Nonlinear Dynamic Behavior of a Generally Restrained Pre-Pressure Beam with a Partial Non-Uniform Foundation of Nonlinear Stiffness

Abstract

For some transmission shafting, nonlinear supports are connected to beam structures through the pattern of the contact surface. Nonlinear foundations are typically installed to the beam structure for a limited range. The unsuitable installation mode of nonlinear foundations will make the parameters of nonlinear foundations no longer uniform. Most existing studies ignore the boundary rotational restraints of beam structures and concentrated mass introduced by the nonlinear supports or foundations. To improve the engineering acceptance of beam structures with nonlinearity, it is of great significance to study the dynamic behavior of the generally restrained pre-pressure beam structure with a partial non-uniform foundation of nonlinear stiffness. This study establishes the nonlinear vibration model of the beam structure with a local non-uniform nonlinear stiffness distribution. Nonlinear dynamic responses of the beam structure are predicted by the Galerkin truncation method (GTM). Mode functions of the generally restrained pre-pressure beam structure are set as the trail and weight function. The correctness of the GTM for dynamic prediction of the beam structure with a partial non-uniform nonlinear foundation is verified by using the harmonic balance method (HBM). The influence of sweeping ways of excitations and parameters of the partial non-uniform nonlinear foundation on nonlinear dynamic responses of the beam structure are investigated. Dynamic responses of the beam structure with a partial non-uniform nonlinear foundation are sensitive to their initial values. Vibration states of the beam structure are transformed effectively by changing parameters of the partial non-uniform nonlinear foundation. The vibration at both ends of the beam structure can be suppressed by applying suitable parameters of the partial non-uniform nonlinear foundation.