Fluid Structure Interactions
Research Group
Modelling, Characterisation and Development of New Magnetorheological
Materials With Enhanced Vibration Control Performance
K. Sapouna,
Supervisors: Y.P. Xiong and R.A. Shenoi
Faculty of Engineering and the Environment, University of Southampton, UK
ks9g09@soton.ac.uk
Background
Modelling Methodology
Magnetorheological elastomers (MRE) are solid materials composed of
magnetisable (usually iron) particles suspended in a low permeability carrier
matrix (usually rubber). They are the solid equivalent of magnetorheological
fluids that already find applications in vibration isolation systems. In the
presence of an external magnetic field the particles are magnetized and form
chains while trying to align in the direction of the field. As a consequence the
viscoelastic behaviour of the material can be controlled. In vibration control
system design, materials with dynamically variable stiffness and damping,
like magnetorheological elastomers, could be useful tools. When an external
field is applied to the MR elastomer during curing, the filler particles tend to
align parallel to the direction of the magnetic field forming anisotropic
elastomers. On the other hand, when the elastomer is cured without the
presence of the field the particles are randomly dispensed inside the matrix
forming an isotropic material.
MR elastomers, are governed by a nonlinear stress-strain relationship with a
complex modulus of elasticity that depends weekly on the frequency and
strongly on the applied magnetic field. To model the material the simple
Kelvin Voight viscoelastic model is used where both stiffness and damper are
amplitude, frequency and magnetic field dependent.
Aims
 Investigate the mechanical characteristics of the MR elastomers
 Develop a mathematical model capable of predicting the response of the
material
 Manufacture a vibration isolator prototype device for marine applications
Storage modulus 𝐸 ′ 𝑒, 𝜔, 𝛣 = 𝐾 𝑒, 𝜔, 𝛣
Loss modulus 𝐸 ′′ 𝑒, 𝜔, 𝛣 = 𝑐𝜔 𝑒, 𝜔, 𝛣
Damping factor tand=
Figure 1: Kelvin Voight viscoelastic model
𝑁
𝐸 ′ 𝑒, 𝜔, 𝛣 =
𝑁
𝑎𝑖 (𝜔, 𝛣)𝑒𝑥𝑝𝑏𝑖
𝜔,𝐵 𝑒
𝐸 ′ ′ 𝑒, 𝜔, 𝛣 =
𝑖=0
𝑐𝑖 (𝜔, 𝛣)𝑒𝑥𝑝𝑑𝑖
𝜔,𝐵 𝑒
𝑖=1
e=strain amplitude, ω=2 π f, B= intensity of the magnetic field
𝑀−𝑖
Where
𝑎𝑖 𝜔, 𝛣 =
𝑝𝑖𝑗 𝛣
𝑗=0
Material Characterisation
The mechanical properties characterization of silicon MR elastomers were
performed under static and dynamic loading conditions for a range of
frequencies and amplitudes following the directions of British standard BS ISO
4664-1:2005 for compression loads in rubber.
𝐸 ′′
𝐸′
𝜔
2𝜋
𝑀−𝑖
𝑗
𝑏𝑖 𝜔, 𝛣 =
𝑞𝑖𝑗 𝛣
𝑗=0
𝐿
and
𝑗
𝐿
𝑝𝑎𝑖𝑗𝑙 𝐵𝑙
𝑝𝑎𝑖𝑗 𝛣 =
𝜔
2𝜋
𝑝𝑐𝑖𝑗𝑙 𝐵𝑙
𝑝𝑐𝑖𝑗 𝛣 =
𝑙=0
𝑙=0
Transmissibility of a SDOF system
F1
M
𝐸 ∗ = 𝐸′(1 + 𝑗 𝑡𝑎𝑛𝑑)
F2
Figure 2: Modulus E of anisotropic MRE at zero field and 0.3T magnetic field
Figure 6: Transmissibility curves for isotropic
MRE at different strain amplitudes
𝐹2 ∗
𝑇=
=
𝐹1
1 + 𝑡𝑎𝑛𝑑𝜔 2
𝜔
1− 𝜔
𝑛
2
𝐸′
𝜔=𝜔𝑛
𝐸′𝜔
2
+ 𝑡𝑎𝑛𝑑𝜔 2
Figure 7: Transmissibility curves for anisotropic
and isotropic MRE at zero and 0.3T field
Figure 3: Damping factor tand of anisotropic MRE at zero field and 0.3T magnetic field
Conclusion
 Isotropic MREs have a higher MR effect than anisotropic MREs
 When the field is applied the natural frequency and damping factor changes
 Transmissibility and damping factor depends heavily on the amplitude of the
applied force and thus a nonlinear model is needed
Figure 4: Damping factor tand of isotropic MRE at zero field and 0.3T magnetic field
Further Work
 Manufacture natural rubber MRE
 Investigate the dynamic properties of MRE under multi loading conditions
 Derive a constitutive equation model for both types of MRE
 Design and manufacture a semi active vibration isolation device and the
Figure 5: Modulus E of isotropic MRE at zero field and 0.3T magnetic field
This project is funded by:
appropriate control system
FSI Away Day 2012