重量物を有する弾性支持はりの非支持はりの非線形強制振動

概要

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Abstract　This paper is concerned with the non-linear forced and free vibrations of an elastically hinged beam carrying a concentrated mass at an arbitrary point under the influence of gravity. Non-linear elastic terms arising from longitudinal stretching of the beam, and non-linear inertia terms arising from longitudinal inertia of the concentrated mass are included in the non-linear equation of motion. Using the Galerkin method and the one mode approximation, the equation of motion is reduced to a non-linear ordinary differential equation. The harmonic balance mothod is applied to solve the equation and the dynamic response of a concentrated mass is derived. By numerical examples the effects of the vertical and longitudinal stiffnesses at ends of the beam, and the effects of the weight, the location and the vibratory amplitude of the concentrated mass on the natural frequencies and the dynamic responses are indicated. The stability of the steady state solutions is also investigated by using the variational method and the Routh's stability criterion.
山形大学の論文
1984-01-20