Vibration Analysis Of a Self-Excited Elastic Beam

The vibration behavior and the energy exchange among the normal modes of a clamped-free self-excited elastic beam are analyzed in this work. To model this kind of beam, the damping term of a van der Pol oscillator is directly added to the equation of a linear elastic beam, yielding a single nonlinear partial differential equation. To solve this equation, a spectral method is employed. Three vibration modes are considered in the analysis, and the values of the self-exciting constant are varied in order to cover from linear to nonlinear vibration behavior. Multiple frequencies of the nonlinear beam are determined through the power spectral density of the beam free-end time series. Given that this relatively simple model mimics at least in a qualitative way some key issues of the fluid-structure problem, it could be potentially useful for fatigue studies and vibration analysis of rotating blades in turbomachinery.