Dynamic modelling and response of elastic structures

Research focus

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Research Focus A: cables and cable systems The non-linear dynamics of suspended cables has been explored in free, harmonically forced and random oscillations. Due attention is paid to the influence of axial deformation, higher-order modes and variable excitation. A three-node isoparametric element for cables under wind loading was developed, taking into account geometric and aerodynamic non-linearities. This is based on local aerodynamic (sectional) forces and a complete and consistent derivation of global generalized components of aerodynamic forces. Aerodynamic contributions to the effective damping matrix are disregarded. The capability and limitations of finite element (FE) modelling and analytical Galerkin reduced models in reproducing the effects of turbulence and galloping were investigated. The comparison between the two approaches was extended to study the capability of reduction techniques, applied for both loading and cable description, in reproducing the response of suspended cables excited by a 3D turbulent wind field. The mechanical system and the spatially varying wind velocities are projected onto the base of cable eigenfunctions, retaining only selected degrees-of-freedom associated with the low frequency modes. The numerical study of significant stretches of transmission lines, including the supporting towers, was eased devising a reduced model for these often complex structures. Buffeting and aeroelastic phenomena due to ice accretion were studied for cableways considering three-dimensional wind field, its variability in space and time and aerodynamic forces on the track rope and the passengers-cabin, modelled within finite-rotation kinematics as a 3D rigid body. Research Focus B: mooring systems and submerged floating tunnels Submerged Floating Tunnels (SFTs), or “Archimedes Bridges”, are an innovative concept for crossing waterways using a tube-like structure, floating below the water table and moored by a suitable anchoring system. In deep-water crossings the anchoring system behaviour is important for the dynamic response. Ad hoc numerical tools for moorings by slender bars or cables were developed and implemented in an ad-hoc finite element code. When slender bars acts as anchoring elements an ad hoc 3D FE, called NWB, was used; the formulation, based on the hypotheses of hinged element ends and constant axial force, involves the use of relative coordinates to model local transverse oscillations of the bar. Axial deformation, small and constant along the bar, is expressed as a quadratic function of nodal displacement, including the effect of transverse motion. For cable anchored tunnels the three-node isoparametric FE previously described is adopted. Finally, a different 3D beam element based on the co-rotational formulation was developed and investigated. Slender submerged structures can be prone to vortex induced excitation; a continuous fluid oscillator model (DVL) for the prediction of induced vibration response of flexible cylinder such as cables and pipes was proposed and applied to SFTs, consistent with the NWB approach for anchoring bars. Research focus C: direct frequency domain analysis of linearized mechanical systems DFDA represents a powerful tool for treating a large class of problems in linear structural dynamics. At a simpler level, DFDA allows for the use of the linear hysteretic damping model. The possibility of using mixed (hysteretic+viscous) damping makes DFDA more suitable than modal analysis for treating dynamic models where dissipation is highly non homogeneous: introduction of iso110 lation devices, linearized interaction effects such as soil-structure (radiation damping) or fluidstructure (aerodynamic or hydrodynamic damping). DFDA procedure requires, at each frequency of interest, a linear system solution with a complex, symmetric and indefinite coefficient matrix. To improve the method efficiency, the development of iterative procedures for the simultaneous system solution for a large number of frequency values was addressed. Projection methods using Krylov subspaces for approximating the system solution were considered, particularly the GMRES procedure, very efficient for medium-size systems (order of 104-105 DOFs). As an alternative a technique was developed, based upon the Lanczos method, for generating the Krylov vectors; this is suitable for treating larger systems and exploits the symmetry of the problem at hand. The procedure at study requires the factorization of the stiffness matrix; for very large systems such task is performed with an iterative scheme, giving rise to a “inner-outer iteration” procedure. Efficient stopping criteria are important: a procedure has been devised for dynamic control of the inner tolerance as a function of the approximation level of the outer iteration. Finally, the procedure is capable of handling the case of singular stiffness matrix through the use of a modified version of the Conjugate Gradient algorithm.

Dipartimento di afferenza

Dipartimento di Ingegneria Strutturale (DIS)

Docenti afferenti

Full Professors
Federico Perotti
Assistant Professors
Luca Martinelli