This work deals with an extension of the reduced-order models (ROMs) that are classically constructed by modal analysis in linear structural dynamics of complex structures for which the computational models are assumed to be uncertain. Such an extension is based on a multilevel projection strategy consisting in introducing three reduced-order bases (ROBs) that are obtained by using a spatial filtering methodology of local displacements. This filtering involves global shape functions for the kinetic energy. The proposed multilevel stochastic ROM is constructed by using the nonparametric probabilistic approach of uncertainties. It allows for affecting a specific level of uncertainties to each type of displacements associated with the corresponding vibration regime, knowing that the local elastic modes are more sensitive to uncertainties than the global elastic modes. The proposed methodology is applied to the computational model of an automobile structure, for which the multilevel stochastic ROM is identified with respect to experimental measurements. This identification is performed by solving a statistical inverse problem.

In this paper, an efficient numerical procedure is proposed, adapted to the modal analysis of a fully-loaded spent nuclear fuel canister, which exhibits distinct structural levels associated with a hierarchy of components. On the one hand, the fully-loaded spent nuclear fuel canister is constituted of the repetition of identical components, resulting in a pseudo-periodicity; and the components of a given level are separated from each other and only connected to their upper level through localized attachments, which gives rise to an advantageous structural connectivity that can be exploited for efficiency. On the other hand, the necessary fine mesh resolution of the small levels leads to a high-dimensional computational model and, in addition, the independent resonant vibrations of each of the components produce a very large number of vibration eigenmodes. The aforementioned opportunities and difficulties are respectively leveraged and tackled by an adapted method that combines domain decomposition, shift-invert Lanczos eigenvalue solver, and Craig-Bampton substructuring technique. A parallel eigensolution via spectrum slicing is facilitated by an efficient block factorization by Schur complement that is enabled by the sparsity of the Craig-Bampton matrices. A computational gain of four orders of magnitude is obtained, at the expense of negligible errors that are exactly characterized. The proposed methodology enables a high-fidelity vibration analysis of the sealed fully-loaded spent nuclear fuel canister, useful for non-intrusive inverse identification of the structural integrity of the internal structural levels holding the nuclear material.

Christian Soize. Multilevel reduced-order computational model in structural dynamics for the low-and medium-frequency ranges. Computers and Structures, Elsevier, 2015, 160, pp.111-125. 10.1016/j.compstruc.2015 AbstractThis work deals with the dynamical analysis of complex structures composed of several structural levels and characterized by the presence of numerous local elastic modes intertwined with global modes, in the medium-frequency range as well as in the low-frequency range. For constructing the ROM, a family of globaldisplacements eigenvectors are calculated and are used instead of the classical elastic modes. Since it is also of importance to adapt the physical models (damping, level of uncertainties, etc) to each one of the structural levels, a multilevel ROM is proposed. A validation is performed for an automobile complex structure.

In this paper, an extension of modal analysis in linear computational structural dynamics is presented to deal with complex structures characterized by the presence of numerous local vibration modes and for which the high modal density leads to high-dimension reduced-order models. These local modes consist of isolated vibrations that are dissociated from the global vibrations of the structure skeleton and that turn out to often be of negligible contribution to the global dynamics. Therefore, an automatic mode sorting procedure is proposed to extract the dominant modes that represent the global dynamics of the skeleton. Next, an alternative filtering methodology based on a modified eigenvalue problem is presented, which allows to build, a priori, a small-dimension reduced-order basis of dominant global modes. The two methods are compared to classic modal analysis using three applications, namely, a heterogeneous plate, a simplified nuclear fuel assembly, and a detailed boiling water reactor fuel assembly.