Stochastic Reduced-Order Model in Low-Frequency Dynamics in Presence of Numerous Local Elastic Modes

Abstract

This paper deals with the nonusual case in structural dynamics for which a complex structure exhibits both the usual global elastic modes and numerous local elastic modes in the ¡ow-frequencv range. Despite the presence of these local elastic modes, we are interested in constructing a stochastic reduced-order model using only the global modes and in taking into account the local elastic modes with a probabilistic approach. In the ftrst part, a formulation and an algorithm, which allow the "global elastic modes" and the "local elastic modes" to be calculated, are presented. The second part is devoted to the construction of the stochastic reduced-order model with the global elastic modes and in taking into account the uncertainties on the effects of the local elastic modes by the nonparametrlc probabilistic approach. Finally, an application, which validates the proposed theory is presented.

Multilevel reduced-order computational model in structural dynamics for the low- and medium-frequency ranges

“…This work is a continuation of previous research [14,15,16]. The general strategy proposed in this work relies on the separation of the displacements associated with each structural level (the different levels of stiffness of parts of the structure).…”

“…(5), σ α is the positive eigenvalue associated with ψ α and rM Ag s is the modified mass matrix that depends on the approximation subspace A g associated with a choice of reduced kinematics for the kinetic energy. In previous work [14], the domain of the structure is partitioned into N s subdomains, Ω 1 , . .…”

“…The objective of this section is the construction of basis matrix rBs of A g , subspace in which any vector v can be written as v " rBs c. In the work initialized in [14] and applied in [15,16], the construction of the reduced kinematics is based on a partitioning of domain Ω into N s subdomains Ω 1 , . .…”

“…, Ω Ns of a partition of Ω. If such a partition is introduced, and if the degree N d of the polynomial approximation is chosen, for each subdomain, as (i) N d " 0 (which corresponds to a constant displacement field by subdomain), we then obtain the formulation introduced in [14] and in such a case, the projector is defined by Eq. (6) for the continuous case.…”

Multilevel Stochastic Reduced-Order Model in Linear Structural Dynamics for Complex Structures

“…For such complex structures, besides the absence of separation of scales, the global displacements (or global modes) cannot easily be identified because coupled with the large-amplitude local displacements (or local modes). For constructing an adapted reduced-order model of such complex structures, a first version of a two-levels reduced-order model has been proposed [5], and then has been extended and applied to complex mechanical systems [6,7]. Then the methodology has been generalized [8] for constructing multilevel reduced-order models.…”