Advanced Computational Dissipative Structural Acoustics and Fluid-Structure Interaction in Low-and Medium-Frequency Domains. Reduced-Order Models and Uncertainty Quantification

Abstract

This paper presents an advanced computational method for the prediction of the responses in the frequency domain of general linear dissipative structural-acoustic and fluid-structure systems, in the low-and medium-frequency do mains and this includes uncertainty quantification. The system under consideration is constituted of a deformable dissipative structure that is coupled with an internal dissipative acoustic fluid. This includes wall acoustic impedances and it is surrounded by an infinite acoustic fluid. The system is submitted to given internal and external acoustic sources and to the prescribed mechanical forces. An efficient reduced-order computational model is constructed by using a finite element discretization for the structure and an internal acoustic fluid. The external acoustic fluid is treated by using an appropriate boundary element method in the frequency domain. All the required modeling aspects for the analysis of the medium-frequency domain have been introduced namely, a viscoelastic behavior for the structure, an appropriate dissipative model for the internal acoustic fluid that includes wall acoustic impedance and a model of uncertainty in particular for the modeling errors. This advanced computational formulation, corresponding to new extensions and complements with respect to the state-of-the-art are well adapted for the development of a new generation of software, in particular for parallel computers. Key words:Computational mechanics, Structural acoustics, Vibroacoustic, Fluid-structure interaction, Uncertainty quantification, Reduced-order model, Medium frequency, Low frequency, Dissipative system, Viscoelasticity, Wall acoustic impedance, Finite element discretization, Boundary element method Nomenclature a ijkh = elastic coefficients of the structure b ijkh = damping coefficients of the structure c 0 = speed of sound in the internal acoustic fluid c E = speed of sound in the external acoustic fluid f = vector of the generalized forces for the internal acoustic fluid f S = vector of the generalized forces for the structure g = mechanical body force field in the structure i = imaginary complex number i k = wave number in the external acoustic fluid n = number of internal acoustic DOF n s = number of structure DOF n j = component of vector n n = outward unit normal to Abstract This paper presents an advanced computational method for the prediction of the responses in the frequency domain of general linear dissipative structural-acoustic and uid-structure systems, in the low-and medium-frequency domains and this includes uncertainty quantication. The system under consideration is constituted of a deformable dissipative structure that is coupled with an internal dissipative acoustic uid. This includes wall acoustic impedances and it is surrounded by an innite acoustic uid. The system is submitted to given internal and external acoustic sources and to the prescribed mechanical forces. An efcient reduced-order computational model is constructed by using a nite element discret...

Uncertainty Quantification

“…For instance, − in linear viscoelastic structural dynamics [154,155,156], [D(ω)] is the reduced damping matrix and [K(ω)] is the reduced stiffness matrix that is positivedefinite (if the possible rigid body displacements are removed). For instance, − in linear viscoelastic structural dynamics [154,155,156], [D(ω)] is the reduced damping matrix and [K(ω)] is the reduced stiffness matrix that is positivedefinite (if the possible rigid body displacements are removed).…”

A nonparametric probabilistic approach for quantifying uncertainties in low‐dimensional and high‐dimensional nonlinear models

“…This nonparametric probabilistic approach was extended for different ensembles of random matrices and linear boundary value problems . It was also experimentally validated and applied for linear problems in composites , viscoelasticity , dynamic substructuring , vibroacoustics , soil–structure interaction and earthquake engineering , and robust design and optimization . More recently, it was further extended to account for some nonlinear geometrical effects in structural analysis .…”

Nonlinear model reduction for computational vibration analysis of structures with weak geometrical nonlinearity coupled with linear acoustic liquids in the presence of linear sloshing and capillarity

“…Concerning nonlinear sloshing and capillarity for incompressible liquids in rigid tanks submitted to rigid body motions, see [34,35,36,37,38]. Concerning computational reduced-order models for the linear vibration of structures containing compressible liquids without surface tension and without sloshing effects, we refer the reader for instance to [13,39,40,41,5]. Note that the case of a structure with weak geometrical nonlinearities coupled with a linear acoustic fluid has been investigated in the high-frequency domain in [42].…”