Reduced-order nonlinear modal equations of curved beams by using pseudo-mode

The finite element method is used to investigate steady-state vibrations of a curved beam with geometrical nonlinearity. The nonlinear strain-displacement relation is employed and the in-plane displacement in middle plane is included in the model. Equations of motion are derived by applying the principle of virtual work. A reduced-order model is derived by transforming the equations of motion from the physical coordinates to the modal coordinates on the pseudo-mode space. We can obtain only a few d.o.f. equations of motion in the modal coordinates, and present numerical results are compared with results obtained by applying a numerical integration directly to the equations of motion in the physical coordinates.