tesi R. Valiante.pdf - EleA@UniSA

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∆ i
2
where { ( ) }
n φi
ω = α
n
T { ε n ( φi
) } [ k n ] { ε n ( φi
) }
T { φ } [ M ]{ φ }
i
i
(1.4)
ε are the n-th member’s deformations computed on the basis
of the undamaged mode shapes φ i , while [ M ] and [ n ]
k describe the mass of
the structure and the stiffness of the n-th member. This equation directly relates
the effect of damage on a specific component n to the corresponding shift in
frequency, under the assumption that the evaluation of this direct relation can be
performed on the basis of pre-damage modal information. The hypothesis that
damage only produces a change in stiffness [ δ K ] is exploited in Richardson and
Mannan [15], where the orthogonality properties of the damaged and undamaged
structure is used to obtain the following sensitivity equation:
T
( d )
{ } [ δ ]{ φ } ω
( )
( ) ( ) 2
2 u
φ = −
(1.5)
i K i i ωi
where it is again assumed that damage causes a negligible change in the
mode shapes.
1.5.2. MODE SHAPE CHANGES
Mode shape changes are found to be quite sensitive to damage, especially
when higher modes are considered and are able to directly provide damage
location information. The problem associated with mode shape monitoring is
clearly related to the need of sufficient spatial measurement resolution, which
complicates the experimental procedure. The required measurement resolution
can be easily achieved through the use of a Scanning Laser Doppler Vibrometer,
which has become an important tool for dynamic testing. Alternatively, the
number of measurement locations can be reduced if the FE model of the
structure under investigation is available for its use in increasing the information
on the structure’s behaviour and for interpolation purposes. Most of the early
work, on mode shape analysis, considers the Modal Assurance Criterion (MAC)
to compare measured or damaged modes with undamaged or numerical ones.
For example, West [16] used the MAC to correlate the modes of an undamaged