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SUMMARYSolutions for the displacements caused by dynamic loads in a viscoelastic transversely-isotropic medium are derived. The medium extends horizontally to infinity, but is bounded below by a rigid base. Stratification of the medium presents no difficulties. The medium is discretized in the vertical direction only; discretization in the horizontal direction is obviated by use of analytical solutions to the equations of motion.Application of the displacement solutions to soil-structure interaction is illustrated. A soil flexibility matrix (and hence, a stiffness matrix) for a surface foundation follows directly from the displacement solutions. A simple modification to obtain the soil stiffness for an embedded foundation of arbitrary geometry is described. Stiffnesses of rigid surface and embedded foundations are computed and compared with previously published results. In addition, the dynamic stiffness of a rigid surface foundation on a soil layer with linearly increasing shear modulus is compared to that for a homogeneous soil layer. A reduction in radiation damping is found to result from the inhomogeneity.

The dynamic properties of Tuned Mass Dampers (TMD's) used to reduce the vibrations of footbridges are generally based on the optimization criterion of Den Hartog. However the spring, mass and damper of a TMD may possess slight fabrication tolerances or change its damping element properties due to temperature, which can result in a detuning of a TMD. The study presented deals with the influence of a detuning on the performance of a TMD. A simplified model for beam-like footbridges under pedestrian loading is proposed. It is shown that a 2-DOF-system in harmonic stationary motion represents a good approximation of the beam structure under transient time-dependent load. Graphs are given to assess the increase of acceleration and the decrease of effectiveness due to detuning. A case study on a footbridge with a span of 45 m demonstrates its accuracy.

A tight verified solution enclosure is obtained for the node displacements of a simple truss model, whose parameters, including the node locations, are uncertain. The solution is based on a monotonicity analysis of these interval parameters.