In countries with a moderate seismic hazard, the classical methods developed for strong motion prone countries to estimate the seismic behaviour and subsequent vulnerability of existing buildings are often inadequate and not financially realistic. The main goals of this paper are to show how the modal analysis can contribute to the understanding of the seismic building response and the good relevancy of a modal model based on ambient vibrations for estimating the structural deformation under moderate earthquakes. We describe the application of an enhanced modal analysis technique (Frequency Domain Decomposition) to process ambient vibration recordings taken at the Grenoble City Hall building (France). The frequencies of ambient vibrations are compared with those of weak earthquakes recorded by the French permanent accelerometric network (RAP) that was installed to monitor the building. The frequency variations of the building under moderate earthquakes are shown to be slight (~2%) and therefore ambient vibration frequencies are relevant over the elastic domain of the building. The modal parameters extracted from ambient vibrations are then used to determine the 1D lumped-mass model in order to reproduce the inter-storey drift under weak earthquakes and to fix a 3D numerical model that could be used for strong earthquakes. The correlation coefficients between data and synthetic motion are close to 80% and 90% in horizontal directions, for the 1D and 3D modelling, respectively.

In this paper, a method for the construction of a cracked beam finite element is presented. The additional flexibility due to the cracks is identified from three-dimensional finite element calculations taking into account the unilateral contact conditions between the crack lips. Based on this flexibility, which is distributed over the entire length of the element, a cracked beam finite element stiffness matrix is deduced. Considerable gain in computing efforts is reached compared to the nodal representation of the cracked section when dealing with the numerical integration of differential equations in structural dynamics. The stability analysis of a cracked shaft is carried out using the Floquet theory.

We present a systematic approach to deal with the modeling and analysis of the cracked rotating shafts behaviour. We begin by revisiting the problem of modelling the breathing mechanism of the crack. Here we consider an original approach based on the form we give to the energy of the system and then identify the mechanism parameters using 3D computations with unilateral contact conditions on the crack lips. A dimensionless flexibility is identified which makes the application of the approach to similar problems straightforward. The additional flexibility due to the crack is then introduced in a simple and comprehensive dynamical system (2 DOF) to characterize the crack effects on the dynamical response of a rotating shaft. Many results could help in early crack detection.