Abstract
This paper presents an analytical method for determining the vibration modes of geometrically nonlinear beams under various edge conditions. The method assumes a continuum periodic solution which allows the harmonic balance principle to be employed to derive modal components that satisfy the equation of motion exactly. Nonlinear normal modes are constructed from four such components and used to compute the natural frequencies for beams with restrained ends and for cantilevered beams. Numerical results for beams with restrained ends show good agreement with those available from other techniques.
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