Bernard Troclet

Identification of Overpressure Sources at Launch Vehicle Liftoff Using an Inverse Method

A = source operator projection A = operator projection A for Dirac source excited at time ti B = incident field operator projection B = incident field operator B projection for Dirac source excited at time ti c = sound speed in the air Dok = delta of pressures computed for the kth couple of sensors Domesk = delta of pressures measured for the kth couple of sensors e = Dirac source excited at time ti operator H = Hessian approximation it = iteration j p J O p = cost function L = Lagrangian l = iteration optimizer N = no. of solver time iterations NDF = no. of degrees of freedom on the obstacle boundary Ncoupl = no. of diametrically opposed pressure sensors Nparam = no. of source parameters Nobs = no. of pressure sensors n = discrete current iteration O p x; t = total pressure field computed Oi = pressure at the ith receiver Omes x; t = measured observed pressure at sensors Odiff x; t = scattered field outside the obstacle Odiff x; t = scattered field inside the obstacle Opinc x; t = incident field for source p O = adjoint total field O i = adjoint field at the ith sensors p = source parameter vector pi = component of excitation parameter at time t ti Q k = scattered matrices adjoint posttreatment R = integral surface operator R k = surface integral adjoint matrices S p = boundary traces of the incident field source parameter p t = time variable U = acoustic pressure jump across the boundary U = adjoint pressure jump V = unitary jump pressure for Dirac source excited at time ti W = unitary pressure for Dirac source excited at time ti x, y = spatial variables in 3-D x0 = location of source label p = obstacle boundary t = time step = test function (in variational formulation) e = exterior domain obstacle i = interior domain obstacle rj rpi = unitary gradient for Dirac source excited at time ti Received 6 December 2005; accepted for publication 26 May 2006. Copyright ©2006 by theAmerican Institute ofAeronautics andAstronautics, Inc. All rights reserved. Copies of this paper may be made for personal or internal use, on condition that the copier pay the

Modeling of random aerodynamic loads applied on fluid‐structure coupled systems using rain‐on‐the‐roof equivalent excitation

10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0022-4650/07

Wave Finite Element Formulation of the Acoustic Transmission Through Complex Infinite Plates

10.00 in correspondence with the CCC. Expert in Structural Analysis, Missile Structural Analysis Department. Research Development Engineer, Simulation Systems and Information Technology Department. Manager of Applied Mathematics and High Performance Computing Team, Simulation Systems and Information Technology Department. JOURNAL OF SPACECRAFT AND ROCKETS Vol. 44, No. 3, May–June 2007

On a structural–acoustic panel cavity modelling in the mid-high frequency domain

Purpose – The purpose of this paper is to extend statistical energy analysis (SEA)‐like modeling to fluid‐structure coupled systems.Design/methodology/approach – An equivalent approach of aerodynamic loads is applied to a SEA‐like modeling of a panel‐cavity coupled system with rain‐on‐the‐roof excitation. Two aerodynamic excitations are presented: turbulent boundary layer (TBL) and diffuse field excitation. The energetic description of the coupled system is studied with both aerodynamic excitations, taking in account the coincidence effects. In order to extent the approach to more general systems, some parameters of the coupled system are also modified and the accuracy of the coupled system modeling is investigated.Findings – The boundary conditions of the panel and the coupling strength between the panel and the cavity have been modified. As it was expected, the accuracy of equivalent approach is shown to be independent of such modifications. The interest of such calculation is thus highlighted: modeling...

Robust Design Optimization by First Design Method

A finite element-based derivation of the transmission loss (TL) of anisotropic layered infinite plates is presented in this paper. The wave-finite element method (WFE) is used to represent the plate with a finite element model of a single unit cell. The incident acoustic field is a known plane wave, and the reflected and transmitted pressures are supposed to be plane waves with unknown amplitudes and phases. The periodicity conditions on the unit cell allow to find a simple matrix equation linking the amplitudes of the transmitted and reflected fields as a function of the incident one. This approach is validated for several cases against classical analytical models for thin plates and sandwich constructions, where the results agree perfectly for a reasonable mesh size. The method is then used to study the effect of stacking order in a laminated composite plate. The main interest of the method is the use of finite elements, which enables a relative easy modelling since most packages readily include different formulations, compared to analytical models, where different formulations have to be implemented for every kind of material.

Thermoacoustic effects on layered structures for the evaluation of structural parameters

This article presents a fluid–structure interaction modelling, based on a coupling between component mode synthesis or finite element and statistical energy analysis (SEA). The hybrid strategy is applied on a panel–cavity coupled system using a modal analysis with uncoupled modes of the subsystems and through a finite element model of the coupled system. The determination of the energy transfer parameters is then considered. The hybrid SEA model is then validated in the high-frequency domain by comparison with an SEA model. Finally, a parametric survey is offered through the established modelling and conclusions on its validity domain are drawn.

EFFICIENT CALCULATION OF THE RESPONSE OF A STRUCTURAL ACOUSTIC SYSTEM UNDER AERODYNAMIC EXCITATIONS

ak = Fourier coefficients corresponding to the cosine terms bk = Fourier coefficients corresponding to the sine terms c = vector of the Fourier coefficients d = distance from the optimal set of natural frequencies E = energy of the excitation f t = excitation signal related to time fi = frequency of the ith natural mode fi opt = frequency of the ith optimized natural mode Hi = matrix representing the transfer function Hi ! = transfer function of a 1-degree-of-freedom system N = number of elements of the vector defining the excitation p = number of frequencies taken into account in the Fourier series pc = crossover probability by bit pm = mutation probability by bit Te = time step of the vector defining the excitation Xi = ith design parameter Xi opt = optimized ith design parameter x4000 t = horizontal displacement at node 4000 related to time zi t = vector of the responses to the harmonic excitations of the Fourier series 4000, 3203 = vibratory levels at nodes 4000 and 3203 of the finite element model

Modeling the response of composite panels by a dynamic stiffness approach

The temperature dependent material characteristics of a layered panel are experimentally measured using a Thermal Mechanical Analysis (TMA) configuration. The temperature dependent wave dispersion characteristics of the panel are subsequently computed using a Wave Finite Element Method (WFEM). The WFEM predictions are eventually used within a wave context SEA approach in order to calculate the temperature dependent Sound Transmission Loss (STL) of the layered panel. Results on the STL for temperatures varying between -100 °C to 160 °C are computed for a structure operating at sea level. The importance of the glass transition region on the panel’s vibroacoustic response is exhibited and discussed.

Computing the broadband vibroacoustic response of arbitrarily thick layered panels by a wave finite element approach

Abstract. The problem of the dynamic response of a structural-acoustic system in the midfrequency range is hereby considered. The system is initially modelled using finite elements, and is subsequently reduced using the Second Order Arnoldi Reduction method (SOAR) resulting in radical reduction of calculation times. The fully coupled system is modelled using a Statistical Energy Analysis like (SEA-like) approach, and the energetic characteristics for each subsystem are computed and compared to the direct FEM solution. The error with respect to the full FE solution is presented and the limits of the reliability of the reduction are explored. The loading applied to the model comprises typical random aeroacoustic excitations, such as a diffused sound field and a Turbulent Boundary Layer (TBL) excitation.