Vibration of a Beam with Concentrated Masses on Elastically Damping Supports

Abstract

Objective. The aim of the study is to study the operation of multi-span beams with point masses under the simultaneous action of vector kinematic and force loads. Taking into account the influence of elastic-damping supports.Method. The study is based on the solution of the boundary value problem and modeling.Result. Free transverse vibrations of multi–span beams of constant cross-section (within each j-th span Aj, and Gj) are investigated taking into account elastic-damping discrete supports. Free and forced harmonic vibrations of the beam from vector kinematic and force perturbations are considered. Examples of solutions for various conditions of fixing a three-span beam at different point masses are given.Conclusion. The author’s development can be adapted to the fluctuations of the continuo-discrete rods. This algorithm allows you to determine the natural frequencies and forms of free oscillations. It is also possible to calculate multi-span rods for the simultaneous action of vector kinematic and dynamic loads.

Keywords

• beam
• viscous friction
• elastic support
• frequency
• amplitude
• complex functions
• eigenforms
• dynamic and kinematic vector perturbations