The Parametric Response of a Horizontal Beam Carrying a Concentrated Mass Under Gravity

This investigation treats the steady-state response of parametric vibration of a simply supported horizontal beam, carrying a concentrated mass under the influence of gravity. Nonlinear terms arising from moderately large curvatures, longitudinal inertia of the beam and concentrated mass, and rotatory inertia of the concentrated mass are included in the equation of motion. By using the one mode approximation and applying Galerkin’s method, the governing equation of motion is reduced to a nonlinear ordinary differential equation with periodic coefficient. The harmonic balance method is applied to solve the equation and the dynamic response is derived. The effects of the weight, the rotatory inertia, the location, and the vibratory amplitude of the concentrated mass on the natural frequency are also discussed.