Numerical studies on vibration propagation and damping test V1

Earthquakes and aircraft impacts induce vibrations that propagate throughout the entire building and they need to be considered in designing SSCs (Structures, Systems and Components). Mainly linear calculation methods have been in use in design practice and the codes and standards consider damping ratios only for linear structural analyses. Induced vibrations, especially in damaged concrete structures, have not been studied extensively enough for optimization of structural frameworks and/or qualified systems and components. Experimental data on damping properties of damaged reinforced concrete are needed also for benchmarking analysis programs and methods.

Recently, within IMPACT project, a new type of test series considering vibration propagation has been carried out at VTT. The test target is a reinforced concrete structure with two parallel walls connected to a floor slab. The front wall is additionally supported by triangular shaped side walls which are connected to the floor slab too. The test structure is supported on elastomeric bearing pads, with back pipes effective mainly in compression and with bars effective in tension. In order to obtain information on vibration propagation in damaged concrete structure at different levels of damage grades the same structure was tested six times. At each time the mass of the deformable stainless steel missile was 50 kg. The hit point located in the middle of the front wall. The impact velocity was about 110 m/s in the first four tests (V1A-D) and about 60 m/s in the remaining two tests (V1E and F). In this paper, numerical results on tests V1A and V1F are compared with the corresponding experimental ones.

The calculated results, such as accelerations, displacements, their response spectra and strains, are compared with experimental measurements. Five finite element (FE) programs are used in computations: Abaqus, Europlexus, LS-DYNA, SOFiSTiK and an in-house code (IHC).

Most of the FE-codes in the present study use shell elements. In Abaqus and SOFiSTiK non-linear behaviour of shell section is modelled by dividing the cross section into layers. Reinforcements are also modelled as layers. In Europlexus and IHC, an alternative approach is adopted in which the non-linear behaviour of concrete and reinforcement is homogenized beforehand in the shell thickness direction obtaining relations between stress resultants and generalized strains valid for the shell section. In LS-DYNA, 3D solid elements for modelling concrete and beam elements for modelling reinforcements are used.

Equations of motion are integrated with explicit central difference time integration method, except in SOFiSTiK implicit integration method is used. Modelling and computations with the mentioned FE-programs are made independently of each other. Computations with LS-DYNA are carried out as blind exercises.

Consideration of the results from benchmarking point of view is still on-going. However it is evident that analysed results follow reasonable well test results in main design parameter level such as maximum displacements, accelerations and strains. Also frequency spectra are estimated reasonably well.

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