Modal Identification of Non- Modal Identification of Non- Classically damped structures Classically damped structures Sigurbjörn Bárðarson Dr. Rajesh Rupakhety, Dr. Ragnar Sigbjörnsson Objective This thesis focuses on modal identification of structural systems. System identification using experimental modal analysis is an important field in the study of dynamic systems. It can be used to create mathematical models of structures which can then be used in simulation and design. It can also be used in structural health monitoring. Modal identification also provides a valuable means of calibrating, validating, and updating finite element models of structures. Introduction All real physical structures behave dynamically when subjected to time dependent loads or displacements. If the forces or displacements are applied very slowly, the inertia effects can be neglected and a static analysis can be justified. Dynamic excitations such as wind loads, seismic loads, blast loads, and vibration-induced loads can impose unexpected demand on structures. A time dependent force, even of relatively low amplitude, can induce, on certain dynamic systems, significant consequences. The models used for design of structures are based on certain key parameters that control the dynamic response, such as the frequencies, mode shapes, and damping mechanisms. What the models used don’t adequately account for is that when a structure goes under extreme loading once, or repeated loading for long periods, the structure begins to deteriorate. Micro-cracks in concrete form, steel begins to yield or corrode, and bolts used get strained due to fatigue, and when such things happen, the system parameters change, albeit slowly. The process of monitoring those changes in the structural parameters is called structural health monitoring (SHM). The ultimate goal is to detect damage before it poses a risk. By doing so, the life time of a structure can be increased due to timely remedial actions and lower maintenance cost due to early detection. The findings of a SHM are used to update finite elements models which then again are used to verify the integrity of the structure. In time, the structure will have to lower its design forces or the structure replaced. January 2015 Case study – Óseyri Bridge As a case study, system identification of a base- isolated highway bridge was undertaken. The bridge selected was Óseyri bridge, located in the south of Iceland. A simple finite element model was created in SAP2000, using structural drawings. Results The modes identified had, in general, very high participation factors. Modes with higher participation factors have more effect on the motion of the bridge, so high participation in identified modes was expected. With increased damping, the damping ratios for periods in the mass proportional regime of the Rayleigh damping model seem to be more affected. A modified Rayleigh damping model could be fitted to account for the additional damping. Overall, the results fit well with the modal analysis. Even though only 6 degrees of freedom were used to represent the movement of the whole system, the results obtained are satisfactory. System identification is a very powerful tool which can yield results, given a limited amount of data, although more data is always preferred. Acknowledgements Much gratitude towards the Earthquake Engineering Research centre located in Selfoss, for providing me with a work area and invaluable experience in working with professionals. The bridge was modelled using frame elements with different cross sections and nonlinear link elements to represents rubber joints which lay on top of the pillars and carry the bridge deck. The bridge deck was modelled with two different cross sections: one which represents the deck over the pillars and another which represents the deck over the spans. The pillars were modelled using three different sections, due to the varying cross sectional area with height. The rubber bearings work as seismic base isolation devices. The rubber bearings have lead cores with layers of steel plates and rubber. The lead gives the bearing its initial horizontal stiffness, and energy dissipation capacity by virtue of its low yield strength. The steel plates contribute to the vertical stiffness while the rubber gives the post yield horizontal stiffness. For non-classically damped models, additional damping force is added to the rubber bearings, in 5% increments damping force of critical damping for the fundamental period. This model was excited with three component ground motion and the excitation and displacement response used for system identification. Figure 2 : Identified periods and damping ratios for no additional damping in the rubber bearings vs 30% damping in the rubber bearings compared to the original Rayleigh Damping model A C D
Poster made from a thesis about modal identification
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Modal Identification of Non-Classically damped structures
Sigurbjrn BrarsonDr. Rajesh Rupakhety, Dr. Ragnar
SigbjrnssonObjectiveThis thesis focuses on modal identification of
structural systems. System identification using experimental modal
analysis is an important field in the study of dynamic systems. It
can be used to create mathematical models of structures which can
then be used in simulation and design. It can also be used in
structural health monitoring. Modal identification also provides a
valuable means of calibrating, validating, and updating finite
element models of structures.IntroductionAll real physical
structures behave dynamically when subjected to time dependent
loads or displacements. If the forces or displacements are applied
very slowly, the inertia effects can be neglected and a static
analysis can be justified. Dynamic excitations such as wind loads,
seismic loads, blast loads, and vibration-induced loads can impose
unexpected demand on structures. A time dependent force, even of
relatively low amplitude, can induce, on certain dynamic systems,
significant consequences. The models used for design of structures
are based on certain key parameters that control the dynamic
response, such as the frequencies, mode shapes, and damping
mechanisms. What the models used dont adequately account for is
that when a structure goes under extreme loading once, or repeated
loading for long periods, the structure begins to deteriorate.
Micro-cracks in concrete form, steel begins to yield or corrode,
and bolts used get strained due to fatigue, and when such things
happen, the system parameters change, albeit slowly. The process of
monitoring those changes in the structural parameters is called
structural health monitoring (SHM). The ultimate goal is to detect
damage before it poses a risk. By doing so, the life time of a
structure can be increased due to timely remedial actions and lower
maintenance cost due to early detection. The findings of a SHM are
used to update finite elements models which then again are used to
verify the integrity of the structure. In time, the structure will
have to lower its design forces or the structure replaced. January
2015Case study seyri BridgeAs a case study, system identification
of a base-isolated highway bridge was undertaken. The bridge
selected was seyri bridge, located in the south of Iceland. A
simple finite element model was created in SAP2000, using
structural drawings. ResultsThe modes identified had, in general,
very high participation factors. Modes with higher participation
factors have more effect on the motion of the bridge, so high
participation in identified modes was expected. With increased
damping, the damping ratios for periods in the mass proportional
regime of the Rayleigh damping model seem to be more affected. A
modified Rayleigh damping model could be fitted to account for the
additional damping. Overall, the results fit well with the modal
analysis. Even though only 6 degrees of freedom were used to
represent the movement of the whole system, the results obtained
are satisfactory. System identification is a very powerful tool
which can yield results, given a limited amount of data, although
more data is always preferred.AcknowledgementsMuch gratitude
towards the Earthquake Engineering Research centre located in
Selfoss, for providing me with a work area and invaluable
experience in working with professionals.
The bridge was modelled using frame elements with different
cross sections and nonlinear link elements to represents rubber
joints which lay on top of the pillars and carry the bridge deck.
The bridge deck was modelled with two different cross sections: one
which represents the deck over the pillars and another which
represents the deck over the spans. The pillars were modelled using
three different sections, due to the varying cross sectional area
with height. The rubber bearings work as seismic base isolation
devices. The rubber bearings have lead cores with layers of steel
plates and rubber. The lead gives the bearing its initial
horizontal stiffness, and energy dissipation capacity by virtue of
its low yield strength. The steel plates contribute to the vertical
stiffness while the rubber gives the post yield horizontal
stiffness. For non-classically damped models, additional damping
force is added to the rubber bearings, in 5% increments damping
force of critical damping for the fundamental period. This model
was excited with three component ground motion and the excitation
and displacement response used for system identification.Figure 2 :
Identified periods and damping ratios for no additional damping in
the rubber bearings vs 30% damping in the rubber bearings compared
to the original Rayleigh Damping modelACD
