Transverse vibrations of a single-span girder bridge are considered in the article; the pile part of the bridge interacts with the surrounding soil under seismic action. We assume that the strain of the structure does not go beyond the elastic limit, and the vibrations are linear. The bridge supports are assumed to be immersed in soil and interact with a rigid body under the impact of unsteady dynamic influences. We consider the case when the right and left supports have equal masses and interact with the surrounding soil. Here the symmetry condition is applied, so it is sufficient to consider the equation for the right half of the girder. The problems are solved by the analytical Fourier method under given boundary conditions. The results obtained are analyzed and presented in the form of the distribution of displacements and stresses over the time and length of the bridge structures.

The simultaneous equations of longitudinal and transverse vibrations of an underground polymeric L-shaped pipeline under the arbitrary direction of seismic load were derived in the paper. A computational scheme of the problem was constructed using central finite-difference relations. The analysis of the results obtained on the simultaneous longitudinal and transverse vibrations of underground polymeric L-shaped pipelines under seismic loading was conducted. The stress-strain state of the L-shaped polymeric pipeline subjected to seismic effect was determined, and the axial forces and bending moments arising in curved pipelines during an earthquake were determined.