The application of the response spectra method for extended damped systems with a point support on the base is considered. The support excitations can be different. External and internal damping is taken into account, it being assumed proportional i.e. admitting an exact or approximate decomposition of motion according to the undamped system modes. It is noted that the presence of externaldamping leads to additional system perturbation, i.e. to additional members appearance in the right part of motion equations. It is shown that well-known formulas of the response spectra method for systems on a rigid platform are kept intact, but the vector of load projections on the directions of generalized coordinates is modified taking into account the influence of support displacements on generalized loads in the system.

The purpose of the research is to show the main features of calculating bridge taking into account the inhomogeneous acceleration field along the structure length. The bridge is considered to be a linear structure with point bearings on the soil base. For long bridges it is typical, that their bearings are located in different seismogeological conditions. This result in inhomogeneity of the acceleration field under the piers and non-synchronous pier excitations. The motion equations of the system under consideration are constructed and their decomposition into vibration modes is performed without the account of external and internal damping in the system and with the account of it. Based on the proposed decomposition, formulas for determining seismic loads taking into account various seismicity under piers are obtained. The result obtained show that the peculiarities considered can be easily taken into account in existing software packages. As an example, the authors analyzed the results of calculating a four-span beam railway bridge. In calculating it was taken into account that the first and second piers are located on sandstone, and the rest of them are on water-saturated loose sand. The analysis showed that the account of the non-synchronous support point excitation of the extended system reduces inertial seismic loads on its elements significantly.