is presented.