Page 43 - MSAM-1-4

Materials Science in Additive Manufacturing Acoustic performances of SC lattices fabricated by DLP

based on the ISO-10534-2 standard. The average room d D R. (III)
temperature and relative humidities are 26°C and 60%, p 2
respectively. Every cylindrical SC lattice was inserted into The airflow resistivity σ of the SC-Truss lattices was
the 30 mm diameter holder of the impedance tube. About obtained as follows :
[17]
five measurements of the sound absorption coefficients

were recorded and averaged. The frequency range of 36 1 , (IV)
interest is between 1000 Hz and 6300 Hz. d RUC
2
2
2.3. Numerical modeling of acoustic properties Where η is the dynamic viscosity of the air at 26°C,
-5
In this work, the acoustic properties of the SC-Truss taken as η = 1.84×10 kg/(m.s). Based on Equations I to
lattice cells were analyzed analytically using two different IV, the airflow resistivity σ of the SC-Truss lattices was
modeling approaches: the DB model [8,12] for porous determined based on the air volume V f, strut lengths
materials and the TMM [24,25] of which some sub-domains of and radii, porosity φ and the dynamic viscosity of the air
the air within the cells were modeled as resonant materials. within the lattice cells. Calculated values of the tortuosity
χ, representative unit cell dimension d and airflow
RUC
2.3.1. Delany-Bazley (DB) model resistivity σ are tabulated in Supplementary Text 2 in the
To use the DB model to simulate the sound absorption Supplementary File.
properties of the SC-Truss lattices, knowledge of their flow
resistivity σ is required. These values were calculated by 2.3.2. Multi-layered micropore-cavity (MMC) model
considering the SC-Truss unit cell as a representative unit The MMC model is a mathematical model that integrates
cell (RUC) as shown in Figure 2. the use of the TMM and the theories of MPPs to model
According to Fourie and Du Plessis’s work , the RUC the sound propagation in multi-layered Helmholtz
[26]
dimension d can be calculated as a function of air volume Resonator structures. Unlike the DB model that views the
V , pore size d , and tortuosity χ of the unit cell, given by: SC-Truss lattices as homogeneous porous materials, this
a
p
model views the lattices as multiple layers of micropores
V with air cavities in between. The TMM is a powerful
d RUC d a 2 . (I) analytical method to model the propagation of acoustic
p
waves in one-dimensional problems involving multiple
The tortuosity χ is a geometry-dependent parameter discrete layers of acoustic material [12,27] . The general
of porous materials that characterizes the dispersion expression of the TMM for n heterogeneous layers in
of microscopic velocity of a flowing fluid within the series is as follows:
materials [12,26] . It can be derived in terms of the porosity φ
as following: p p

T layer1 T layer 2 T layern

4 1 v y x0 v y xL

22cos cos 1 2 1 . (II) ,

p
p

3 3 T 11 T 12

T (V)

v
total
v
T
Moreover, the pore dimension d , which is derived xt 21 T 22 xL
y
y y

p
from the simple cubic structure, is the function of the strut
length D and strut radius R as follows: where T layerx is the transfer matrix for Layer x. To

model the acoustic properties of the SC-Truss lattices using
A B the TMM, the air domain within the SC-Truss unit cell, as
shown in Figure 1, needs to be discretized into sub-
domains and the acoustic properties determined
individually. The sub-domains consist of two narrow tubes
of square cross-section and a central open cavity similar to
that of the unit cell, as shown in Figure 3. The narrow tubes
on both ends of the cavity have a side length of d = D – 2R
tube
R
and a thickness of t = . The latter dimension results
tube
2
from the cylindrical cross-sectional geometry of the
individual struts. The cavity is then modeled as a layer of
R
Figure 2. (A) Simple cubic unit cell. (B) Representative unit cell. air of thickness l cav D 2 t tube D 2 .
Volume 1 Issue 4 (2022) 4 https://doi.org/10.18063/msam.v1i4.22