Experimental and numerical studies of plastic deformations
Studies of the single degree of freedom elasto-plastic oscillator is well-known in the literature. Some of these works use an associated linear system to describe special features in non-linear domains. One very successful work of this kind uses the socalled Slepian model process related to the associated linear system, and this work is used as a basis in trying to extend the model to several degrees of freedom. The system is modelled as a modal system with lumped masses and given stiffnesses and modal damping ratios. The system can be describecl as a shear-wall building with elasto-plastic stiffness properties in the connection between the top-storey and the storey right below, while the rest of the system is acting purely elastic. Some works based on the Slepian model approach to a multi-degree-of-freedom system are reported elsewhere and deals with the description of the plastic deformations in terms of density functions. Since these works show promising results it was decided to verify the results through experiments. The test-model is made as a 4-degree-of-freedom shear-wall building. This report describes the experimental setup, determination of system parameters and calculation of plastic deformations from test results.Experiments have been performed for two different load levels. At each level 50 repetitions have been made in order to have a sufficient sample size for various statistical calculations. Since the Slepian model is less accurate at high load levels the experiments are compared with calculations using a direct time simulation. The simulation procedure uses a linear elastic-ideal plastic relation for the non-linear part of the structure. By demanding that variances of the plastic drift as a function of time must be the same in the experiments as in the simulations an equivalent ideal yield limit is found. Results obtained by using the calibrated elasto-plastic oscillator in the simulations are compared to results obtained by the experiments. Keywords: Random vibrations, Slepian models, MDOF elasto-plastic oscillator, Erarth quake induced vibrations, Random plastic displacements.Nøgleord: Stokastiske vibrationer, Slepianmodeller, Elasto-plastisk oscillator, Jordskælvsinducerede svingninger, Stokastiske plastiske flytninger.