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# Active SHM using Magnetostrictive: Material Laminated beam subjected to mechanical input Notes | EduRev

## : Active SHM using Magnetostrictive: Material Laminated beam subjected to mechanical input Notes | EduRev

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Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

The Lecture Contains:
Laminated beam subjected to mechanical input
Numerical analysis for MS composites
Symmetric laminate with MS layer at the mid plane
Symmetric laminate with MS layer at mid plane subjected to mechanical input
Symmetric laminate with MS layer away from mid plane

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM]
Page 2

Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

The Lecture Contains:
Laminated beam subjected to mechanical input
Numerical analysis for MS composites
Symmetric laminate with MS layer at the mid plane
Symmetric laminate with MS layer at mid plane subjected to mechanical input
Symmetric laminate with MS layer away from mid plane

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Laminated beam subjected to mechanical input
A mechanical force of the form of  is assumed to be acting on the beam. Assuming mid plane strain and curvature
as  and t
Strain in the MS layer

Corresponding stress in the MS layer
(32.1)
Hence, the voltage response can be obtained as
(32.2)
With the increase in mechanical load, the stresses in different layers will increase. Depending upon the elastic properties of the
individual lamina and its orientation, the lamina which reaches the stress just beyond its allowable limit will delaminate. Voltage
response at this point is the delaminating voltage. Delaminating stress may be determined using an appropriate failure theory.

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_2.html [4/4/2013 3:57:09 PM]
Page 3

Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

The Lecture Contains:
Laminated beam subjected to mechanical input
Numerical analysis for MS composites
Symmetric laminate with MS layer at the mid plane
Symmetric laminate with MS layer at mid plane subjected to mechanical input
Symmetric laminate with MS layer away from mid plane

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Laminated beam subjected to mechanical input
A mechanical force of the form of  is assumed to be acting on the beam. Assuming mid plane strain and curvature
as  and t
Strain in the MS layer

Corresponding stress in the MS layer
(32.1)
Hence, the voltage response can be obtained as
(32.2)
With the increase in mechanical load, the stresses in different layers will increase. Depending upon the elastic properties of the
individual lamina and its orientation, the lamina which reaches the stress just beyond its allowable limit will delaminate. Voltage
response at this point is the delaminating voltage. Delaminating stress may be determined using an appropriate failure theory.

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_2.html [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Numerical analysis for MS composites
Using the basis presented in the previous section, voltage output in magnetostrictive sensory layer has been numerically
determined using symmetric as well as asymmetric laminates.
The effect of mechanical input along with magnetostriction is also presented taking both symmetric and asymmetric laminate
configurations. Numerical inputs used in the analysis are presented in Table 32.1
Table.32.1. Numerical details used in the analysis
Composite carbon - epoxy
Symmetric laminate stacking [0/90/0/45/m/45/0/90/0]
Asymmetric laminate stacking [0/90/0/45/0/90/m/90/0]
[45/-45/0/0/90/90/0/0/-45/m/45]
Thickness of the composite lamina 0.4 mm
Thickness of the MS layer 0.4 mm
Elastic modulus of the carbon fiber 350 GPa
Elastic modulus of the epoxy matrix 3.50 GPa
Elastic modulus of Terfenol-D 30 GPa
Volume fraction of the fiber 0.16
Volume fraction of Terfenol-D 0.0224
Poisson's ratio of the carbon fiber 0.3
Poisson's ratio of the epoxy matrix 0.4
Poisson's ratio for Terfenol-D 0.25
Number of turns in the coil per meter 1000
Carrier frequency,? 1000 Hz
Carrier current 0.4 A
Piezo-magnetic coefficient, d
1.5 e
-8
m/A
Permeability, µ
14.13e
-7
Coupling coefficient of Terfenol-D, k 0.75
Tensile strength of Terfenol-D 28 MPa
Compressive strength of Terfenol-D 700 MPa
Fracture toughness of MS layer
30 MPa-m
1/2
Size of crack at delamination, c 2 mm
Length of beam, l
100 mm
Width of beam, b 20 mm

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_3.html [4/4/2013 3:57:09 PM]
Page 4

Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

The Lecture Contains:
Laminated beam subjected to mechanical input
Numerical analysis for MS composites
Symmetric laminate with MS layer at the mid plane
Symmetric laminate with MS layer at mid plane subjected to mechanical input
Symmetric laminate with MS layer away from mid plane

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Laminated beam subjected to mechanical input
A mechanical force of the form of  is assumed to be acting on the beam. Assuming mid plane strain and curvature
as  and t
Strain in the MS layer

Corresponding stress in the MS layer
(32.1)
Hence, the voltage response can be obtained as
(32.2)
With the increase in mechanical load, the stresses in different layers will increase. Depending upon the elastic properties of the
individual lamina and its orientation, the lamina which reaches the stress just beyond its allowable limit will delaminate. Voltage
response at this point is the delaminating voltage. Delaminating stress may be determined using an appropriate failure theory.

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_2.html [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Numerical analysis for MS composites
Using the basis presented in the previous section, voltage output in magnetostrictive sensory layer has been numerically
determined using symmetric as well as asymmetric laminates.
The effect of mechanical input along with magnetostriction is also presented taking both symmetric and asymmetric laminate
configurations. Numerical inputs used in the analysis are presented in Table 32.1
Table.32.1. Numerical details used in the analysis
Composite carbon - epoxy
Symmetric laminate stacking [0/90/0/45/m/45/0/90/0]
Asymmetric laminate stacking [0/90/0/45/0/90/m/90/0]
[45/-45/0/0/90/90/0/0/-45/m/45]
Thickness of the composite lamina 0.4 mm
Thickness of the MS layer 0.4 mm
Elastic modulus of the carbon fiber 350 GPa
Elastic modulus of the epoxy matrix 3.50 GPa
Elastic modulus of Terfenol-D 30 GPa
Volume fraction of the fiber 0.16
Volume fraction of Terfenol-D 0.0224
Poisson's ratio of the carbon fiber 0.3
Poisson's ratio of the epoxy matrix 0.4
Poisson's ratio for Terfenol-D 0.25
Number of turns in the coil per meter 1000
Carrier frequency,? 1000 Hz
Carrier current 0.4 A
Piezo-magnetic coefficient, d
1.5 e
-8
m/A
Permeability, µ
14.13e
-7
Coupling coefficient of Terfenol-D, k 0.75
Tensile strength of Terfenol-D 28 MPa
Compressive strength of Terfenol-D 700 MPa
Fracture toughness of MS layer
30 MPa-m
1/2
Size of crack at delamination, c 2 mm
Length of beam, l
100 mm
Width of beam, b 20 mm

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_3.html [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Symmetric laminate with MS layer at the mid plane
In the first case, a nine layer symmetric laminate beam [0/90/0/45/m/45/0/90/0] with MS layer in the middle is subjected to
actuating current causing magnetostriction to develop in the MS layer leading to compression in it and equivalent balancing
stresses in other layers. With increase in magnetostriction by increasing the current rating, the stress and strain level at various
interfaces will increase. Variation of stress and strain at various interfaces including the MS layer and voltage induced in MS layer
at the time of delamination are shown in Figures 32.1, 32.2 and 32.3.

Figure 32.1 Stress variations at various interfaces and in MS layer at the time of
delamination when the laminate is subjected to only actuator current

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_4.html (1 of 3) [4/4/2013 3:57:10 PM]
Page 5

Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

The Lecture Contains:
Laminated beam subjected to mechanical input
Numerical analysis for MS composites
Symmetric laminate with MS layer at the mid plane
Symmetric laminate with MS layer at mid plane subjected to mechanical input
Symmetric laminate with MS layer away from mid plane

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_1.htm [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Laminated beam subjected to mechanical input
A mechanical force of the form of  is assumed to be acting on the beam. Assuming mid plane strain and curvature
as  and t
Strain in the MS layer

Corresponding stress in the MS layer
(32.1)
Hence, the voltage response can be obtained as
(32.2)
With the increase in mechanical load, the stresses in different layers will increase. Depending upon the elastic properties of the
individual lamina and its orientation, the lamina which reaches the stress just beyond its allowable limit will delaminate. Voltage
response at this point is the delaminating voltage. Delaminating stress may be determined using an appropriate failure theory.

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_2.html [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Numerical analysis for MS composites
Using the basis presented in the previous section, voltage output in magnetostrictive sensory layer has been numerically
determined using symmetric as well as asymmetric laminates.
The effect of mechanical input along with magnetostriction is also presented taking both symmetric and asymmetric laminate
configurations. Numerical inputs used in the analysis are presented in Table 32.1
Table.32.1. Numerical details used in the analysis
Composite carbon - epoxy
Symmetric laminate stacking [0/90/0/45/m/45/0/90/0]
Asymmetric laminate stacking [0/90/0/45/0/90/m/90/0]
[45/-45/0/0/90/90/0/0/-45/m/45]
Thickness of the composite lamina 0.4 mm
Thickness of the MS layer 0.4 mm
Elastic modulus of the carbon fiber 350 GPa
Elastic modulus of the epoxy matrix 3.50 GPa
Elastic modulus of Terfenol-D 30 GPa
Volume fraction of the fiber 0.16
Volume fraction of Terfenol-D 0.0224
Poisson's ratio of the carbon fiber 0.3
Poisson's ratio of the epoxy matrix 0.4
Poisson's ratio for Terfenol-D 0.25
Number of turns in the coil per meter 1000
Carrier frequency,? 1000 Hz
Carrier current 0.4 A
Piezo-magnetic coefficient, d
1.5 e
-8
m/A
Permeability, µ
14.13e
-7
Coupling coefficient of Terfenol-D, k 0.75
Tensile strength of Terfenol-D 28 MPa
Compressive strength of Terfenol-D 700 MPa
Fracture toughness of MS layer
30 MPa-m
1/2
Size of crack at delamination, c 2 mm
Length of beam, l
100 mm
Width of beam, b 20 mm

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_3.html [4/4/2013 3:57:09 PM]
Objectives_template
Module 4: Active SHM using Magnetostrictive Material
Lecture 32: Laminated beam subjected to mechanical input

Symmetric laminate with MS layer at the mid plane
In the first case, a nine layer symmetric laminate beam [0/90/0/45/m/45/0/90/0] with MS layer in the middle is subjected to
actuating current causing magnetostriction to develop in the MS layer leading to compression in it and equivalent balancing
stresses in other layers. With increase in magnetostriction by increasing the current rating, the stress and strain level at various
interfaces will increase. Variation of stress and strain at various interfaces including the MS layer and voltage induced in MS layer
at the time of delamination are shown in Figures 32.1, 32.2 and 32.3.

Figure 32.1 Stress variations at various interfaces and in MS layer at the time of
delamination when the laminate is subjected to only actuator current

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_4.html (1 of 3) [4/4/2013 3:57:10 PM]
Objectives_template
Figure 32.2 Stress variations at various interfaces and in MS layer at the time of
delamination when the laminate is subjected to only actuator current

Figure 32.3 Open circuit voltage in MS layer at the time of delamination when the laminate
is subjected to only actuator current

file:///D|/neha%20backup%20courses%2019-09-2011/structural_health/lecture32/32_4.html (2 of 3) [4/4/2013 3:57:10 PM]
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