study of the vibro-acoustic behaviour of composite sandwich structures … leuven full paper.pdf ·...

Study of the vibro-acoustic behaviour of composite sandwich structures by means of a novel test setup

M.Vivolo1, B.Pluymers

1, B.Van Genechten

2, D.Vandepitte

1, W.Desmet

1

1 KU Leuven, Department Mechanical Engineering

Celestijnenlaan 300 B, B-3001, Heverlee, Belgium

e-mail: [email protected]

2 LMS International

Interleuvenlaan 68, B-3001 Leuven, Belgium

Abstract In this paper an experimental-numerical approach is presented to tackle the vibro-acoustic characterization

of composite sandwich structures. A novel experimental setup allows for fast and comprehensive

understanding of the NVH behaviour of composite sandwich panels. This information can then be further

exploited in numerical model updating and design tools for optimized solutions. Experimental modal

analysis and acoustic insertion loss tests are carried out in order to verify the structural and acoustic

numerical models of a given sandwich panel. The symmetric motion coincidence frequency is used to

retrieve the compression modulus of the core foam material. Later on a second design, derived from the

first, is considered. The predicted improvements in NVH behaviour are experimentally verified with good

accuracy. The vibro-acoustic test rig is shown to be a valuable support for the design of composite

structures when NVH performance is a key indicator attribute.

1 Introduction

Lightweight structures find wide application in modern automotive, marine, aerospace and many other

technology areas. The significant weight saving offered usually results in unsatisfactory NVH behaviour.

Hence, a proper knowledge of noise reduction characteristics of unconventional constructions and

materials becomes fundamental. This work presents the design procedure of a composite sandwich

structure based on experimental and numerical studies. A lightweight structure able to satisfy specific

structural and noise reduction specifications is sought. The study starts from an initial layout, implemented

for acoustic test rig constructions in the automotive sector [1]. Modal behaviour and acoustic Insertion

Loss (IL) are tested in order to build up and check the structural Finite Element (FE) model and the fully

coupled vibro-acoustic FE-Indirect Boundary Element (FE-IBEM) model. The Young’s modulus of the

core foam material is updated on the base of the symmetric motion coincidence frequency. Making use of

the revised material properties database, a second panel is designed with constraints on the global dynamic

stiffness and final weight. The new configuration is elaborated in function of the manufacturability

flexibility offered by the producer with respect to core thickness and core stiffeners configuration. The

final layout is experimentally tested and verified with good accuracy. All NVH tests are carried out using

a dedicated setup for vibro-acoustic characterisation of lightweight panels at KU Leuven [2]. The latter is

proved to be a helpful tool for design of composite structures with specific NVH requirements.

1921

2 Experimental and numerical investigation of NVH properties

2.1 The case of a composite sandwich panel

Based on an extensive literature review it was found that some alternative materials are sometimes used

instead of a conventional concrete walls solution [3] to create rigid acoustic cavities. As reported in [4]

when describing the main guidelines for constructing reverberation chambers for automotive testing

purposes, the authors explicitly mention that, apart from the traditional constructions of solid masonry,

some alternative prefabricated acoustic panels can be used to ensure both a proper room sound isolation

and notable reflecting surfaces inside the cavity. They refer to panels typically fabricated of heavy gauge

sheet steel backed with gypsum drywall able to produce a massive, sound reflecting enclosure. In the

present study, however, the authors focus on lightweight solutions. A composite sandwich panel

implemented in the construction of acoustic test facilities for automotive applications is the case initially

tackled by the authors. The first sample is tested and numerically studied with the final aim of designing a

stiffer solution still complying with an assigned weight restrictions. Results from this first phase are used

to generate and update a corresponding structural FE model.

The composite panel (660 x 860 x 55 mm³) consists of glass fibre (GF)-epoxy resin face sheets sandwich,

in which several layers are stacked according to a specific layout and the core is filled with polyurethane

foam, in which unidirectional stiffeners spaced 400 mm from each other are present, as shown in Figure 1.

Figure 1: Composite sandwich panel. FE model on the right side

2.1.1 Vibro-acoustic experimental campaign

Experimental modal tests (EMA) are carried out on the freely suspended sample. Lightweight

accelerometers PCB 352A24, a PCB 086C03 load cell, an LMS SCADAS III acquisition system, LMS

Test.Lab9B and Virtual.Lab Acoustics Rev.8b are used to carry out and post-process the experimental

tests database and numerical analyses results. The nominal geometric and material properties are specified

in Table 1. They are partially given by the manufacturer and partially taken from literature, like the shear

modulus and Poisson ratio of the face sheet material. Using these initial nominal values a correlation is

established between the FE model and the experimental database. A good match of mode shapes up to 1

kHz is observed, although a shift in terms of natural frequencies is apparent. In general, the numerical

model appears to be more flexible than the actual structure resulting in lower predicted natural

frequencies. Figure 2 and Figure 3 show the Modal Assurance Criterion (MAC) values for the first ten

experimental modes and their numerical counterparts.

A novel experimental setup [3] is used to evaluate the vibro-acoustic behaviour of the baseline panel. The

test rig is specifically developed for the experimental investigation of noise reduction and acoustic

absorption characteristics of lightweight structures. It consists of a concrete cavity of 0.83 m3 irregularly

shaped to ensure an even distribution of the acoustic natural frequencies at frequencies below the diffuse

field region. At this end the inner walls of the volume are not parallel [3]. The pressure field is excited by

means of a loudspeaker put in one of the corners, which provides a flat spectrum from 100 Hz to 15 kHz.

1922 PROCEEDINGS OF ISMA2012-USD2012

FACE SHEET and CORE STIFFENERS

Face sheet Layout [0,90,+45,-45]s Face sheet Thickness [m]

Core stiffeners Layout Core stiffeners Thickness [m]

0.0025 2x[0,90,+45,-45]s

0.0050 Material E11 [Pa] E22 [Pa] G12 [Pa]

[kg/m3]

GF-epoxy resin 13.50 109 6.30 109 3.70 109

0.25 1610

CORE

Thickness [m] 0.050 Material E [Pa] G [Pa]

[kg/m3]

PU-foam 5.50 107

2.20 107

0.25 60

Table 1: Nominal geometric and material properties of the initial sandwich panel

Figure 2: MAC Experimental-numerical modal analyses

Figure 3: Correlated mode shapes between experimental (red thick line) and numerical (blue thin line)

models

LIGHTWEIGHT PANELS AND STRUCTURES 1923

The cavity can be fully closed by a rigid front wall for the acoustic absorption test configuration, or an

aperture can be made on the front wall to host test specimens of different sizes and thicknesses. In the

latter configuration the setup allows the evaluation of the acoustic Insertion Loss (IL). The experimental

procedure necessitates two measurements of the sound power to determine the IL, i.e. with and without

the test panel at the wall aperture, see Figure 4 (left and right respectively). Additionally this setup allows

an accurate identification of vibro-acoustic coincidence frequencies.

Figure 4: Vibro-acoustic setup at KU Leuven: open (left) and closed configuration (right)

A pink noise signal is sent to the system with frequency content from 0 Hz to 1.6 kHz. The radiated

acoustic power intensity is recorded outside by scanning the test area in the two different scenarios. The

vibrating surface is divided into 70 sub-surfaces of equal extension and intensity is measured at the central

points of these areas. Intensity probe measurements are performed using a B&K probe type 3584. The

spacer set in between the probe’s microphones is 50 mm, restricting the measurement range to [20 Hz –

1.25 kHz]. The cavity front wall has an A2 sized window. An additional frame clamps the sample all

around its edges (Figure 4 on the right). The measured third octave band average IL is shown in Figure 5,

together with the numerical prediction that will be discussed in details in the next section. Bands at and

below 100 Hz are discarded due to the low frequency limitation of the loudspeaker.

Figure 5: Experimental and numerical evaluation of acoustic IL


The radiated acoustic intensity measured over the panel surface and the numerical prediction of the

radiated acoustic power are plotted in Figure 6. On the same graph the natural frequencies of the

uncoupled acoustic domain (green squares) and those of the clamped panel (red diamonds) are indicated.

As evident from Figure 6, the acoustic power intensity scan allows for an easy and full understanding of

the coupled behaviour between the structural component and the acoustic cavity. The three structural

modes falling within the considered frequency range are coupled to the acoustic field inside the cavity.

Figure 6: Experimental acoustic intensity radiated by the panel (blue line) – Numerical evaluation of the

acoustic power radiated by the panel (red line) – Natural frequencies of the uncoupled acoustic volume

(green squares) - Natural frequencies of the clamped isolated panel (red diamonds) and corresponding

mode shapes and acoustic intensity colour maps measured at the same frequencies

The source input in the numerical model is an acoustic monopole emitting a flat unit power spectrum up to

1 kHz. As long as the assumption of linearity holds, the shape and the level of the input signals have no

influence on the final IL, being the latter simply the difference of the acoustic powers radiated in the two

configurations with and without the sample. This explains the difference shown in Figure 6 between

numerical radiated power and measured acoustic intensity curves.

Adopting a smaller spacer (12 mm) on the intensity probe, intensity measurements provide acoustic IL up

to 7 kHz. Figure 7 also clearly shows the first coincidence frequency of the examined sample. Looking at

the narrow band results (dotted blue curve), a strong coupled modal behaviour exhibited by the system

(panel and cavity) is evident up to 900 Hz. Above this region, similar as for the case of acoustic

Transmission Loss (TL) of panels, the IL is controlled by the structural mass and it follows a 2dB/octave

positive slope trend. The frequency band at 4 kHz is characterised by the coincidence phenomenon. This

occurs at around 4.3 kHz and causes a clear dip in the IL curve. Above coincidence the IL starts rising

again, this time with an increase of 6dB/octave.


Figure 7: Narrow band and third octave band average IL

The nature of the coincidence dip is related to the symmetric motion of the sandwich structure and can be

estimated as described in [5]. Symmetric motion involves deformation of the core in the thickness

direction (Figure 8).

Figure 8: Symmetric (on the top) and anti-symmetric (on the bottom) motions in a sandwich panel

This kind of coincidence appears near the double wall frequency, determined by the mass of the two face

sheets and the compressive stiffness of the core. It can be approximated as reported in [6]

21

11

2

1

ffc

c

DoubleWallmmt

Ef

(1)

where Ec and tc are the Young’s modulus and thickness of the sandwich core and mf1 and mf2 the surface

mass of the two face sheets respectively. Approximating the Young’s modulus of the core with the

Young’s modulus of the foam material (neglecting the stiffeners contribution) the formula above gives a

fDoubleWall = 3.80 kHz, which is still a good indication for the measured value.

Further studies carried out with the intent of verifying the nature of this physical phenomenon, showed

that it is actually the central part of the sandwich panel, delimited in the area between the two stiffeners, to

be featured by the symmetric motion. This additionally justifies the assumption made by considering the

core foam material as solely contribution to the core compression stiffness in equation (1). Seven


lightweight accelerometers are placed on one side of the panel mounted on the test rig and seven are

correspondently positioned on the other face. Specifically, on each face two accelerometers are placed on

the stiffener lines and three are distributed along the central line. Regardless of the input signal sent to the

loudspeaker, the response of the system at 4205 Hz looks as depicted in Figure 9.

Figure 9: Experimental deflection shape of the two face sheets at the symmetric motion coincidence

Based on this response shape the Young’s modulus of the core foam material can now be inversely

retrieved. Using equation (1) for the calculation of Ec, the new value of the compressive stiffness of the

PU foam is increased from 5.5 107 Pa to 7.34 10

7 Pa, which is about 33% higher. Once the FE model

introduced above is modified taking into account the last value for Ec, the shift previously observed

between the numerical and experimental natural frequencies of the freely suspended panel drastically

reduces to less than 2% as starting from 500 Hz (beyond the 6th free-free mode). The error on the first six

natural frequencies still maintains around and below 10%. Not ideal free boundary conditions can explain

this discrepancy at lower frequencies.

2.1.2 Numerical model

The FE model of the structural component mentioned above is now implemented to study the panel’s

vibro-acoustic behaviour. Nominal geometric and material values are firstly used and any kind of

structural damping is discarded. The FE model consists of 12600 linear 8-noded solid elements to model

the foam core, 2520 4-noded shell elements for each of the faces and 420 for the stiffeners (ref. Figure 1).

A numerical modal analysis on the isolated panel case with clamped edges is carried out using MD

Nastran 3Rb. The resulting modal structural FE model is then coupled with an indirect BE model of the

acoustic cavity and a fully coupled FE-IBEM analysis is carried out in LMS Virtual.Lab Acoustics Rev.8b

to evaluate the IL. The relative simplicity of the geometry allows for accurate numerical modelling and a

Wave Based (WB) model can also be adopted to overcome the limitations of standard numerical

techniques (FEM/IBEM) at higher frequencies [7]. The latter however is out of the scope of the present

work and discussed in more detail in [8]. The source input is modelled as an acoustic monopole emitting a

flat unit power spectrum up to 1 kHz and located at the central point of the actual speaker inside the

cavity. Any speaker’s directivity is neglected. The shape and the level of the input signals have no

influence on the final IL, since this quantity is the difference of the acoustic powers radiated with and

without the sample, as long as the assumption of linearity is valid. The third octave band IL is compared to

the experimental results in Figure 5. Simulations using both nominal and updated foam Young’s moduli

are reported. Although improvements in terms of IL coming from this second model are not so evident in

all the third octave bands, this update is kept because of the better simulation of the modal behaviour of

the examined system showed before. To increase the fidelity of the numerical model a real frequency

independent valued acoustic normal impedance boundary condition (14E+4 kg/m2/s) is applied at the

inner cavity walls to take into account their finite (although very small) acoustic absorption [9]. Even


though the structural damping is neglected in the present simulation, the numerical prediction is very close

to the measured IL in the whole examined frequency region with a maximum deviation of 4dB (see Figure

5). Use of structural damping and frequency dependent absorption characteristics of the acoustic volume

could further improve the numerical results.

2.2 Derived design

A second design is derived from the initial layout. It is geometrically more complex with a core stiffeners

pattern as shown in Figure 10.

Figure 10: Core stiffeners configuration of the second panel

The final application of this construction required a higher dynamic stiffness than the previous case, in the

frequency range up to 1 kHz. This solution represents the trade-off between satisfactory dynamic

behaviour and weight minimisation complying with the manufacturability limitations. Table 2 indicates

the main features of the two constructions.

INITIAL PANEL CONFIGURATION DERIVED PANEL CONFIGURATION

FACE SHEET

Layout [0,90,+45,-45]s [0,90,+45,-45]s Thickness [m] 0.0025 0.0025

Material GF-epoxy resin GF-epoxy resin

CORE

Thickness [m] 0.050 0.078 Material PU-foam PU-foam

STIFFENERS

Configuration Only longitudinal – 400 mm spaced As shown in Figure 10 Thickness [m] 0.050 0.050

Material GF-epoxy resin GF-epoxy resin

Total mass (A2 size) [kg] 3.200 5.470

Table 2: Some geometric and material properties of the initial and the derived sandwich panels

3.2.1 Vibro-acoustic study

Experimental and numerical tests are carried out similarly as for the case of the first panel. An FE-IBEM

model is built and the acoustic IL is calculated (with same boundary conditions). Numerical and

experimental results are compared in Figure 11. Simulations are run for both the nominal material


properties dataset and for the updated values based on the approach explained previously. The new

stiffness of the core foam leads to improved prediction of the noise reduction properties. At two third-

octaves (at 400 Hz and 500 Hz) a larger approximation error is observed. Possible frequency dependency

of the acoustic absorption properties at the cavity walls might explain this mismatch. In fact this frequency

region is still well below the first structural natural frequency of the sandwich panel, which only comes at

about 850 Hz. On-going studies are seeking for the full characterisation of the cavity acoustic absorption

properties to explain the observed discrepancies.

Figure 11: Experimental and numerical evaluation of acoustic IL

As shown by the IL comparison in Figure 12, the second configuration indeed offers better noise reduction

performance than the initial panel, due both to the increased global weight and stiffness. The IL increase is

more than 5 dB in almost all third-octave bands analysed up to 1 kHz. Stiffening the structure has an

especially strong effect on those frequency regions which are affected by the presence of resonance

frequencies of the initial structure (400 Hz, 500 Hz and 630 Hz bands). This gain is reduced though at 800

Hz due to the presence of the first resonance frequency of the second sandwich panel. The stiffening effect

is also visible in the coincidence frequency that shifts to the lower band at 3.15 kHz as shown in Figure

13. If now one approximates the Young’s modulus of the core component only with that of the updated

foam material (neglecting the stiffeners contribution, as done for the initial system), equation (1) gives

fDoubleWall = 3.44 kHz, which is again a good indication of the measured value. However in this last case the

complex layout of the core reinforcements brings a much more substantial contribution to the out-of-plane

core stiffness, making this assumption less meaningful.


Figure 12: Experimental IL: initial and final sandwich panels

Figure 13: Narrow band and third octave band average IL

4 Conclusions

A composite sandwich structure is tested and analysed to identify its vibro-acoustic behaviour. A finite

element numerical model is built up on the base of nominal geometrical and material properties, partially

provided by the manufacturer and partially found in literature. The model is coupled to a boundary

element model of an irregularly shaped acoustic cavity representing the experimental test setup. The test

rig allows fast acoustic insertion loss measurements. Good agreement is found between simulations and

experiments, although no structural damping was considered. The symmetric motion coincidence

frequency is used to retrieve the compression modulus of the core foam material. The model is then

updated and used to derive a second design with improved stiffness and minimised global weight, while

keeping satisfactory noise reduction performances. Using the same experimental and numerical


approaches the acoustic IL of the second layout is verified with good accuracy. The vibro-acoustic test rig

also allows for identification of the structural-acoustic coupling and location of the coincidence frequency.

It is shown to be a valuable support for the design and study of composite structures when NVH

performance is a key design parameter.

Acknowledgements

The authors would like to thank the EC for supporting the presented research via the Marie Curie IRSES

project SUPERPANELS (GA 247536) and the Marie Curie ITN GRESIMO project (GA 290050).

Furthermore, the IWT Flanders is gratefully acknowledged for its support via the O&O ASTRA research

project and also the Fund for Scientific Research – Flanders (F.W.O.) and the Research Fund of KU

Leuven are gratefully acknowledged for their support.

The authors also thank the NV engineers at Toyota Motor Europe in providing the tested panels.

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