Multiple-mode nonlinear free and forced vibrations of beams using finite element method

Effects of large deflection geometric nonlinearity and multiple modes for free and forced vibrations of beams are investigated. Inplane displacement and inplane inertia are included in the formulation. The finite element method is employed. A harmonic force matrix is derived for forced vibration analysis. The relations of amplitude, frequency ratio and forcing intensity for beams of different boundary conditions and various load conditions are presented.