Non-planar vibrations of beams with geometric imperfections and hysteretic boundary conditions.

The non-planar vibration response of a beam with initial geometric imperfections is investigated through the development of a geometrically nonlinear beam model. The equations of motion are derived through the application of Lagrange's equation and accounting for the interaction of the initial deviations from straightness and the transverse bending deformations. The experimental frequency response of a nuclear fuel rod supported by two prototypical spacer grids is described by the response in the driven direction and the response in the non-driven direction. The beam model also includes a hysteretic restoring moment at the ends to represent the constraint of the spacer grid and the associated reduction in resonant frequency as the applied force is increased. A pseudo-arc-length continuation algorithm is used to solve the equations of motions and calculate the periodic solution. Comparison between the nonlinear beam model response and the experimental data shows good agreement around the resonant frequency of the first bending mode for both the driven and companion modes. [ABSTRACT FROM AUTHOR]