Because of the complexity fluid flow solvers, non-intrusive uncertainty quantification techniques have been developed in aerodynamic simulations order to compute quantities interest required an optimization process, for example. The objective function is commonly expressed terms moments these quantities, such as mean, standard deviation, or even higher-order moments. Polynomial surrogate models based on polynomial chaos expansions often implemented this respect. original approach using...

Abstract We present a sub‐structuring method for the coupling between large elastic structure, and stratified soil half‐space exhibiting random heterogeneities over bounded domain impinged by incident waves. Both media are also weakly dissipative. The concept of interfaces classically used in methods is extended to ‘volume interfaces’ proposed approach. dimension stochastic fields modelling reduced introducing Karhunen–Loéve expansion these fields. coupled overall problem solved Monte‐Carlo...

This paper deals with some of the methodologies used to construct polynomial surrogate models based on generalized chaos (gPC) expansions for applications uncertainty quantification (UQ) in aerodynamic computations. A core ingredient gPC is choice a dedicated sampling strategy, so as define most significant scenarios be considered construction such metamodels. desirable feature proposed rules shall their ability handle several random inputs simultaneously. Methods identify relative...

Spatial structures are often subjected to impulse loads which give rise high-frequency (HF) waves. The objectives of the research outlined in this paper twofold: (i) develop a reliable direct model transient dynamic response built-up such and (ii) use time-reversal inverse process order possibly detect location shocks. present study is more particularly focused on beam assemblies, as typically encountered aerospace applications. At first, transport describing evolution HF vibrational energy...

Abstract We use some recent mathematical results obtained for the high-frequency asymptotics of hyperbolic partial differential equations to derive exact transient power flow vibrations randomly heterogeneous cylindrical shells. The theory shows that angularly resolved energy densities an heterogeneous, elastic medium satisfy transport at higher frequencies. behaviour solutions such short their diffusion limit—if any—is fundamentally different from solution a equation, although latter one is...

The theory of microlocal analysis hyperbolic partial differential equations shows that the energy density associated to their high-frequency solutions satisfies transport equations, or radiative transfer for randomly heterogeneous materials with correlation lengths comparable (small) wavelength. main limitation existing developments is consideration boundary interface conditions and power flow densities. This paper deals regime in coupled structures. An analytical model derivation...

The theory of microlocal analysis shows that the energy density associated with high-frequency vibrations a three-dimensional Timoshenko beam satisfies Liouville-type transport equation. In present application, material is assumed to be isotropic. Its parameters are allowed vary along axis at length scales much larger than wavelength waves traveling in it. Moreover, curvature and torsion accounted for. first part paper focuses on derivation model for single beam. order extend this trusses,...

The results of an experimental study the vibrations a complex, three-dimensional heterogeneous structure under broadband excitations and comparisons with numerical simulations are presented. so-called midfrequency range is exhibited for tested structure, modeling strategy proposed on basis physical observations from measured frequency response functions mechanical energies. A time-frequency algorithm used analyses at intermediate frequencies, which reveal current shortcomings available methods.

The evolution of the high-frequency vibrational energy density slender heterogeneous structures such as Timoshenko beams or thick shells is depicted by transport equations radiative transfer (RTEs) in presence random heterogeneities. A diffusive regime arises when their correlation lengths are comparable to wavelength, among other possible situations, and waves multiply scattered. purpose this paper expound how diffusion approximations RTEs for elastic can be derived discuss relevance...

The theory of microlocal analysis hyperbolic partial differential equations shows that the energy density associated to their high-frequency solutions satisfies transport equations, or radiative transfer for randomly heterogeneous materials with correlation lengths comparable (small) wavelength. main limitation existing developments is consideration boundary interface conditions and power flow densities. This paper deals regime in coupled structures. An analytical model derivation...

Some recent mathematical results are used to study the propagation features of high-frequency vibrational energy density in three-dimensional fluid-saturated, isotropic poro-visco-elastic media. The theory asymptotics solutions hyperbolic partial differential equations shows that their satisfies Liouville-type transport or radiative transfer for randomly heterogeneous materials. For long times these can be approached by diffusion equations. corresponding parameters—mean-free paths and...

Abstract An integral equation for the representation of response a structure impinged by an incident wave field including soil–structure interaction is proposed. It requires knowledge fundamental solution overall domain when unit load applied to structure. This obtained means substructuring technique and boundary equations using Green tensors homogeneous or horizontally stratified soil media. The effects non‐stationary modulated random are addressed in terms instantaneous power spectral...