amplitude and frequency dependence of magneto-sensitive rubber in a wide frequency range

Material Behaviour

Amplitude and frequency dependence of magneto-sensitive

rubber in a wide frequency range

Peter Blom*, Leif Kari

The Marcus Wallenberg Laboratory for Sound and Vibration Research (MWL), Royal Institute of Technology, 100 44 Stockholm, Sweden

Received 23 February 2005; accepted 1 April 2005

Abstract

Two new aspects of the dynamic behaviour in the audible frequency range of magneto-sensitive (MS) rubber are highlighted:

the existence of an amplitude dependence of the shear modulus—referred to as the Fletcher–Gent effect—for even small

displacements, and the appearance of large MS effects. In order to illustrate these two features, results are presented of

measurements performed in the audible frequency range on two different kinds of rubber: silicone and natural rubber with a

respective iron particle volume concentration of 33%. The particles used are of irregular shape and randomly distributed within

the rubber. An external magnetic field of 0–0.8 T is applied. Both kinds of rubber are found to be strongly amplitude dependent

and, furthermore, displaying large responses to externally applied magnetic fields—a maximum of 115%. Also included are

graphs of measurements on silicone and natural rubber devoid of iron particles. Those results support the conclusion that

introducing iron particles in the rubber gives rise to a strong, non-negligible, amplitude dependence in the entire frequency

range.

q 2005 Elsevier Ltd. All rights reserved.

Keywords: Magneto-sensitivity; Fletcher–Gent effect; Rubber; Amplitude dependence; Audible frequency range

1. Introduction

Vibrations are omnipresent and linked problems are

manifold. In structures, vibrations cause damage; in the

audible frequency range, when transmitted from structures

into the air, they are perceived by the human ear as sound.

One commonly used means to reduce energy transmission

travelling in the shape of vibrations is to decouple the source

from the receiver by inserting a flexible element. Rubber

possesses the proper characteristics and such isolators are

consequently used in various industrial applications.

Different applications and conditions require different

isolators. However, once an isolator has been installed in

an application, its frequency dependent properties become

difficult to alter. This presents a well-known problem in

0142-9418/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.polymertesting.2005.04.001

* Corresponding author. Tel.: C46 8 7909202; fax: C46 8

7906122.

E-mail address: [email protected] (P. Blom).

industry as well as normal life, often overcome by not

lingering too long on critical frequencies, such as rigid body

eigenfrequencies and dynamic stiffness peak frequencies.

Magneto-sensitive (MS) elastomers constitute a new group

of smart materials, with the potential of providing more

viable solutions. Indeed, recent years have witnessed a rapid

growth of interest in this class of smart materials, consisting

fundamentally of rubber and similar elastomers carrying a

large content of magnetically polarisable particles, usually

iron. In contrast to their non-polarisable counterparts, MS

materials benefit from the fact that their properties can be

varied rapidly, continually and reversibly.

Research into the field of magneto-sensitive materials

was started in the end of the 1940s by Rabinow [1] who was

working on magneto-sensitive fluids. Concurrently, Win-

slow [2] was working on electro-sensitive (ES) fluids.

In tandem with their discoveries, research on MS and ES

materials gained momentum, but focus has until recently

primarily been set on ES materials. Nevertheless, MS

materials have proven more commercially successful

Polymer Testing 24 (2005) 656–662

www.elsevier.com/locate/polytest

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P. Blom, L. Kari / Polymer Testing 24 (2005) 656–662 657

and over the last 10 years their large potential has been

increasingly recognised; this has prompted a large number

of publications of research reports on MS fluids and solids

alike [3–5,16,19]. Since MS fluids operate essentially in the

yield region and MS solids in the pre-yield region, their

utilities are of different character; thus, they serve as

complementary materials, suitable for different applications.

Whereas the quasi-static behaviour of MS rubber has

lately been studied extensively [6–10,18], the dynamic

properties, ranging into the audible frequency range, have

been given less attention. Some research has yielded

promising results in displaying among other things large

responses to externally applied magnetic fields. Kari [11]

has studied the MS effects over the same frequency range as

in this work; however, since the displacement amplitude

was not constant, the influence of the Fletcher–Gent effect

[13] alone could not be observed. Lokander and Stenberg

[12] have studied amplitude phenomena in the low

frequency range (!50 Hz), thus considering the Fletcher–

Gent effect, but only for such large strains as 1.1% and more.

Displacement amplitudes corresponding to strains of that

magnitude are not likely to be encountered in the audible

frequency range. Bellan and Bossis [15], and Bossis et al.

[17], have studied the amplitude dependence and magnetic

sensitivity of the E modulus for strains of varying order, but

only for low frequencies (5 and 1 Hz, respectively). This

article works in the audible frequency range of

100–1000 Hz. Due to this wide frequency span, it covers

visco-elastic effects in addition to magnetic ones, while

simultaneously at all strains allowing for observation of the

Fletcher–Gent effect—the rubber is subjected to constant

shear strains as small as 0.0084%. In this manner, a more

complete understanding of the separate effects and their

relative importance is obtained. Surprising results were

obtained: a strong, non-negligible amplitude dependence

within a wide frequency band for even the smallest strains

and substantially larger responses to applied magnetic fields

in the audible frequency range than has previously been

reported.

2. Experimental

2.1. Materials

The iron particles used were irregularly shaped, pure iron

particles ASC300 from Hoganas, with a particle size

distribution of 77.7%: 0–38 mm, 15.6%: 38–45 mm and

6.7%: 45–63 mm. The rubber matrix materials were natural

rubber (SMR GP) and silicone rubber (Elastosil R 101/25

from Wacker). The vulcanisation system for the natural

rubber was a conventional sulphur curing system. The

natural rubber contained 100 phr rubber, 6 phr zinc oxide

(ZnO), 0.5 phr stearine, 3.5 phr sulphur, 0.5 phr mercapto-

benzothiazole and 40 phr hydrocarbon oil, Nytex 840

plasticiser. The silicone rubber was vulcanised with

0.7 phr curing agent C6 from Wacker. The iron particles

were mixed into the silicone and natural rubber in a

Brabender internal mixer for approximately 5 min at a

rotation frequency of 30 rpm. The natural rubber was

vulcanised at 150 8C for 30 min, and the silicone rubber at

170 8C for 5 min. The applied pressure was approximately

12 MPa. After the rubber samples were vulcanised their

densities were measured in order to verify the degree of iron

content. This set-up is based on Archimedes’ principle [14].

Three pair of samples, with an iron particle volume

concentration 0, 26 and 33%, of each rubber were tested.

The results from the 26% rubber tests are not discussed in

this article since the observed effects are virtually the same

as for the 33% rubber, albeit somewhat smaller.

2.2. Dynamic shear modulus measurements

A test rig (Fig. 1) was designed for dynamic shear

modulus measurements. Two test samples of dimensions

L!W!TZ20 mm!15 mm!2 mm (length, width and

thickness), are sandwiched between two brass plates used

as fixtures. They are glued to the brass plates with a

cyanoacrylate adhesive (Loctite 406). The blocking mass is

mounted on three symmetrically placed soft rubber

isolators. Excitation is provided by an electrodynamic

vibration generator mounted via a set-up on the floor. The

magnetic field is generated by an electro-magnet made by a

power-supplied coil wired round an iron C-frame directing a

magnetic field perpendicularly to the shear direction.

The excitation gives rise to a vertical motion that is

transmitted by the brass plates to the test segments that in

turn set the blocking mass in motion. Knowledge of test

sample dimensions along with data obtained from piezo-

electric accelerometers—on relative displacement of the

samples and acceleration of the blocking mass—yield an

expression for the shear modulus. According to Newton’s

second law applied to the blocking mass

~Fbm Z2LWGð ~Ubp K ~UbmÞ

TzKu2 ~UbmMbm:

This yields an expression for the shear modulus

GzKu2Mbm

T ~Ubm

2LWð ~Ubp K ~UbmÞ;

where G represents the shear modulus, u the angular

velocity, Ubp and Ubm the vertical displacement of the brass

plates and of the blocking mass, respectively, defined in the

same direction, and ð ~$ÞZÐNKNð$Þexp K ðiutÞdt the temporal

Fourier transform. The frequency analyser employs auto and

cross-spectrum densities—mathematically simplified for

practical purposes—to create a response function. The

auto spectrum density is defined by the temporal Fourier

transform of the auto correlation function

CðX;XÞ Z limT/N

1

T

ðN

KNXðrÞXðr C tÞdr

Table 1

Measurement instruments

Instruments Type Number

Vibration Exciter B&K 4817 1

Amplifier B&K 2708 1

Accelerometer (11 g) B&K 4371V 3

Accelerometer (84 g) Rion PV-84 1

Charge amplifier B&K 2635 2

Wire coil Home made 1000 wounds 1

Power Supply SM Delta Elektronika 70-22 1

Gaussmeter Magnet-Physik FH31 1

Frequency analyser Siglab 20-42 1

Computer Aquila Pentium III MMX 1

Fig. 1. Measurement set-up.

P. Blom, L. Kari / Polymer Testing 24 (2005) 656–662658

and the cross-spectrum by the temporal Fourier transform of

the cross-correlation function

CðX;YÞ Z limT/N

1

T

ðN

KNXðrÞYðr C tÞdr:

The expression of the frequency response function is

calculated as

~HðX; YÞ Z~CðX; YÞ

~CðX;XÞ;

resulting in the theoretical shear modulus expression used in

the analysis

GzMbm

T

2LW

1~CðUbp ;UbpÞ

~CðUbp ;AbmÞC 1

u2

:

The weight of the blocking mass MbmZ50 kg. The tests

were performed at room temperature 21G0.5 8C. The

excitation signal was a stepped sine signal, starting at

100 Hz and increasing with a constant frequency step of

10 Hz to the maximum frequency—1000 Hz for the three

smallest amplitudes. The amplitude of the signal was

constant at all frequencies and set to seven different values,

ranging from 0.11 to 0.00017 mm. The signal was recorded

within a 10 Hz bandwidth, averaged five times and delayed

300 ms between every recording. Each series of tests

including all seven amplitudes was performed for four

different magnetic inductions: 0, 0.3, 0.55 and 0.80 T. These

values were verified for given currents passing through the

coil by means of a Gaussmeter.

In Table 1, the instruments used in the measurements are

displayed. A personal computer is used to process the

measurements and is connected to a frequency analyser that

collects data and supplies the signal to the vibration

generator via an amplifier. The motion of the brass plates

is captured by three piezo-electric accelerometers, almost

symmetrically positioned on a horizontal surface between

the brass plates and the shaker and coupled in parallel to the

charge amplifier. The electric signal is then conditioned and

time integrated twice in the charge amplifier yielding an

electrical input to the frequency analyser directly pro-

portional to the displacement of the brass plates. This signal,

ascribed a given value for every amplitude in order to

achieve a constant displacement amplitude for growing

frequencies, is the control signal for the frequency analyser.

Fig. 2. Shear modulus magnitude jGj and loss factor Imag G/Real G

versus frequency at induced magnetic field of 0, 0.3, 0.55 and 0.8 T,

and constant displacement amplitude of 0.112 mm.





The signal to the vibration generator is then automatically

adjusted in a control loop in the software with regard to the

control signal. An accelerometer placed in the centre on the

bottom side of the blocking mass measures the acceleration

of the blocking mass and that signal is conditioned without

time integration in a charge amplifier.




3. Results and discussions

3.1. Shear modulus

Analysis of the measurement data was performed with

Matlabw which was also used for graphical representations.

The magnitude and loss factor of the dynamic shear

modulus in the frequency range of 100–1000 Hz, at

magnetic inductions of 0, 0.3, 0.55, 0.80 T, are displayed

in Figs. 2–8, for silicone rubber containing 33% iron, and in

Figs. 9–15, for natural rubber containing 33% iron. The

dynamic shear modulus for each of the two materials

displays an amplitude dependence that is relatively large for

even the smallest amplitudes. This can be deduced by

comparing the zero field amplitudes in Figs. 6–8, represent-

ing in decreasing order the smallest amplitudes for the

silicone rubber. Comparison of those graphs leads to




the following: a decreasing vibration amplitude gives rise

to an increasing magnitude and decreasing loss factor of the

shear modulus. Similar observations can be made for the

natural rubber by studying Figs. 13–15. This behaviour

derives from a phenomenon referred to as the Fletcher–Gent

effect [13], whose influence on rubber subjected to small

deformations is normally negligible. However, our obser-

vations reveal that in the entire frequency range the

Fletcher–Gent effect is a highly important feature of MS










Fig. 11. Shear modulus magnitude jGj and loss factor Imag G/Real

G versus frequency at induced magnetic field of 0, 0.3, 0.55 and

0.8 T, and constant displacement amplitude of 0.012 mm.





rubber, therefore not to be disregarded even for very small

amplitudes—these are of special interest in a structure-

borne sound context where strains are often of small order,

comparable to the ones presented in these experiments. In

contrast to normal rubber, MS rubber contains large

quantities of particles, typically iron, which intensifies the

Fletcher–Gent effect. This statement is borne out by

measurements performed for the five lowest amplitudes on

silicone and natural rubber with 0% iron, respectively

(Figs. 16 and 17). Indeed, the magnitude and loss factor of




the shear modulus are seen to be almost constant with

respect to amplitude when iron particles are absent.

Nonetheless, small deviations can be detected, in particular

for the silicone rubber. This almost negligible Fletcher–Gent

effect can be attributed to filler particles in the materials,

essentially the silica particles in the silicone rubber, and the

sulphur particles in the natural rubber. In all graphs, the

shear modulus magnitude and loss factor grow with

frequency in the expected fashion. In Figs. 2 and 9, the

magnitude of the shear modulus appears to be decreasing

initially when moving from left to right on the frequency











G versus frequency for five constant displacement amplitudes and

no applied magnetic field.


G versus frequency for five constant displacement amplitudes and

no applied magnetic field.


axis. It is the influence of the measurement set-up rigid body

resonances that causes this physically contradictory appear-

ance, a fact established by Kari [11].

The influence of the applied magnetic field at all seven

amplitudes can be viewed in Figs. 2–8 for the silicone

rubber and in Figs. 9–15 for the natural rubber. At 0.5–0.8 T,

saturation can be assumed to have occurred whereby those

curves represent the maximum response to applied magnetic

field. Following the development of the 0.8 T shear modulus

magnitude curve through Figs. 2–8, relative to the zero field

curve in each graph, respectively, it can be seen that with




smaller amplitudes the relative magnitude difference

becomes larger. Indeed, at the smallest amplitude (Fig. 8),

the increase in magnitude between saturation and 0 T

surpasses 100% over the entire dynamic range, reaching

nearly 115% around 200 Hz and decreasing slightly with

increasing frequency. For the natural rubber the correspond-

ing increase (Fig. 15) is somewhat less: a maximum increase

of approximately 85% decreasing to approximately 75% for

the highest frequencies. Nevertheless, the tendency of the

increase over the dynamic range bears a strong resemblance

to that of the silicone rubber. Providing an explanation for

the observed discrepancies in sensitivity between the two

kinds of rubber is beyond the scope of this article. For both

the silicone (Figs. 2–8) and natural rubber (Figs. 9–15) the

loss factor varies only slightly with applied magnetic field,

and that primarily at the highest and smallest amplitudes.

4. Conclusion

Experiments performed on MS rubber samples in the

audible frequency range reveal that both the magnitude and

loss factor of the shear modulus are strongly amplitude

dependent even for very small amplitudes. Furthermore,

when applying an external magnetic field, a maximum

increase in stiffness of 115% is observed. The observed


amplitude dependence in the audible frequency range of

100–1000 Hz of the natural and silicone rubber with

randomly dispersed and irregularly shaped particles of

micrometre size has implications for the modelling of the

behaviour of MS rubber for which the usually applied

elastic/visco-elastic models are not sufficient. The steep

stiffness increase with magnetic strength enhances the

notion of the vast potential of magneto-sensitive rubber

compared to standard isolators: active, instant and reversible

controlling of stiffness over large intervals grants amelio-

rated damping properties and more effective isolation, not

least in the audible frequency range where strains in

structure-borne sound applications are usually small,

yielding large magnetic sensitivity as shown for the smaller

strains in this article.

Acknowledgements

The author gratefully acknowledges the Swedish

Research Council for financial support (Contract no.:

621-2002-5643) and Dr Mattias Lokander at the Department

of Fibre and Polymer Technology of the Royal Institute of

Technology, for helpful assistance throughout the work.

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amplitude and frequency dependence of magneto-sensitive rubber in a wide frequency range

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