Vibro-acoustic analysis of micro-perforated sandwich structure used in space craft industry

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Abstract

In satellite telecommunications lightweight parabolic reflectors are made with multilayered composite material. During launcher lift-off and the first stage of the flight, vibro-acoustic excitations due to the thrust system and aerodynamic forces are the most critical. The random acoustic load applied to the antenna structure becomes very important and can damage the structure and its equipments. To reduce the acoustic loads, micro-perforated thin shell structures are used in order to reduce the acoustic load applied. CAD and numerical software tools are needed to design and optimise such structures. The computation of the acoustic load induced by a diffuse field on a micro-perforated structure is not classical. The aim of this study is to develop a numerical local impedance model to represent the effect of the perforation to be used within vibro-acoustic software.

Introduction

In space craft industry, structures are usually made with thin and lightweight composite materials. In particular for telecommunication satellite the parabolic antenna reflectors are made with sandwich composite material based on a honeycomb core covered with multilayered thin and micro-perforated shell structure obtained by weaving like in textile.

This manufacturing process permits an important reduction of the mass and also an important reduction of the acoustic load applied to the structure. However during the liftoff and the first stage of the atmospheric flight of the launcher vehicle, the vibro-acoustic excitations due to the propulsion system and to the aerodynamic forces are the most critical and can be over 140 dB. The random acoustic excitation induced on the antenna commonly known under “blocked pressure” becomes very high and can cause damage to the structure and to the equipments. To avoid these damages, micro-perforated structures can be used, which permit the structure to breathe and then reduce the pressure loading applied to the structure.

The use of this technology for the lightweight antenna is limited to the Ku emission frequency band [12–14 GHz] due to the perforation size between 1 and 2 mm. To cover a higher frequency of emission within the Ka band [20–30 GHz], it is necessary to reduce the size of the perforations to get a correct electromagnetic efficiency of the antenna. Unfortunately, the reduction of the perforation size will increase automatically the pressure jump “the blocked pressure” applied on the structure.

For these reasons, it is very important to have a numerical model describing the impedance of micro-perforated sandwich behaviour to be used as boundary condition in a CAE/CAD software tool for vibro-acoustic prediction.

After a brief survey of the state of the art on the analytical and experimental investigations on the acoustic absorption effects due to perforated plates and boards, a new appropriate analytical homogenized model of impedance is developed in this paper, more adapted for a composite structure with a honeycomb core covered by two micro-perforated thin shell panels. The numerical results delivered by the developed analytical model are compared to the measured results using the Kundt tube.

Section snippets

State of the art

The use of micro-perforated plates (MPP) for noise reduction is well known and constitutes a good alternative to the use of classical absorbing material like foam and fibres mainly when these materials cannot be used for safety or for functional reasons. These classical absorbing materials are flammable and opaque. MPP can be used in a very large application field such as in architecture and urbanism, in the automotive and transportation industry and in aeronautic and space industries.

For

Kirchhoff’s equations

The basic linear equations proposed by Kirchoff to describe the thermo-dynamical behaviour of gas submitted to a small disturbance are [7], [11], [15]ρ0vt=Pa+43μ(·v)μ××vρt=ρ0·vκΔT=T0P0(ρ0CvPatP0Cpρt)Pat=P0ρ0T0(ρ0Tt+T0ρt)

Eqs. ((1), (2), (3), (4)) correspond, respectively, to the conservation of the momentum and mass, thermal conduction and the state behaviour of gas. Pa, v, ρ and T are the gas pressure, the acoustic velocity, the mass density and the

Impedance of micro-perforated sandwich panel

Several authors [14], [15], [17] have developed a mathematical model of a perforated board system like a sandwich where only one face sheet is perforated. Such material is an efficient absorbing material more adapted for noise reduction.

However the sandwich panel of interest is not dedicated to noise reduction but is used to relax the high level acoustic pressure loading applied to the structure.

Based on the analytical model of the acoustic impedance of MPP defined by Eqs. (7), (8), the goal of

Experimental validation

Two micro-perforated disc specimens of sandwich have been used (Fig. 4a and b) to test the developed analytical model of the acoustic impedance defined by Eq. (19). The geometrical parameters of the specimens are given in Table 1. Details on the perforation size and shape are shown in Fig. 4c.

Conclusion and perspectives

In this study we developed an analytical model of the surface homogenized acoustic impedance and absorption spectrum in terms of pressure jump, adapted to micro-perforated sandwich honeycomb panels used in aerospace industry.

This model is based on the available analytical model of the simple MPP. The developed model has been validated with tests and has shown correct results. In the future, this model will be used as surface boundary condition within vibro-acoustic commercial software to

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