Determination of the own forms of vibration of the span of beam bridges on elastic supporting parts

The authors consider the determination of the eigenforms of a beam on elastic support parts. Elastic support parts made of rubber and laminated metal plates find a wide use for seismic isolation of bridges in earthquake-resistant construction. Determination of eigenforms of structures is the main stage when designing the buildings and structures for resisting the seismic impacts. The span structure of girder bridges is considered as a system of uniformly distributed load, the free vibrations of which are described by a homogeneous fourth-order partial differential equation. By solving the differential equation, formulas for determining the eigenforms of a beam on elastic support parts were obtained. The reliability of the obtained formulas is confirmed with the substitution of other boundary conditions of the beam. The formulas obtained are considered as a general case, and from them the special cases for different ways of fixing of beams can be obtained