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SUMMARYThe paper deals with the representation of dissipative effects by means of equivalent viscous forces. A brief review of the classical analytical treatment of the subject is first presented devoting particular attention to the topics of hysteretic and modal damping. The problem of forming viscous matrices in the case of systems which are non-homogeneous from the point of view of dissipation is then addressed; soil-structure systems are first considered and some accepted techniques for forming the structure contribution to the viscous matrix are reviewed. A different technique is then proposed which avoids some of the drawbacks of the previously quoted methods. In the final section of the paper it is shown how this technique is easily applicable also in the case of systems having internal concentrated dampers of viscous type, this being a situation which is difficult to tackle with usual criteria.

Submerged Floating Tunnels are a promising alternative to bridges and underground tunnels for crossing sea straits or, in general, waterways. The dynamic behavior of SFTs involves complex design and analysis issues, mainly related to the response to environmental actions. Within this context, the modeling of tethering elements of seabed anchored floating structures is here addressed, with particular reference to the crossing of deep waters; attention is devoted to the design solution encompassing slender bars as anchor elements. Two numerical tools are proposed: first, a geometrically non-linear finite element (NWB model), developed in previous work, has been refined in order to capture the effect of higher flexural modes of anchor bars. Secondly, a 3D beam element, based on the classical corotational formulation (CR), has been developed and coded. Both elements are implemented in a numerical procedure for the dynamic time\ud domain step-by-step analysis of non-linear discretized systems; seismic loading is introduced by generating artificial time-histories of spatially variable seismic motion.\ud An example of application of the NWB element is shown regarding the behavior of the dynamic model of a submerged tunnel proposed for the Messina Strait crossing. The model was subjected to extreme multiple-support seismic loading. The behavior under seismic loading is here illustrated and commented, especially in light of the effect of higher local vibration modes of the anchor bars

The modeling and seismic analysis of Qiandao lake submerged floating tunnel (SFT) is addressed with particular attention to the mooring system, to dissipation issues and to the spatial variability of the excitation, within a numerical procedure developed by the research group to perform the step-by-step dynamic analysis of iscretized non-linear structural systems. The procedure, which can handle arbitrary external loading allowing for multiple-support seismic excitation, is enhanced by enriching the mooring cables model adding non-linear hydrodynamic loads. Different dissipation models account for hydrodynamic damping, structural damping and radiation damping which are included, respectively, as non-linear forces, as linear viscous damping equivalent to linear hysteretic by means of an iterative procedure, and as linear viscous damping. A possible solution is here studied to define an adequate cable discretization in order to correctly model nonlinear geometric effects and to avoid fictitious compressions. A uniformly modulated random process, whose spatial variability is governed by a single coherency function, is deemed adequate to model multi-support seismic input for the given structure. A novel method to obtain response spectrum compatible accelerograms is here proposed