A Finite Element Method for Nonlinear Forced Vibrations of Beams,
OLD DOMINION UNIV NORFOLK VA DEPT OF MECHANICAL ENGINEERING AND MECHANICS
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Many optimum or minimum-weight designed structural components are under severe operational conditions. In many cases, the small deflection linear structural theory is no longer applicable. Considerable research effort has been devoted to obtain the approximate solutions for nonlinear response of beam structures under harmonic excitation. The common approach is to assume some form for the spatial solution, usually a linear mode shape, and then solve the governing nonlinear partial differential equation using Galerkins method. This reduces the governing equation to a nonlinear ordinary differential equation of the Duffing type. Most of the investigations have been concerned with beams of simply supported ends.