Concepts and Applications of Lamb WavesDepartamento de Engenharia Mecânica Av. Brasil Centro, 56...

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GMSINT Unesp - Ilha Solteira

Departamento de Engenharia Mecânica

Av. Brasil Centro, 56 – Ilha Solteira SP – CEP 15385000

E-mail: [email protected]

Concepts and Applications of Lamb Waves

Prof. Dr. Vicente Lopes Junior

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Outline

Introduction

Fundaments and Analysis of Lamb Waves

Activating and Receiving Lamb Waves

Application of Algorithms for Identifying Structural Damages - Case

Studies

Textbooks

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1. Introduction

The recognition of safety, integrity and durability as the principal priorities for engineered structures and assets has entailed intensive research and development of nondestructive evaluation (NDE) techniques.

Boeing 737-300 after a 6 ft (1.83 m) hole appeared in the top of the airplane's fuselage above the cabin

April 3rd, 2006 at Dover Air Force Base

http://en.wikipedia.org/wiki/Boeing_737�http://en.wikipedia.org/wiki/Boeing_737�http://en.wikipedia.org/wiki/Boeing_737�http://en.wikipedia.org/wiki/Fuselage�

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1. Introduction

Lamb waves are guided waves that propagate in thin plate or shell structures.

Lamb-wave-based Damage Identification

With advantages including capability of propagation over a significant distance and high sensitivity to abnormalities and inhomogeneity near the wave propagation path, elastic waves can be energized to disseminate in a structure, and any changes in material properties or structural geometry created by a discontinuity, boundary or structural damage can be identified by examining the scattered wave signals.

The classical problem of Lamb wave propagation is associated with wave motion in a traction-free homogeneous and isotropic plate.

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Key questions to be answered by an elastic-wave-based damage identification approach are:

Two basic configurations are usually used in elastic-wave-based damage identification, ‘pitch-catch’ and ‘pulse-echo’

(i) is there damage?

(ii) where is the damage?

(iii) what is its size or severity?

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Approach Mechanism Merits and applications

Demerits and limitations

Modal-data-based (eigenfrequency, mode shape and curvature, strain energy, flexibility, sensitivity, damping properties, etc.)

Presence of structural damage reduces structural stiffness, shifts eigenfrequencies, and changes frequency response function and mode shapes.

Simple and low cost; particularly effective for detecting large damage in large infrastructure or rotating machinery.

Insensitive to small damage or damage growth; difficult to excite high frequencies; need for a large number of measurement points; hypersensitive to boundary and environmental changes.

Electro-mechanical-impedance-based

Presence of damage modifies the impedance in a high frequency range, normally higher than 30 kHz.

Low cost and simple for implementation; particularly effective for detecting defects in planar structures.

Unable to detect damage distant from sensors;

Static-parameter-based (displacement, strain, etc.)

Presence of damage causes changes in displacement and strain distribution in comparison with benchmark.

Locally sensitive to defects; simple and cost-effective

Relatively insensitive to undersized damage or the evolution of deterioration

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Approach Mechanism Merits and applications

Demerits and limitations

Acoustic emission Based on the fact that rapid release of strain energy generates transient waves, whereby presence or growth of damage can be evaluated by capturing damage-emitted acoustic waves.

Able to triangulate damage in different modalities including matrix crack, delamination, microscopic deformation, welding flaw and corrosion; able to predict damage growth; surface mountable and good coverage

Contamination by environmental noise; complex signal; for locating damage only; passive method; high damping ratio of the wave, and therefore suitable for small structures only

Elastic-wave-based (Lamb wave tomography, etc.)

Based on the fact that structural damage causes unique wave scattering phenomena and mode conversion,

Cost-effective, fast and repeatable; able to inspect a large structure in a short time; sensitive to small damage; no need for motion of transducers; low energy consumption; able to detect both surface and internal damage.

Sophisticated signal processing, multiple wave modes available simultaneously; difficult to simulate wave propagation in complex structures; strong dependence on prior models or benchmark signals

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the capacity to inspect a large area using few transducers (it has been demonstrated that the ratio of the planar area of the plate that can be inspected to the area of a circular wave transducer can be about 3000:1 [Cesnik, 2007]); the ability to examine the entire cross-sectional area of the structure in terms of multiple wave modes, thereby detecting internal damage as well as surface defects; the capability of classifying various types of damage using different wave modes; high sensitivity to damage and therefore high identification precision; the possibility of inspecting coated or insulated structures such as pipeline under water/ground; the potential for integration with engineered structures and assets for developing online automated damage detection and SHM techniques; low energy consumption with great cost-effectiveness;

complexity of signal appearance, requiring well-calibrated signal processing and interpretation techniques.

SHM using Lamb waves is a promising method comparing with traditional NDE approaches because:

but…

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2. Fundaments and Analysis of Lamb Waves

The beginning… Rayleigh, L.: Waves propagated along the plane surface of an elastic solid. Proceedings of the London Mathematical Society 20, 225–234 (1889) Lamb, H.: On waves in an elastic plate. Proceedings of the Royal Society, A: Mathematical, Physical and Engineering Sciences 93, 114–128 (1917)

Amongst such wave modalities, Lamb waves refer to those in thin plates (with planar dimensions being far greater than that of the thickness and with the wavelength being of the order of the thickness) that provide upper and lower boundaries to guide continuous propagation of the waves

Elastic waves in a solid medium can be one of the modalities described in Table below.

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Wave type Definition and characteristics

Graphic description

Longitudinal wave

Travelling in a medium as a series of alternate compressions and rarefactions, a longitudinal wave vibrates particles back and forth in the direction of wave propagation

Shear wave Also termed a transverse wave, a shear wave is generated under vibration of particles perpendicular to the direction of wave propagation

Rayleigh wave

Rayleigh wave exists along the free surface of a semi-infinite (or very thick) solid, decaying exponentially in displacement magnitude with distance from the surface

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Wave type Definition and characteristics Graphic description

Lamb wave

Infinite wave modes are available in a finite body, and their propagation characteristics vary with entry angle, frequency and structural geometry.

Stonely wave

Stonely wave is a kind of wave existing at the interface between two media or in the neighbourhood of a free surface

Creep wave

Also called a head wave, a creep wave is generated by refraction of a longitudinal wave from a boundary with the same propagation velocity. It has similar behavior to a longitudinal wave

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SV waves

Conventional P and S Waves P waves

vertical anti-symmetric motion (i.e., Ai mode) which is sometimes termed the shear vertical (SV) mode

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Flexural Waves Euler-Bernoulli Beam

Rayleigh Waves

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Symmetric Lamb Wave

Asymmetric Lamb Wave Waves

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2.1 Theory of Lamb Waves

In a thin isotropic and homogeneous plate, the waves, can generally described in a form of Cartesian tensor notation as

ui and fi are the displacement and body force in the xi direction, ρ and μ are the density and shear modulus of the plate, λ = is the Lamé constant;

(1)

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Helmholtz Decomposition is an efficient approach to decompose (1) into two uncoupled parts under the plane strain condition

(2)

where

(3)

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A1 , A 2 ,B1 , B2 = constants determined by the boundary conditions. k , ω and λwave = wavenumber, circular frequency and wavelength of the wave cL and cT = velocities of longitudinal and transverse/shear modes

E = Young’s modulus of the medium. It can be seen that Lamb waves are actually the superposition of longitudinal and transverse/shear modes. An infinite number of modes exist simultaneously, superimposing on each other between the upper and lower surfaces of the plate, finally leading to well-behaved guided waves.

(4)

( )ν1μ2E +=

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As a result of plane strain, the displacements in the wave propagation direction ( x1 ) and normal direction ( x3 ) are:

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( )( )

1

222

22

)(4

tantan

±

−

−=

qkpqkk

pdqd

22

22 k

cq

T

−=ω

22

22 k

cp

L

−=ω

( )( )ν

νµ21

122−

−=ρ

cL ( ) ρμEcT =+

=νρ 12

2

ν)(Eμ+

=12 Constante de Lamé

Equação de Rayleigh-Lamb - Resumo

+1 corresponde ao modo simétrico (S) -1 corresponde ao modo Anti-simétrico (A)

waveFck

λπω 2

==

(5)

(6)

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Symmetric wave mode is often described as ‘compressional’, showing thickness bulging and contracting; Antisymmetric mode is known as ‘flexual’, presenting constant-thickness flexing

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2.2 Lamb Waves in Plate of Multiple Layers

The anisotropic nature of multi-layered structures introduces many unique phenomena such as directional dependence of wave speed, differences in phase and group velocities

For an N-layered laminate, the displacement field, u , within each layer must satisfy the Navier’s displacement equations , and for the nth layer,

(7)

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2.3 Shear Horizontal Waves and Love Waves

Alongside the two basic Lamb modes, Si and Ai, which dominate the radial in-plane and out-of-plane (vertical) motion of particles in the plate, respectively, there is another kind of possible motion of particles, namely in-plane but in a direction perpendicular to the direction of wave propagation

This wave is referred to as the shear horizontal (SH) wave mode, and it was first captured by Love in 1927

SH wave mode in a thin plate of 2h in thickness

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2.4 Cylindrical Lamb Waves

Lamb waves can also be identified in curved panels or tubular structures such as a pipe, provided the tangential dimensions of the structures are much greater than the thickness.

Waves in a cylindrical pipe of thin wall are called cylindrical Lamb waves or helical waves

Cylindrical Lamb waves are distinguished and labelled with L , T and F in a tubular structure, corresponding to the longitudinal (similar to Lamb modes in a flat plate), torsional (similar to SHi modes in a flat plate) and flexural modes

Application: detection of corrosion in pipes D. N. Alleyne and P. Cawley, Journal of Nondestructive Evaluation, VoL 15, No. 1, 1996

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At low frequencies, longitudinal, torsional and flexural modes dominate in wave signals, but at high frequencies the waves in the pipe behave more and more like the normal Lamb modes in a plate or shell.

Cylindrical Lamb modes are defined as L (n,m), T (n,m), F (n,m), where n and m (n,m = 0,1, … ) are two integers. n is associated with the geometric properties of tubular structures

m is the order of the wave modes.

n = 0 indicates that the pipe is axially symmetric (most engineering applications)

L(0,1) propagates similarly to the A0 mode in flat plates, and L(0,2) has properties similar to the S0 mode in flat plates, in terms of the vibration of particles

Both L(0,1) and L(0,2) are preferable to other modes for damage identification

2.4 Cylindrical Lamb Waves

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Lowe MJ, Cawley P, Galvagni A, Monitoring of corrosion in pipelines using guided waves and permanently installed transducers., J Acoust Soc Am, 2012, Vol:132 Guided Wave Testing (GWT) of pipelines for the detection of corrosion has been developed over about 20 years and is now a well established method worldwide, used mostly in the oil and gas industry.

Ribichini R, Cegla F, Nagy PB, et al, Study and Comparison of Different EMAT Configurations for SH Wave Inspection, IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL, 2011, Vol:58, Pages:2571-2581, ISSN:0885-301 Guided wave inspection has proven to be a very effective method for the rapid inspection of large structures. The fundamental shear horizontal (SH) wave mode in plates and the torsional mode in pipe-like structures are especially useful because of their non-dispersive character.

D. N. Alleyne and P. Cawley, The Excitation of Lamb Waves in Pipes Using Dry-Coupled Piezoelectric Transducers, Journal of Nondestructive Evaluation, VoL 15, No. 1, 1996 detection of corrosion in pipes L(0,2) mode at a frequency of 70 kHz

Application

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Disadvantages 1. Interpretation of data is highly operator dependent.

2. Difficult to find small pitting defects.

3. Not very effective at inspecting areas close to accessories.

4. Needs good procedure

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2.5 Propagation Velocity Phase vs. Group Velocities

The propagation of Lamb waves can be characterized by the phase (cp) and group (cg) velocities. cp is referred to as the propagation speed of the wave phase of a particular frequency contained in the overall wave signals, which can be linked with the wavelength

wavepc λπω2

=

The group velocity is referred to as the velocity with which the overall shape of the amplitudes of the wave (known as the modulation or envelope of the wave) propagates through space, which is the actual velocity captured in experiments (the velocity of wave energy transportation). The group velocity is dependent on frequency and plate thickness, formulated by

( ) ( ) ( )

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...

−

−=

dfddc

dfccdfc pppg

where f is the central frequency of the wave (f = ω/2π) . Note that, when the derivative of cp with respect to f.d becomes zero, cp = cg

(9)

(8)

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Propagating in isotropic plates, Lamb waves travel with the same velocity unidirectional and the wavefront forms a circle. However, it is not the case in non-isotropic materials.

Measured and calculated velocities of S0 and A0 modes in carbon fibre-reinforced epoxy (CF/EP) of different configurations

Measured at 0.5 MHz to avoid wave dispersion

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2.6 Dispersion

As with most guided waves, Lamb waves are dispersive, and their velocities are dependent on wave frequency and plate thickness

Lamb waves after propagating a certain distance, excited at a central frequency of 300 kHz The S0 mode peaks at 293 kHz and the A0 mode at 332 kHz

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Dispersion Curve of Lamb Waves

For a plate made of isotropic materials, eq (4) can be rearranged as

for symmetric modes(S)

for anti-symmetric modes (A)

(10)

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Dispersion Curve of Lamb Waves

SHi = symmetric SH mode

SHA i = anti-symmetric SH modes

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2.7 Attenuation of Lamb Waves

The energy of Lamb waves dissipates with distance, manifesting as the gradual reduction in magnitude of wave signals. * It has been observed that 52% of the total energy dissipates when Lamb waves pass through a damage area of 7 mm in diameter in a composite laminate (100 mm ×100 mm)

* Prasad, S.M., Balasubramaniam, K., Krishnamurthy, C.V.: Structural health monitoring of composite structures using Lamb wave tomography. Smart Materials and Structures 13, N73–N79 (2004)

Note that ‘attenuation’ is different from ‘dispersion’, which refers to changes in propagation velocity and signal bandwidth subject to wave frequency

Magnitude of Lamb waves in a plate decays at a rate that is proportional to the inverse square root of the propagation distance.

(11)

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** Attenuation coefficients of Lamb waves in composite materials

Pierce, S.G., Culshaw, B., Manson, G., Worden, K., Staszewski, W.J.: The application of ultrasonic Lamb wave techniques to the evaluation of advanced composite structures. In: Claus, R.O., Spillman Jr., W.B. (eds.) Proceedings of the SPIE, vol. 3986, pp. 93–103 (2000)

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3. Activating and Receiving Lamb Waves

3.2.1 Ultrasonic Probes

Preferred for their high precision and good controllability These transducers can be actively tuned to selectively produce a specific Lamb wave mode Without the complexity caused by multiple wave modes, captured signals are easy to interpret.

a. angle-adjustable ultrasonic probe; b. comb ultrasonic probe c. Hertzian contact probe

3.2 Transducers of Lamb Waves

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3.2.2 Piezoelectric Wafers and Piezocomposite Transducers

Small and light transducers packaged in various modalities it can be directly inserted into or mounted on a host structure wide frequency responses with low power consumption/acoustic impedance/cost

PZTs

PIEZO SYSTEMS, INC.

http://www.cedrat-technologies.com/

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piezocomposite transducers, macro fibre composites (MFC)

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3.2.3 Laser-based Ultrasonics

Flexibly controllable, a laser source can be designed to be broadband or

narrowband depending on the application

effective for irregular surfaces, complex geometry or stringent environments

where direct access of transducers to the object is not feasible

short laser pulse excites a broad bandwidth signal with several Lamb modes,

permitting selective generation of a desired wave mode

bulkiness and high cost of equipment, and therefore may not be easily adopted for practical application.

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3.2.4 Interdigital Transducers

Interdigital transducers (IDTs) using polyvinylidene fluoride (PVDF) piezoelectric polymer films have been introduced to cater for more versatile applications (flexibility and greater ease of handling).

Through careful design of the electrodes and adjustment of the spacing between interdigital electrodes, a specific Lamb wave mode with the desired bandwidth, focused propagation direction and customized wavelength can be generated

This capacity for activating Lamb waves with controllable wavelength and even dispersion properties has attracted great attention in recent research and development of SHM techniques *

* Quek, S.T., Tua, P.S., Jin, J.: Comparison of plain piezoceramics and inter-digital transducer for crack detection in plates. Journal of Intelligent Material Systems and Structures 18, 949–961 (2007)

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3.2.5 Fiber-optic Sensors – Reception Only

wide bandwidth, good compatibility, immunity to electromagnetic interference, long service life, low power consumption, and in particular light weight and tiny volume

careful analysis of the output is necessary to correctly extract the axial composition of the measurements, since the response captured by a fiber-optic sensor is of a three-dimensional nature

can be affected by environmental conditions and the alignment of sensors

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3.3 Activation of Desired Lamb Waves

Activation of a diagnostic Lamb wave signal with an appropriate mode in an appropriate waveform and of an appropriate frequency is vital for Lamb-wave-based damage identification. At a rudimentary level, a diagnostic Lamb wave should, if possible, feature: i. non-dispersion, ii. low attenuation, iii. high sensitivity to damage, iv. easy excitability, and v. good detectability

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3.3.1 Selection of Appropriate Wave Mode

i. lower attenuation (the A0 mode usually presents higher attenuation during propagation because of the dominant out-of-plane movement of particles in the mode shape)

ii. faster propagation velocity, which means that complex wave reflection from the boundary can sometimes be avoided; and

iii. lower dispersion in the low frequency range, benefiting signal interpretation.

Usually , the S0 mode is selected for damage identification, due to, in contrast to the A0 mode, its:

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i. shorter wavelength at a given excitation frequency (half wavelength of a selected wave mode must be shorter than or equal to the damage size to allow the wave to interact with the damage);

ii. larger signal magnitude (the A0 mode in a wave signal is usually much stronger than the S0 mode if two modes are activated simultaneously, giving a signal with high signal-to-noise ratio (SNR),

iii. easier means of activation (the out-of-plane motion of particles in a plate can be more easily activated).

On the other hand, there has been increasing awareness of using the A0 mode for damage identification. Its merits, in comparison with the S0 mode, include:

Generally speaking, both the S0 and A0 modes are sensitive to structural damage, and both can be used for identifying damage, though the S0 mode exhibits higher sensitivity to damage in the structural thickness and delamination in particular, whereas the A0 mode outperforms the S0 mode with higher sensitivity to surface damage such as surface cracks, corrosion, or surface crack growth.

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Wave mode tuning techniques

A PZT wafer bonded in a host structure generates both symmetric and anti-symmetric modes simultaneously, which superimpose and influence each other

when dual wafers are energized in-phase (Terminals B are activated ), symmetric electric fields will be applied on both wafers, to activate the S0 mode with the dominant signal energy, and the weak A0 mode. when dual wafers are energized out-of-phase (Terminals C are activated ), anti-symmetric electric fields will be applied on both wafers, to activate the A0 mode when either of the two wafers is energized, both the S0 and A0 modes will be activated simultaneously.

Using one pair of PZT controlled by a electric circuit

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Using one pair of PZT bonded a certain distance

This approach offers a practical way to produce a desired Lamb wave mode along the projection of connection between two PZT elements on the same side of a plate, via the superposition of waves generated by them with an appropriately selected distance

Grondel, S., Paget, C., Delebarre, C., Assaad, J., Levin, K.: Design of optimal configuration for generating A0 Lamb mode in a composite plate using piezoceramic transducers. Journal of the Acoustical Society of America 112(1), 84–90 (2002)

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A particular wave mode can be activated by PWASs to dominate the signal energy, when the side length of the square PZT element in PWASs equals an odd multiple of one-half the wavelength ( λwave /2) of such a wave mode (provided that the inter-element distance of PWASs remains constant)

Using a piezoelectric wafer active sensors’(PWAS)

Example in a aircraft panel It was found that the PWASs (7 mm ×7 mm ×0.2 mm for each wafer in the array) could activate the S0 and AO modes of different energy intensities at different excitation frequencies

Giurgiutiu, V.: Tuned Lamb wave excitation and detection with piezoelectric wafer active sensors for structural health monitoring. Journal of Intelligent Material Systems and Structures 16, 291–305 (2005)

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Actuator

Sensor

Structure Pulse

Generation of Lamb Waves Input Signal

Basic Concepts of Lamb Waves

4. Application

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PWAS – “Wafer” Piezelétrico de Sensores Ativos

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Propriedade Valor Módulo de Young (GPa) 70 Espessura (m) 0.0015 Comprimento/Largura (m) 0.24 Densidade (Kg/m3) 2710

4.1 Análise da Região de Influência da falha

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O PZT 2 foi designado como atuador enviando uma onda na superfície da placa e o PZT 3 foi designado como sensor, recebendo os sinais.

Setup Experimental Esquema atuador/sensor

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1. A primeira linha foi desenhada próxima ao PZT 2 (atuador).

2. A segunda linha foi desenhada na região central da placa (na outra diagonal da placa, unindo o PZT 1 e o PZT 4).

3. A terceira linha foi desenhada próxima ao PZT 3 (sensor).

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• Primeiramente, os testes foram realizados na estrutura sem falha, obtendo-se a condição baseline para estrutura saudável.

• Em seguida, outro teste foi realizado com a estrutura sem a falha, a fim de se verificar a repetibilidade dos resultados.

• A falha foi simulada por uma massa adicional (porca de 1g) colada na superfície da falha.

• Três sequências de testes adicionais foram realizados, agora com a adição de massa em três condições de falhas diferentes:

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0

0.05

0.1

Nor

ma

H2

0

100

200

300

RM

SD

0

2

4

6 x 107

IFM

S.F. 10mm 20mm 30mm 40mm 50mm0

0.02

0.04

0.06

CC

DM

Distância (mm)

• Para a Condição de Falha 1 (falha nas proximidades do PZT 2)

A falha não é mais detectada quando é posicionada a uma distância de 50mm da linha central.

Máxima Posição da Falha identificada

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0

0.05

0.1

Nor

ma

H2

0

100

200

300

RM

SD

0

2

4

6 x 107

IFM

S.F. 20mm 40mm 60mm 80mm 100mm 120mm0

0.02

0.04

0.06

CC

DM

Distância (mm)

• Para a Condição de Falha 2 (falha na região central),



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0

0.02

0.04

0.06

Nor

ma

H2

0

100

200

300

RM

SD

0

2

4 x 107

IFM

S.F. 10mm 20mm 30mm 40mm 50mm0

0.02

0.04

0.06

CC

DM

Distância (mm)

• Para a Condição de Falha 3 (falha nas proximidades do PZT 3)



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Com os resultados obtidos, é possível identificar a região que a falha pode ser detectada através da metodologia das ondas de Lamb.

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Fotos do painel aeronáutico. Dimensões do painel aeronáutico [mm].

4.2 Localização de Falhas em um Painel Aeronáutico

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Configuração de PZTs formada na superfície externa do painel.

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Sequência de excitação utilizada para identificação de falhas na superfície externa do painel aeronáutico.

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- Condição de Falha 1. A falha (massa de 1g) foi colada na intersecção entre o caminho 5-1 e o caminho 2-4;

- Condição de Falha 2. Caso de falha múltipla: uma falha foi colada na intersecção entre o caminho 5-3 e o caminho 2-6 e a outra falha foi colada entre o PZT 4 e o PZT 7;

- Condição de Falha 3. Um outro tipo de falha, garra de 1.1g, foi acoplado na borda da janela do painel;

- Condição de Falha 4. A falha foi simulada por uma perda de rigidez em uma parte do painel aeronáutico, soltando-se um dos parafusos que prende o painel na base.

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• Condição de Falha 1

0

0.01

0.02

Nor

ma

H2

0

400

800

RM

SD

0

1

2

3 x 107

IFM

5-1 5-2 5-3 5-4 5-6 5-7 5-9 8-7 8-9 8-10 8-11 8-12 2-1 2-3 2-4 2-6 4-1 4-7 6-3 6-9 11-1011-120

0.05

0.1

CC

DM

Caminhos

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0

0.01

0.02

Nor

ma

H2

0

400

800

RM

SD

0

1

2

3 x 107

IFM

5-1 5-2 5-3 5-4 5-6 5-7 5-9 8-7 8-9 8-10 8-11 8-12 2-1 2-3 2-4 2-6 4-1 4-7 6-3 6-9 11-1011-120

0.05

0.1

CC

DM

Caminhos

• Estrutura Reparada

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0 0.5 10

0.5

1

2-10

0.010.02

0 0.5 10

0.5

1

2-30

0.010.02

0 0.5 10

0.5

1

4-10

0.010.02

5-1 2-40

0.010.02

5-20

0.010.02

5-3 2-60

0.010.02

6-30

0.010.02

0 0.5 10

0.5

1

5-40

0.010.02

0 0.5 10

0.5

1

5-60

0.010.02

0 0.5 10

0.5

1

4-70

0.010.02

5-70

0.010.02

5-90

0.010.02

6-90

0.010.02

0 0.5 10

0.5

1

8-70

0.010.02

8-90

0.010.02 0 0.5 1

0

0.5

1

0 0.5 10

0.5

1

8-100

0.010.02

8-110

0.010.02

8-120

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0.010.02

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Caminhos

Norm

a H2

PZT 1 PZT 2 PZT 3

PZT 7

PZT 4 PZT 5 PZT 6

PZT 8

PZT 10 PZT 11 PZT 12

PZT 9

0 0.5 10

0.5

1

2-10

5001000

0 0.5 10

0.5

1

2-30

5001000

0 0.5 10

0.5

1

4-10

5001000

5-12-40

5001000

5-20

5001000

5-32-60

5001000

6-30

5001000

0 0.5 10

0.5

1

5-40

5001000

0 0.5 10

0.5

1

5-60

5001000

0 0.5 10

0.5

1

4-70

5001000

5-70

5001000

5-90

5001000

6-90

5001000

0 0.5 10

0.5

1

8-70

5001000

8-90

5001000 0 0.5 10

0.5

1

0 0.5 10

0.5

1

8-100

5001000

8-110

5001000

8-120

5001000

0 0.5 10

0.5

1

11-100

5001000

0 0.5 10

0.5

1

11-120

5001000

0 0.5 10

0.5

1

CaminhosR

MSD

PZT 1 PZT 2 PZT 3

PZT 7

PZT 8

PZT 9


PZT 4 PZT 5 PZT 6

Representação da Falha no Painel Aeronáutico

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0 0.5 10

0.51

2-1024 x 10

7

0 0.5 10

0.51

2-3024 x 10

7

0 0.5 10

0.51

4-1024 x 10

7

5-1 2-4024 x 10

7

5-2024 x 10

7

5-3 2-6024 x 10

7

6-3024 x 10

7

0 0.5 10

0.51

5-4024 x 10

7

0 0.5 10

0.51

5-6024 x 10

7

0 0.5 10

0.51

4-7024 x 10

7

5-7024 x 10

7

5-9024 x 10

7

6-9024 x 10

7

0 0.5 10

0.51

8-7024 x 10

7

8-9024 x 10

70 0.5 1

00.5

1

0 0.5 10

0.51

8-10024 x 10

7

8-11024 x 10

7

8-12024 x 10

7

0 0.5 10

0.51

11-10024 x 10

7

0 0.5 10

0.51

11-12024 x 10

7

0 0.5 10

0.51

Caminhos

Índi

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Mét

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PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7 PZT 9

PZT 8


0 0.5 10

0.5

1

2-10

0.05

0.1

0 0.5 10

0.5

1

2-30

0.05

0.1

0 0.5 10

0.5

1

4-10

0.05

0.1

5-1 2-40

0.05

0.1

5-20

0.05

0.1

5-3 2-60

0.05

0.1

6-30

0.05

0.1

0 0.5 10

0.5

1

5-40

0.05

0.1

0 0.5 10

0.5

1

5-60

0.05

0.1

0 0.5 10

0.5

1

4-70

0.05

0.1

5-70

0.05

0.1

5-90

0.05

0.1

6-90

0.05

0.1

0 0.5 10

0.5

1

8-70

0.05

0.1

8-90

0.05

0.10 0.5 1

0

0.5

1

0 0.5 10

0.5

1

8-100

0.05

0.1

8-110

0.05

0.1

8-120

0.05

0.1

0 0.5 10

0.5

1

11-100

0.05

0.1

0 0.5 10

0.5

1

11-120

0.05

0.1

0 0.5 10

0.5

1

CaminhosC

CD

M

PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7 PZT 9

PZT 8

PZT 11 PZT 12PZT 10

65


Região da falha identificada: Condição de Falha 1

Posição da falha, confirmando a região identificada.

66


• Condição de Falha 2:

0 0.5 10

0.5

1

2-10

5001000

0 0.5 10

0.5

1

2-30

5001000

0 0.5 10

0.5

1

4-10

5001000

5-12-40

5001000

5-20

5001000

5-32-60

5001000

6-30

5001000

0 0.5 10

0.5

1

5-40

5001000

0 0.5 10

0.5

1

5-60

5001000

0 0.5 10

0.5

1

4-70

5001000

5-70

5001000

5-90

5001000

6-90

5001000

0 0.5 10

0.5

1

8-70

5001000

8-90

5001000

0 0.5 10

0.5

1

0 0.5 10

0.5

1

8-100

5001000

8-110

5001000

8-120

5001000

0 0.5 10

0.5

1

11-100

5001000

0 0.5 10

0.5

1

11-120

5001000

0 0.5 10

0.5

1

CaminhosR

MSD

PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7

PZT 8

PZT 9


0 0.5 10

0.5

1

2-10

0.010.02

0 0.5 10

0.5

1

2-30

0.010.02

0 0.5 10

0.5

1

4-10

0.010.02

5-1 2-40

0.010.02

5-20

0.010.02

5-3 2-60

0.010.02

6-30

0.010.02

0 0.5 10

0.5

1

5-40

0.010.02

0 0.5 10

0.5

1

5-60

0.010.02

0 0.5 10

0.5

1

4-70

0.010.02

5-70

0.010.02

5-90

0.010.02

6-90

0.010.02

0 0.5 10

0.5

1

8-70

0.010.02

8-90

0.010.02 0 0.5 1

0

0.5

1

0 0.5 10

0.5

1

8-100

0.010.02

8-110

0.010.02

8-120

0.010.02

0 0.5 10

0.5

1

11-100

0.010.02

0 0.5 10

0.5

1

11-120

0.010.02

0 0.5 10

0.5

1

Caminhos

Nor

ma

H2

PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7

PZT 8

PZT 8


67


0 0.5 10

0.5

1

2-10

0.05

0 0.5 10

0.5

1

2-30

0.05

0 0.5 10

0.5

1

4-10

0.05

5-1 2-40

0.05

5-20

0.05

5-3 2-60

0.05

6-30

0.05

0 0.5 10

0.5

1

5-40

0.05

0 0.5 10

0.5

1

5-60

0.05

0 0.5 10

0.5

1

4-70

0.05

5-70

0.05

5-90

0.05

6-90

0.05

0 0.5 10

0.5

1

8-70

0.05

8-90

0.050 0.5 1

0

0.5

1

0 0.5 10

0.5

1

8-100

0.05

8-110

0.05

8-120

0.05

0 0.5 10

0.5

1

11-100

0.05

0 0.5 10

0.5

1

11-120

0.05

0 0.5 10

0.5

1

Caminhos

CC

DM

PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7

PZT 8

PZT 9


0 0.5 10

0.51

2-1024 x 10

7

0 0.5 10

0.51

2-3024 x 10

7

0 0.5 10

0.51

4-1024 x 10

7

5-1 2-4024 x 10

7

1024 x 10

7

5-3 2-6024 x 10

7

6-3024 x 10

7

0 0.5 10

0.51

5-4024 x 10

7

0 0.5 10

0.51

5-6024 x 10

7

0 0.5 10

0.51

4-7024 x 10

7

5-7024 x 10

7

5-9024 x 10

7

5-9024 x 10

7

0 0.5 10

0.51

8-7024 x 10

7

8-9024 x 10

7

0 0.5 10

0.51

0 0.5 10

0.51

8-10024 x 10

7

8-11024 x 10

7

8-12024 x 10

7

0 0.5 10

0.51

11-10024 x 10

7

0 0.5 10

0.51

11-12024 x 10

7

0 0.5 10

0.51

Caminhos

Índi

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Mét

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PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7

PZT 8

PZT 9


68


0

0.02

0.04

Nor

ma

H2

0

400

800

1200

RM

SD

0

2

4 x 107

IFM

5-1 5-2 5-3 5-4 5-6 5-7 5-9 8-7 8-9 8-10 8-11 8-12 2-1 2-3 2-4 2-6 4-1 4-7 6-3 6-9 11-1011-120

0.06

CC

DM

Caminhos


69


Posições das falhas, confirmando as regiões identificadas.

Regiões das falhas identificadas: Condição de Falha 2.

70


• Condição de Falha 3:

0 0.5 10

0.5

1

2-10

0.010.02

0 0.5 10

0.5

1

2-30

0.010.02

0 0.5 10

0.5

1

4-10

0.010.02

5-1 2-40

0.010.02

5-20

0.010.02

5-3 2-60

0.010.02

6-30

0.010.02

0 0.5 10

0.5

1

5-40

0.010.02

0 0.5 10

0.5

1

5-60

0.010.02

0 0.5 10

0.5

1

4-70

0.01

0.02

5-70

0.010.02

5-90

0.010.02

6-90

0.010.02

0 0.5 10

0.5

1

8-70

0.010.02

8-90

0.010.02

0 0.5 10

0.5

1

0 0.5 10

0.5

1

8-100

0.010.02

8-110

0.010.02

8-120

0.010.02

0 0.5 10

0.5

1

11-100

0.010.02

0 0.5 10

0.5

1

11-120

0.010.02

0 0.5 10

0.5

1

Caminhos

Norm

a H2

PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7

PZT 10

PZT 8

PZT 11

PZT 9

PZT 12

0 0.5 10

0.5

1

2-10

800

0 0.5 10

0.5

1

2-30

800

0 0.5 10

0.5

1

4-10

800

5-1 2-40

800

5-20

800

5-3 2-60

800

6-30

800

0 0.5 10

0.5

1

5-40

800

0 0.5 10

0.5

1

5-60

800

0 0.5 10

0.5

1

4-70

800

5-70

800

5-90

800

6-90

800

0 0.5 10

0.5

1

8-70

800

8-90

8000 0.5 1

0

0.5

1

0 0.5 10

0.5

1

8-100

800

8-110

800

8-120

800

0 0.5 10

0.5

1

11-100

800

0 0.5 10

0.5

1

11-120

800

0 0.5 10

0.5

1

Caminhos

RM

SD

PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7

PZT 8

PZT 9


71


0 0.5 10

0.51

2-3024 x 10

6

0 0.5 10

0.51

4-1024 x 10

6

5-1 2-4024 x 10

6

5-2024 x 10

6

5-3 2-6024 x 10

6

6-3024 x 10

6

0 0.5 10

0.51

5-4024 x 10

6

0 0.5 10

0.51

5-6024 x 10

6

0 0.5 10

0.51

4-7024 x 10

6

5-7024 x 10

6

5-9024 x 10

6

6-9024 x 10

6

0 0.5 10

0.51

8-7024 x 10

6

8-9024 x 10

60 0.5 1

00.5

1

0 0.5 10

0.51

8-10024 x 10

6

8-11024 x 10

6

8-12024 x 10

6

0 0.5 10

0.51

11-10024 x 10

6

0 0.5 10

0.51

11-12024 x 10

6

0 0.5 10

0.51

Caminhos

Índi

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étri

ca

0 0.5 10

0.51

0 0.5 10

0.51

0 0.5 10

0.51

2-1024 x 10

6

PZT 1 PZT 2 PZT 3

PZT 4 PZT 5 PZT 6

PZT 7

PZT 8

PZT 9


2-105

x 10-3

2-305

x 10-3

4-105

x 10-3

5-1 2-405

x 10-3

5-205

x 10-3

5-3 2-605

x 10-3

6-305

x 10-3

0 0.5 10

0.51

5-405

x 10-3

0 0.5 10

0.51

5-605

x 10-3

0 0.5 10

0.51

4-705

x 10-3

5-705

x 10-3

5-905

x 10-3

6-905

x 10-3

0 0.5 10

0.51

8-70

5x 10

-3

8-90

5x 10

-3

0 0.5 10

0.51

0 0.5 10

0.51

8-1005

x 10-3

8-1105

x 10-3

8-1205

x 10-3

0 0.5 10

0.51

11-1005

x 10-3

0 0.5 10

0.51

11-1205

x 10-3

0 0.5 10

0.51

CaminhosC

CD

M

0 0.5 10

0.51

0 0.5 10

0.51

0 0.5 10

0.51

0 0.5 10

0.51

PZT 1 PZT 2 PZT 3

PZT 4 PZT 6

PZT 7

PZT 8

PZT 9


PZT 5

72


0

0.01

0.02

Nor

ma

H2

0

400

800

RM

SD

0

2

4 x 106

IFM

5-1 5-2 5-3 5-4 5-6 5-7 5-9 8-7 8-9 8-10 8-11 8-12 2-1 2-3 2-4 2-6 4-1 4-7 6-3 6-9 11-1011-120

2

4

6x 10

-3

CC

DM

Caminhos


73


Posição da falha, confirmando a região identificad

Região da falha identificada: Condição de Falha 3

74


Configuração de PZTs formada na superfície interna do painel.

Verificar a influência do stringer

SHM na Superfície Interna do Painel Aeronáutico

75


Sequência de excitação realizada na região interna do painel aeronáutico.

Duas excitações foram realizadas: 1ª: propagação através do stringer 2ª: propagação “livre”

Três condições de falha foram analisadas:

76


- Condição de Falha 1-A. A falha (massa de 1g) foi acoplada entre o PZT 2-A e o PZT 3-A;

- Condição de Falha 2-A. A mesma falha (massa de 1g) foi colada entre o PZT 4-A e o PZT 2-A em uma região próxima do stringer;

- Condição de Falha 3-A. Uma outra falha (garra de 3g) foi acoplada no reforçador, entre o PZT 4-A e o PZT 2-A.

77


0 0.5 10

0.5

1

2-1A0

0.015

0.03

0 0.5 10

0.5

1

2-3A0

0.015

0.03

0 0.5 10

0.5

1

4-1A0

0.015

0.03

4-2A0

0.015

0.03

4-3A0

0.015

0.03

0 0.5 10

0.5

1

Caminhos

Nor

ma

H2

PZT 1-A PZT 2-A PZT 3-A

PZT 4-A

0 0.5 10

0.5

1

2-1A0

100

200

0 0.5 10

0.5

1

2-3A0

100

200

0 0.5 10

0.5

1

4-1A0

100

200

4-2A0

100

200

4-3A0

100

200

0 0.5 10

0.5

1

Caminhos

RM

SD


PZT 4-A

0 0.5 10

0.5

1

2-1A0

5x 10

7

0 0.5 10

0.5

1

2-3A0

5x 10

7

0 0.5 10

0.5

1

4-1A0

5x 10

7

4-2A0

5x 10

7

4-3A0

5x 10

7

0 0.5 10

0.5

1

CaminhosÍnd

ice

de F

alha

Mét

rica


PZT 4-A

0 0.5 10

0.5

1

2-1A0

0.015

0.03

0 0.5 10

0.5

1

2-3A0

0.015

0.03

0 0.5 10

0.5

1

4-1A0

0.015

0.03

4-2A0

0.015

0.03

4-3A0

0.015

0.03

0 0.5 10

0.5

1

Caminhos

CC

DM


PZT 4-A

Índices de falha computados: Condição de Falha 1-A – detecção e localização da falha

78


0 0.5 10

0.5

1

2-1A0

0.005

0.01

0 0.5 10

0.5

1

2-3A0

0.005

0.01

0 0.5 10

0.5

1

4-1A0

0.005

0.01

4-2A0

0.005

0.01

4-3A0

0.005

0.01

0 0.5 10

0.5

1

Caminhos

Nor

ma

H2


PZT 4-A

0 0 .5 10

0 .5

1

2-1A0

500

1000

0 0 .5 10

0 .5

1

2-3A0

500

1000

0 0 .5 10

0 .5

1

4-1A0

500

1000

4-2A0

500

1000

4-3A0

500

1000

0 0 .5 10

0 .5

1

Caminhos

RM

SD


PZT 4-A

0 0.5 10

0.5

1

2-1A0

5x 10

7

0 0.5 10

0.5

1

2-3A0

5x 10

7

0 0.5 10

0.5

1

4-1A0

5x 10

7

4-2A0

5x 10

7

4-3A0

5x 10

7

0 0.5 10

0.5

1

CaminhosÍnd

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de F

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Mét

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PZT 4-A

0 0.5 10

0.5

1

2-1A0

0.04

0.08

0 0.5 10

0.5

1

2-3A0

0.04

0.08

0 0.5 10

0.5

1

4-1A0

0.04

0.08

4-2A0

0.04

0.08

4-3A0

0.04

0.08

0 0.5 10

0.5

1

Caminhos

CC

DM


PZT 4-A


79


0 0.5 10

0.5

1

2-1A0

0.005

0.01

0 0.5 10

0.5

1

2-3A0

0.005

0.01

0 0.5 10

0.5

1

4-1A0

0.005

0.01

4-2A0

0.005

0.01

4-3A0

0.005

0.01

0 0.5 10

0.5

1

Caminhos

Nor

ma

H2


PZT 4-A

0 0.5 10

0.5

1

2-1A0

200

400

0 0.5 10

0.5

1

2-3A0

200

400

0 0.5 10

0.5

1

4-1A0

200

400

4-2A0

200

400

4-3A0

200

400

0 0.5 10

0.5

1

Caminhos

RM

SD


PZT 4-A

0 0.5 10

0.5

1

2-1A05

1015 x 10

6

0 0.5 10

0.5

1

2-3A05

1015 x 10

6

0 0.5 10

0.5

1

4-1A05

1015 x 10

6

4-2A05

1015 x 10

6

4-3A05

1015 x 10

6

0 0.5 10

0.5

1

Caminhos

Índi

ce d

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lha

Mét

rica PZT 1-A PZT 2-A PZT 3-A

PZT 4-A

0 0.5 10

0.5

1

2-1A0

0.005

0.01

0 0.5 10

0.5

1

2-3A0

0.005

0.01

0 0.5 10

0.5

1

4-1A0

0.005

0.01

4-2A0

0.005

0.01

4-3A0

0.005

0.01

0 0.5 10

0.5

1

Caminhos

CC

DM


PZT 4-A


80


3 static tests Coupons: T16, T17 and T18

4.3 SHM in Composite materials

81


Experimental Setup

Number of measurements per each load

6 actuators x 6 sensors x 8 freqs = 288 signals

Actuations frequencies in kHz

100, 150, 200, 250, 300, 350, 400, 450

Path 3-9

82


Data Acquisition

Damage Feature Indices

Normalization

Define Number of Clusters

Apply C-means Clustering

Compute Cluster Centers and Region of each cluster

Temperature

Load Damage

Training Structure Real Structure

Damage Feature Indices

Normalization

Verification

Methodology

Decision

83


Based on ARX Model

Based on H2 norm

Feature indices

Index 1

Index 2

Based on H∞ Norm

Index 3

84


Based on the trace of matrix

Index 4

Spectrogram of the signal is obtained using Short-Time Fourier Transform

STFT t, f( ) = UΣVT

The signal energy map provided by the STFT matrix is decomposed using singular value decomposition.

U and V are the left and right singular vectors of the STFT matrix contains the singular values in the diagonal form

Σ

Feature indices

Σ

85


The subscript h denotes healthy structure and the subscript d denotes the damaged structure

Index(i) = Index(i)h − Index(i)dIndex(i)h

The results are normalized with the maximum value set to unity.

Normalization

86


Measured Conditions

87


Input and Output Signals

Path 3 to 9

Excitation ; Output baseline (test 1) blue

Load Effect

Baseline red; test (3) test (5) green; test (7) black; test (9) magenta

88


Output Signals

Test 20 and 21 Effect of load and damage

Tests 22 and 23 Effect of the damages

89


Example of Feature index

Indices computed for T18 path 3-9 Freq = 300kHz

90


Training for coupon T18: paths 3-9, 4-10 and 5-11

Freq 300kHz

Baseline

X = center of the clusters

Classification on Training Coupon

91


Classification for the path 4-10 F300kHz

Classification on Training Coupon

92


Measured Condition = 7 (Load = 3 Kips)

Path 3-9 300kHz

Tests on Verification Coupons

, blueT17 and green T18

93


Measured Conditions

94



Path 4-10 300kHz


, blueT17 and green T18

95



Path 4-10 300kHz

T16

T17

T18


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Date post:	19-Feb-2021
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Concepts and Applications of Lamb WavesDepartamento de Engenharia Mecânica Av. Brasil Centro, 56...

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