Investigations on the Validity of the Poisson Assumption in Reliability Based Optimization of TMD Parameters

The purpose of the present work is to investigate the validity of the Poisson assumption used in the failure analysis, which is in turn required for the reliability based optimization (RBO) of tuned mass dampers (TMD) parameters. The TMD is a widely used device aiming to mitigate induced vibrations into structures under stochastic loading. The performance of this device is deeply related to its parameters that should be carefully chosen and in this context the RBO strategy can be used. The RBO problem required failure analysis, usually, performed based on analytical approximations and among them we can find: the Poisson, the Vanmarcke and the modified Vanmarcke approximations. The failure analysis based on Poisson assumption is very simple and widely used for its lower computational cost compared with the other approximations. Nevertheless, it’s also known that the Poisson approximation is inappropriate for narrowband process and/or for low threshold values, whereas, the other approximations could be used in such conditions. By studying a single degree of freedom system (SDOF), submitted to stochastic base acceleration, we investigate the relative error, in the optimum TMD parameters, induced by these approximations and we show that the Poisson assumption is relatively accurate and valid for high threshold level, even for narrowband excitations.