Progresses on the vibro-acoustic design of a
class of aluminium sandwich plates
Vincenzo D’Alessandro, Francesco Franco,
Sergio De Rosa, Tiziano Polito
DEMEASS IV, March 26-30 2011
Urspelt (Luxemburg)
ælab ‐Vibrations and Acoustics Laboratory
Department of Aerospace Engineering
Università degli Studi di Napoli “Federico II”
Via Claudio 21, 80125, Napoli, Italy
www.dias.unina.it
Outline
Synopsis
References
DEMEASS III: A Review
ECOCELL Core
Investigated Configurations
Numerical Results
Experimental Tests
Conclusions and Future Work
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 2
Synopsis
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 3
Sandwich panels are widely used in engineering
application because of the extremely high stiffness-to-
mass ratio. The design flexibility associated with such
composite structures provides significant opportunities for
tailoring the structure to the load and dynamic response
requirements.
A new concept of sandwich plate (all aluminum based)
was tested in order to get the typical results available with
more complicated configurations.
This work is the straight continuation of the work
presented in the last DEMEASS.
Activities herein presented will be continued and
extended under the project SUPERPANELS
(www.superpanels.unina.it).
References
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 4
Kurtze and Watters (1959) studied the application of sandwich panels to increase the sound
insulation between adjoining spaces. They investigated the relation between bending and shear
waves and TL characteristics.
Lang and Dym (1975) optimized the design of a sandwich panel with the goal to exceed the TL
values predicted by the mass law by at least 20 dB in a selected frequency range.
Barton and Grosveld (1981) considered an aeronautical application of honeycomb panels to
improve sidewall attenuation in a light twin-engine.
Thamburaj and Sun (2002) demonstrated that an anisotropic core can lead to higher TL and that
the proper design of face sheet thickness can further improve the performance.
NASA tests (2002) about the performance of sandwich structures with a core made of a lattice of
truss elements are available.
Cunefare et al. (2003) gave additional indication that structural acoustic optimization has the
potential to achieve significant gains to reduce interior noise levels in aerospace structures.
Franco et al. (2007) analyzed the optimization of the structural-acoustic characteristics of various
and innovative sandwich configurations. They considered different core configurations, and those
having a truss geometry have been very promising configurations, since it is possible control the
stiffness along the two direction in-plane of the panel.
Franco, De Rosa and Polito (2010) demonstrated that the vibro-acoustic responses can improve
if a random stiffness is imposed over an optimized configuration, highlighting that randomization
represents a very cheap simulation step.
2 m
ete
rsd
ista
nce
DEMEASS III: A Review
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 5
Sandwich panel with truss-core
18128 and 23664 rods along the
X and Z axes, respectively
Effect of a randomization of the stiffness properties on the
optimized configuration has been analyzed.
ECOCELL Core: Concept
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 7
• Stereolithography is a costly and complicated
procedure.
• Need for both simplified plates and related models
able to take into account the peculiarities of the
configurations and results of the sandwich plate with
resin core.
• Thinking to
– the LEGO© elementary brick concept and
– classical carton filler for packaging . . . .
ECOCELL Core: Concept – Basic Unit
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 8
Equivalent COre CELL:
an aluminium (plate-like)
basic element able to
reproduce the complexity
of the resin core cells.
Core modular element (dimensions in mm)
ECOCELL Core: Global view
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 9
Truss-like core
16 stiffeners along x-axis
11 stiffeners along z-axis
ECOCELL Core: Global view of the sandwich
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 10
Basic Sandwich Panel Configuration
Lx=0.640 m, Lz=0.420 m
FE mesh: 10965 grid points
10752 four-point plate element.
2 m
Vibro-acoustic Indicators
QPdSdSPvQv
QPdSdSPvQPk
QPkQv
cdSPvPp
dSPvPvv
S S
S S
S
rad
S
MS
if ,),(),(
if ,),(||
|)|sin(),(
4);();(Real
2
1)(
);();(Real2
1)(
*
*
0
0
2*
*2
Continuos
)()()(4
)(
)()(Real2
1)(
2
2
AvARv
vv
H
a
arad
H
MS
c
v
Discrete
Thus, it is possible, on the base of the results achieved from a frequency
response analysis of the finite element model of a generic plane structure,
to calculate the radiated acoustic power.
v(ω) is the velocity vector
R(ω) is the radiation resistance matrix
A is the nodal equivalent areas matrix
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 11
ECOCELL core configurations (Mcore=0.52 Kg)
Code Stiffeners Configuration
Base Stiffeners in both directions: tx = tz= 1 mm
B No stiffeners along x-axis: tz= 1.9545 mm
C No stiffeners along z-axis: tx 2.0476mm
D Half stiffness along x-axis: tx = 0.6825 mm, tz= 1.3030 mm
E Half stiffness along z-axis: tx = 1.3625 mm, tz= 0.6515 mm
Skin thickness configurations: panel mass distribution
Skin Thickness [mm] Skin Mass [Kg] Sandwich Mass [Kg]
1 0.726 1.972
2 1.452 3.424
3 2.178 4.876
Coding: CODE_THmm
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 12
Investigated Configurations
Numerical Results (cont’d)Influence of Core Configuration
Spatial Mean Square Velocity – Face Sheet Thick 1mm – Panel Weight 1.97Kg – BC = SS
Frequency [Hz]
V2M
S[m
2/s
2]
0 1000 2000 3000 4000 5000
106
105
101
103
102
104
Base_1mm
D_1mm
E_1mm
C_1mm
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 13
30
40
50
60
70
80
Radiated Acoustic Power – Face Sheet Thick 1mm – Panel Weight 1.97Kg – BC = SS
Numerical Results (cont’d)Influence of Core Configuration
Frequency [Hz]
dB
0 1000 2000 3000 4000 5000
C_1mm configuration
Base_1mm
D_1mm
E_1mm
C_1mm
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 14
30
40
50
60
70
80
Radiated Acoustic Power – Different Face-Sheet Thickness
Numerical Results (cont’d)Influence of Face-Sheet Thickness
Frequency [Hz]
dB
0 1000 2000 3000 4000 5000
Base_1mm
Base_2mm
Base_3mm
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 15
Numerical Results (cont’d)Randomness of the Core Stiffness (1/4)
It was investigated the effect of the addition of a random distribution of the
core stiffness. The random distributions were based on two (uncoupled)
Gaussian functions.
Frequency [Hz]
V2M
S[m
2/s
2]
Spatial Mean Square Velocity – Face Sheet Thick 1mm – Panel Weight 1.97Kg – BC = SS
0 1000 2000 3000 4000 5000
106
105
101
103
102
104
sr = 70%
Base_1mm
sr = 40%
sr = 60%
sr = 70%
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 16
Numerical Results (cont’d)Randomness of the Core Stiffness (2/4)
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 17
101
Spatial Mean Square Velocity – Face Sheet Thick 1mm – Panel Weight 1.97Kg – BC = SS
105
Numerical Results (cont’d)Randomness of the Core Stiffness (3/4)
Frequency [Hz]
V2M
S[m
2/s
2]
106
103
102
104
0 1000 2000 3000 4000 5000
C_1mm
C1_1mm
C2_1mm
C3_1mm
C4_1mm
C5_1mm
C6_1mm
C7_1mm
C7_1mm
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 18
20
Radiated Acoustic Power – Face Sheet Thick 1mm – Panel Weight 1.97Kg – BC = SS
Numerical Results (cont’d)Randomness of the Core Stiffness (4/4)
Frequency [Hz]
dB
106
30
40
50
60
70
80
0 1000 2000 3000 4000 5000
C_1mm
C1_1mm
C2_1mm
C3_1mm
C4_1mm
C5_1mm
C6_1mm
C7_1mm
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 19
Optimization of the ECOCELL Core (1/2)
NX NASTRAN optimizer (SOL 200) - Modified Method of Feasible
Directions
Twenty-seven design variables: thickness of the stiffeners
Constraint: weight of the core, i.e. the thickness of the stiffeners are
explicitly linked because is imposed a constraint on their variations so
as to keep the core weight less or equal to the value of the initial
configuration
Objective Functions: the simplest objective function is the average of
the square structural velocity on the radiating face sheet and over the
chosen frequency range
2
,1 1
1 NG NF
i ji j
F VNG NF
• NG = number of discrete sample
points on the face of the panel
• NF = number of frequency sample
points
Numerical Results (cont’d)
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 20
Optimization of the ECOCELL Core (2/2)
NG = 30, NF = 21, Range 1800 – 2300 Hz, base_1mm starting configuration
Frequency [Hz]
V2M
S[m
2/s
2]
1800 2000 2200 2400
101
102
104
103
C7_1mm
Optimizer configuration
Numerical Results (cont’d)
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 21
Experimental Tests – The 1st prototype
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 22
Manufacturing Problems
1. ECOCELL core in steel instead
of aluminum alloy
2. Face sheet 3 mm thick and
grooved in correspondence of
the stiffeners positions to
facilitate their installation
3. Pods filled with epoxy glue
4. There is contact in the
intersection of stiffeners!
Experimental Tests – The 1st prototype
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 23
Modal analysis – Impact testing by using LMS TESTLab
Conclusions and Future Work Concept of ECOCELL core has been introduced
Vibro-acoustic response of several articles with common structure and
difference in skin and core have been analyzed in terms of mean
square velocity and radiated acoustic power, evaluating the influence
of core configurations.
Confirm that randomization approach allows an improvement of vibro-
acoustic behavior.
First experimental test has been introduced, without significant results
due manufacturing problems.
Future Work
Numerical developing: identifying an optimization method that lead an
optimal configuration (multicriteria genetic algorithm)
Find the right technology to manufacture the sandwich panel, in order
to compare numerical and experimental tests.
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 24
Thanks for your attention
Progresses on the vibro-acoustic design of a class of aluminium sandwich plates 25
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