1
GREEN VIBRATIONS: DYNAMIC STIFFNESS AND CONSTITUTIVE
MODELLING OF RECYCLED NONWOVEN MATERIALS FOR SUSTAINABLE
VIBRATION DAMPING IN FLOORING
Fe nandes, Nuno A.T.C.1; Al es, Diana I.2; Rui o, F ancisco1; Fe ei a, Diana P.2; Ca alho, Osca 1*
1 Depa men o Mechanical Enginee ing, Cen e o Mic oelec omechanical Sys ems (CMEMS), Uni e si y o Minho,
Campus de Azu ém, 4800-058, Guima ães, Po ugal
2 Tex ile Science and Technology Cen e (2C2T), Depa men o Tex ile Enginee ing, Uni e si y o Minho, Campus de
Azu ém, 4800-058, Guima ães, Po ugal
* Co espondence au ho : nnuno e [email protected]
ABSTRACT
The inc easing conce n o e en i onmen al sus ainabili y has d i en he explo a ion o was e-based
ma e ials as inno a i e enginee ing applica ions. Dynamic comp essi e mechanical es s we e
pe o med a a ying equencies o e alua e ene gy dissipa ion and s i ness. The esul s show ha
comp essed samples exhibi highe Young's modulus, ensile s eng h, and dynamic s i ness compa ed
o hei uncomp essed coun e pa s, pa icula ly a highe equencies. Howe e , hese comp essed
s uc u es also display g ea e he e ogenei y due o une en ibe dis ibu ion and bonding du ing he
comp ession p ocess. Uncomp essed s uc u es, while mo e lexible and capable o la ge de o ma ions,
dissipa e ene gy mo e e ec i ely a lowe equencies due o hei loose ibe a angemen .
Fu he mo e, he p esence o small ibe black polyes e and oo wea was e in he samples nega i ely
impac s mechanical pe o mance in uncomp essed s uc u es, wi h sho e ibe s hinde ing e ec i e
en anglemen in he ma ix. Comp essed samples wi h low amoun s o black polyes e show imp o ed
homogenei y and mechanical p ope ies. O e all, he s udy demons a es ha comp ession signi ican ly
enhances s i ness and ene gy dissipa ion a highe equencies, while ibe composi ion and dis ibu ion
play c i ical oles in de e mining he mechanical pe o mance o hese ma e ials. A cons i u i e model
based on he Kel in-Voig iscoelas ic model was p oposed o cap u e he complex mechanical
beha io o he nonwo en and comp essed nonwo en s uc u es unde dynamic loading, accoun ing o
he elas ic and iscous p ope ies o he ma e ials. By inco po a ing his model, we can acili a e u he
nume ical s udies ha simula e eal-wo ld condi ions, analyze s ess dis ibu ion, and p edic ma e ial
pe o mance unde a ying equencies and loads.
Keywo ds
Dynamic S i ness; Viscoelas ici y; Nonwo en; Comp essed Nonwo en; Dynamic Comp ession
Analysis; Mechanical P ope ies; Cons i u i e model
1 INTRODUCTION
U ban g ound ib a ions caused by ains and ehicles pose isks o buildings, sensi i e equipmen , and
human heal h. These ib a ions p opaga e h ough he soil, po en ially damaging s uc u es and causing
psychological e ec s such as sleep diso de s [1]. Fac o s such as a ic olume, ehicle ype, and oad
condi ions signi ican ly in luence ib a ion in ensi y. As a esponse, many coun ies ha e implemen ed
egula ions o con ol such dis u bances [2].
Floa ing loo sys ems a e widely used o mi iga e hese ib a ions, especially high- equency
componen s [1]. Howe e , hey can inad e en ly ampli y low- equency ib a ions due o in e ac ions
be ween he loa ing laye , he esilien in e laye , and he unde lying slab [3]. This ampli ica ion is
in luenced by he ma e ial’s damping p ope ies and apped ai , al e ing he sys em’s na u al equency.
Va ious solu ions ha e been de eloped o imp o e ib a ion isola ion unde loa ing loo s. Cons ained
laye damping e ec i ely educes s uc u al ene gy ans e by limi ing in e nal mo ion be ween igid
laye s. Sp ing-suppo ed conc e e slabs o e high isola ion o high equencies bu a e less e ec i e
a low equencies. Recen inno a ions include composi e isola ion pads wi h ca bon nano coils and
s y ene-bu adiene, educing ampli ica ion by o e 8% and o e ing up o 75% noise educ ion. O he
2
e ec i e sys ems include d y- ype double loo s o imbe cons uc ions, decoupled CLT slabs wi h
elas ic in e laye s, and op imized ai ca i ies ha enhance acous ic isola ion by uning esonance
equency [4], [5].
Despi e hei e ec i eness, con en ional damping ma e ials p esen en i onmen al challenges due
o emissions, was e, and poo ecyclabili y. Ma e ials such as asphal con ibu e signi ican ly o CO₂
and phospho us pollu ion. Mo eo e , many exis ing s a egies a e cos ly o imp ac ical o widesp ead
implemen a ion and o en exclude main enance and end-o -li e impac s om sus ainabili y analyses[6],
[7]. These conce ns ha e d i en in e es in eco- iendly cons uc ion ma e ials de i ed om enewable,
biodeg adable, o ecycled sou ces. Tex ile and oo wea was e a e pa icula ly p omising, o e ing low-
cos , as -p oduc ion ma e ials wi h s ong acous ic and he mal insula ion po en ial. Nume ous s udies
ha e success ully in eg a ed hese was es in o nonwo en composi es o use in cons uc ion,
au omo i e, and ag icul u al applica ions[8], [9].
This s udy aims o e alua e he dynamic mechanical beha io o nonwo en s uc u es made om
ecycled oo wea was e. Using he manu ac u ing p ocess de eloped by Al es e al.[10], and applying
he Kel in-Voig iscoelas ic model, we quan i y he dissipa ed ene gy and p opose a cons i u i e
model. These esul s a e in ended o in o m s uc u al design and suppo ini e elemen simula ions o
ecycled damping ma e ials in p ac ical enginee ing con ex s.
2 MATERIALS AND METHODS
2.1 Was e G inding
Th ee ypes o was e we e used: pos -indus ial whi e and black polyes e om oo wea p oduc ion,
and pos -consume oo wea was e. Whi e polyes e was sou ced om AMF Sa e y Shoes (Po ugal),
and he emaining was e om CTCP. All ma e ials we e milled using a cu ing mill wi h 10×10 mm
and 4×4 mm sie es, esul ing in ibe leng hs be ween 1–16 mm, measu ed ia s e eo mic oscopy.
2.2 Nonwo en s uc u es p oduc ion
Ten nonwo en s uc u es we e p oduced using needle-punching o whi e polyes e , black polyes e , and
oo wea was e, wi h a ecycled polyes e ma ix added o imp o e ibe en anglemen (Samples A, C,
E, G, I). Some samples we e u he comp essed a 10 kN and 250 °C o 4 minu es o c ea e dense
s uc u es (Samples B, D, F, H, J), as obse ed in Figu e 1.
Figu e 1 Samples o nonwo en s uc u es.
2.3 Physical p ope ies
The physical p ope ies assessed we e hickness, a ea weigh , and bulk densi y. Thickness was
measu ed pe ISO 9073-4 using en andom poin s pe sample; a ea weigh was de e mined om h ee
samples using an elec onic balance. Bulk densi y was calcula ed om hickness and a ea weigh .
2.4 Tensile mechanical p ope ies
Tensile es s we e pe o med using a 10 kN load cell ollowing ISO 9073-3 o uncomp essed samples
(A, C, E, G, I) and ASTM D3039 o comp essed ones (B, D, F, H, J). Fi e specimens pe sample we e
3
es ed, and a e age s ain and ensile s eng h we e calcula ed. Young’s modulus was ob ained using
Py hon’s RANSAC eg ession o exclude ou lie s and i a linea model up o he ailu e poin .
2.5 Comp essi e dynamic cha ac e iza ion
This s udy e alua ed he comp essi e dynamic p ope ies o ecycled polyes e nonwo en ma e ials o
use as ib a ion dampe s in loo ing. Samples (20×20 mm) we e g ouped by composi ion and
p ocessing and es ed in iplica e unde cyclic sinusoidal loading using a shake se up wi h iaxial
accele ome e s and a load cell. Tes s ollowed a modi ied ISO 9052-1:1989 p o ocol, wi h a s a ic
p eload o 25 N. A e ini ial cycles o s abilize he ma e ial, samples we e es ed ac oss equencies
om 5 o 30 Hz (highe equencies we e excluded due o o e lapping hys e esis cu es). Da a was
p ocessed in Py hon o calcula e s ain, s ess, dissipa ed ene gy, and dynamic s i ness based on
s anda dized equa ions.
3 Theo y and calcula ions
3.1 Polyes e nonwo en cons i u i e model
To model ene gy dissipa ion, he Kel in-Voig iscoelas ic model was selec ed, as i e ec i ely
cap u es he ime-dependen beha io o nonwo en ma e ials unde cyclic loading. This model,
consis ing o a sp ing and dashpo in pa allel, ep esen s bo h elas ic and iscous esponses, making i
well-sui ed o cha ac e izing ecycled polyes e nonwo ens used in ib a ion damping (Figu e 2).
Figu e 2 Kel in-Voig Model, ep esen ing wo pa allel elemen s: he sp ing on he le ( he elas ic
componen ) and he dashpo on he igh ( he iscous componen ).
In he Kel in-Voig model, o al s ess is he sum o elas ic and iscous componen s: he sp ing s o es
ene gy, while he dashpo dissipa es i . Toge he , hey desc ibe he ma e ial's abili y o esis and
dampen de o ma ion, wi h highe iscosi y (η) indica ing g ea e ene gy dissipa ion (equa ion 1).
𝜎 = 𝐸𝜖 + 𝜂 𝑑𝜖
𝑑𝑡
(1)
3.2 Dissipa ed ene gy and hys e e ic beha io
Viscoelas ic ma e ials exhibi hys e esis unde cyclic loading, o ming a s ess-s ain loop whose
enclosed a ea ep esen s he dissipa ed ene gy. Unlike elas ic ma e ials, ene gy inpu is no ully
eco e ed due o in e nal ic ion (Figu e 3).
4
Figu e 3 Illus a ion o he linea elas ic S ess-S ain ela ionship (A) and he nonlinea hys e e ic
beha io o a iscoelas ic ma e ial (B), highligh ing ene gy dissipa ion and he lag be ween s ess and
s ain du ing cyclic loading, ep esen ed by he blue loop in he s ess-s ain cu e."
When a sinusoidal s ain is applied, he dissipa ed ene gy pe cycle can be de i ed analy ically and is
p opo ional o he squa e o s ain ampli ude, iscosi y, and equency. This ela ionship, gi en by
Equa ion 2 is used o quan i y ene gy loss in he s udied nonwo en ma e ials.
𝑊𝑑𝑖𝑠𝑠𝑖𝑝𝑎𝑡𝑒𝑑 = 2𝜖0
2𝜋2𝜂𝑓 (2)
4 Resul s and discussion
4.1 Physical p ope ies
Physical p ope ies o he samples a e shown in Table 1.
Table 1 S a ic mechanical p ope ies o he s uc u es
Sample
Thickness (mm)
A ea Weigh (g/cm2)
Bulk Densi y (g/cm3)
A
10
0.16
0.16
B
5
0.24
0.47
C
10
0.14
0.14
D
6
0.25
0.42
E
8
0.16
0.19
F
4
0.18
0.45
G
8
0.22
0.27
H
4
0.17
0.43
I
6
0.048
0.081
J
5
0.24
0.48
A ea weigh and bulk densi y inc eased in all he comp essed nonwo en s uc u es in Samples B, D, H,
J compa ed o he uncomp essed Samples A, C, G, I due o manu ac u ing comp ession. The excep ions
we e Samples E and F, whe e he comp essed Sample F showed dec eased hickness and inc eased bulk
densi y wi hou a signi ican change in a ea weigh . Fo he o he comp essed samples, he same weigh
was dis ibu ed o e a smalle olume, esul ing in highe a ea weigh and bulk densi y, as e lec ed by
he educed hickness.
4.2 Tensile Mechanical Cha ac e iza ion
The s a ic mechanical p ope ies o he nonwo en s uc u es, including ensile s ain, ensile s eng h,
Young’s modulus and he coe icien o de e mina ion o he linea eg ession used o calcula e young
modulus a e obse ed in Figu e 4.
A
B
5
Figu e 4 Linea eg ession o he ensile mechanical beha io o he samples.
In gene al, Tensile S eng h and Young Modulus inc eased when he samples we e comp essed, while
hei Tensile S ain and coe icien o de e mina ion dec eased when comp essed (Samples B, D, H, J),
when compa ed wi h hei uncomp essed coun e pa s (Samples A, C, G, I). This, howe e , was no
obse ed in Samples E and F, in which he comp essed s uc u e in Sample F had he highes Tensile
S ain (102.3%) o all he samples and a high Tensile S eng h (3099 kPa), Young Modulus (2782 kPa),
while he uncomp essed Sample E had he lowes Tensile S ain (102.3%), lowes Tensile S eng h (26
kPa), a low Young Modulus (224 kPa).
4.3 Comp essi e dynamic loading
The dynamic mechanical p ope ies o he nonwo en s uc u es, namely dissipa ed ene gy and iscous
coe icien a e obse ed in Figu e 5 and Table 2.
A
B
6
Figu e 5 E olu ion o (A) Dissipa ed ene gy and (B) Viscous coe icien o e dynamic comp ession
equency.
O e all, he analysis highligh s how ma e ial composi ion and comp ession in luence he damped
ene gy and iscous coe icien s ac oss di e en equencies, wi h speci ic samples like F and B
demons a ing signi ican ene gy dissipa ion h ough high iscous coe icien s despi e lowe damped
ene gy.
The esul s e eal dis inc a ia ions in damped ene gy and iscous coe icien ac oss he di e en
nonwo en samples (A o J) when subjec ed o equencies o 5, 10, 20, and 30 Hz. No ably, Sample A
exhibi s high damped ene gy and iscous coe icien a lowe equencies (5 and 10 Hz), wi h a
signi ican d op a 20 Hz and ze o alues a 30 Hz. Upon comp ession, Sample B shows a dec ease in
damped ene gy ac oss all equencies bu main ains high iscous coe icien s, especially a 10 Hz and
30 Hz. Sample C displays mode a e damped ene gy wi h a no iceable peak a 10 Hz, while Sample D
shows educed ene gy bu signi ican ly highe iscous coe icien s a 10 and 30 Hz.
Sample E, composed o 60% ma ix and 40% black was e polyes e , s ands ou wi h he highes damped
ene gy a 5 Hz, which dec eases wi h inc easing equency, bu main ains ela i ely low iscous
coe icien s ac oss all equencies. Con e sely, Sample F demons a es lowe damped ene gy bu high
iscous coe icien s, pa icula ly a 5 and 10 Hz, indica ing e ec i e damping wi h a ocus on ene gy
dissipa ion h ough iscous mechanisms.
Sample G shows a mo e consis en pa e n, wi h mode a e damped ene gy and iscous coe icien s ha
peak a lowe equencies and diminish as equency inc eases. Sample H, which is he comp essed
e sion o Sample G, e ains simila ene gy dissipa ion beha io bu wi h sligh ly ele a ed iscous
coe icien s a all equencies, pa icula ly a 10 and 30 Hz. Finally, Sample I and i s comp essed
coun e pa Sample J exhibi mode a e o low damped ene gy and iscous coe icien s, wi h Sample I
peaking a 5 Hz and Sample J showing a simila beha io bu peaking a 10 Hz. These esul s highligh
he signi ican impac o comp ession and ma e ial composi ion on he damping beha io o he
nonwo en s uc u es.
Table 2 Dynamic s i ness o he ob ained samples o nonwo en s uc u es
Sample
Dynamic s i ness (MN/m3)
5 Hz
10 Hz
20 Hz
30 Hz
A
54.34
20.08
10.12
13.80
B
80.53
208.34
138.77
1064.55
C
68.17
26.89
20.67
21.18
D
60.81
164.78
135.34
981.22
E
25.36
28.91
20.89
31.13
F
136.82
157.95
99.12
264.69
A
B
7
G
58.17
33.73
35.45
54.88
H
125.34
221.78
144.99
622.70
I
94.54
112.63
61.09
107.04
J
100.27
125.34
82.24
135.15
In gene al, comp essed samples B, D, F, H, J exhibi highe dynamic s i ness, pa icula ly a highe
equencies (20 Hz and 30 Hz). Sample B shows a no able inc ease in s i ness a 30 Hz (1064.55
MN/m³), while uncomp essed samples A, C, E, G, I display lowe and mo e consis en alues ac oss
all equencies. Sample E s ands ou wi h ela i ely low s i ness a all equencies, while sample F
main ains a balanced inc ease ac oss all equency anges.
4.4 Sugges i e cons i u i e modelling
The sugges ed cons i u i e model pa ame e s o he ob ained samples a e demons a ed in Table 3.
Table 3 Dynamic s i ness o he ob ained samples o nonwo en s uc u es
Sample
Young Modulus (kPa)
Dynamic s i ness (MN/m3)
5 Hz
10 Hz
20 Hz
30 Hz
A
1148
1.57
0.79
0.28
0.53
B
4656
4.07
9.70
2.42
5.11
C
793
3.06
1.48
0.34
1.41
D
2131
4.64
10.72
3.59
19.89
E
224
3.37
1.36
0.27
0.24
F
2782
7.37
7.04
3.08
1.65
G
244
6.96
2.02
0.72
0.32
H
274
7.21
9.39
3.76
7.69
I
161
7.93
2.83
1.06
0.38
J
8696
7.40
3.32
1.26
2.58
The sugges ed Kel in-Voig cons i u i e model e ec i ely cha ac e izes he iscoelas ic beha io o
he nonwo en samples by combining hei elas ic and iscous p ope ies. The model u ilizes Young's
modulus and iscous coe icien s a a ying equencies (5, 10, 20, and 30 Hz) o desc ibe how each
sample esponds o de o ma ion unde cyclical loading.
5 CONCLUSIONS
Comp ession o nonwo en s uc u es signi ican ly a ec ed hei physical and mechanical p ope ies.
Gene ally, comp ession inc eased a ea weigh and bulk densi y by educing hickness, as seen in
samples B, D, H, and J. A no able excep ion was sample F, which main ained simila a ea weigh despi e
inc eased densi y, due o i s unique composi ion o sho black polyes e ibe s and high ma ix con en .
Tensile es s showed ha comp essed samples (B, D, F, H) had highe Young’s modulus and ensile
s eng h bu g ea e he e ogenei y, likely due o une en ibe dis ibu ion. Uncomp essed samples (A,
C, G, I) showed highe s ain due o inc eased lexibili y. Samples wi h high con en o black polyes e
o oo wea was e pe o med wo se mechanically, hough sample F bene i ed om comp ession,
showing imp o ed uni o mi y and s eng h.
Unde dynamic comp ession, comp essed samples dissipa ed mo e ene gy a low equencies (5 Hz),
while uncomp essed ones pe o med be e a 10 Hz due o g ea e lexibili y. A highe equencies
(20–30 Hz), all samples saw educed damping e iciency, bu comp essed s uc u es e ained some
damping h ough mic os uc u al de o ma ions.
Dynamic s i ness es s con i med he supe io pe o mance o comp essed s uc u es, especially a high
equencies, a exceeding alues o comme cial ma e ials like polyu e hane oams. The Kel in-Voig
model e ec i ely cap u ed he iscoelas ic beha io o he ma e ials, suppo ing i s use o p edic ing
pe o mance and op imizing ib a ion-damping designs.
8
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ACKNOWLEDGEMENT
The au ho s acknowledge he inancial suppo om in eg a ed p ojec BioShoes4All – Ino ação e
capaci ação da ilei a do calçado pa a a bioeconomia sus en á el; a iso 02/C12-i01.01/2022;
candida u a n.º 11, n.º p oje o 2372, p omo ed by he Reco e y and Resilience Plan (RRP), Nex
Gene a ion EU, o he pe iod 2023-2026. The au ho s a e also hank ul o p ojec
UID/CTM/00264/2023 o 2C2T—Cen o de Ciência e Tecnologia Têx il, unded by Na ional Founds
h ough FCT/MCTES- Fundação pa a a Ciência e Tecnologia. This wo k is also unde he na ional
suppo o R&D uni ’s g an h ough he e e ence p ojec UIDB/04436/2020 and UIDP/04436/2020
Nuno Fe nandes acknowledges he suppo om FCT o his indi idual PhD g an wi h e e ence
2022.11063.BD (h ps://doi.o g/10.54499/2022.11063.BD). Diana I. Al es acknowledges he suppo
om FCT o he indi idual PhD g an wi h e e ence 2024.00283.BDANA. Diana P. Fe ei a is
hank ul o CEECIND/02803/2017, ounded by Na ional Founds h ough FCT/MCTES.
