Frequency analysis of reinforced concrete structures subjected to accidental impacts

The purpose of our study consists in the research of new ways of designing reinforced concrete structures submitted to commercial aircraft impact. We will particularly focus on the shaking resulting from such load case. The cutoff frequency for this type of loading is typically within the to range, which would be refered to as the medium frequency range [1]. The determination of the shaking induced by an aircraft impact on an industrial structure requires dynamic simulation. The response, especially during the transient stage, cannot be completely described using classical finite element method associated with explicit numerical schemes. Indeed, the medium frequency range is often ignored unless the calculation is carried out with a very refined mesh and consequently, a refined time discretization. This could lead to prohibitive computation times. The linear behaviour is not questioned outside the impact area, however, the non-linearity of the portion of the impacted structure can have a significant influence. The method consists in an initial FFT (Fast Fourier Transform) of the signal loading. The VTCR then ensures an efficient calculation of the response of the structure. The obtained signals are then processed by inverse FFT (IFFT) to reconstruct a time signal and a response spectrum. A new multiscale computational strategy, the Variational Theory of Complex Rays [2], is developed for the analysis of the vibration of structures in the medium frequency regime. Using two-scale shape functions which satisfy the dynamic equation and the constituve relation within each substructure, the VTCR can be viewed as a mean of expressing the power balance at the different interfaces between substructures in a variational form. The solution is searched as a combination of propagative and evanescent waves. Only the amplitude of these waves, which are slowly varying quantities of the solution, is discretized. This leads to a numerical model with few degrees of freedom in comparison with a Finite Element model. The aim is to develop a robust method to get mid-frequency spectra generated by an aircraft impact on a simplified structure.