Grandstand Terraces. Experimental and Computational Modal Analysis

Experimental, and Finite Element (FE) Modal Analyses were used to determine the natural
frequencies and mode shapes of a single and a double precast concrete terrace unit under
laboratory conditions. The units were simply supported on steel ‘stools’ at the four corners with
polychloroprene (neoprene) pads inserted at their interface, between steel and concrete. The
stools were part of a specially manufactured steel frame of rectangular hollow section (RHS),
firmly resting on the strong laboratory concrete floor.
The laboratory equipment consisted of a Shaker, (vibrator, or exciter), an Amplifier, a Signal
Generator, a Spectrum Analyser and a series of Accelerometers. Two sets of modal testing
results identifying modes of vibration in the vertical plane for single and double terrace units
were obtained. The results from the excitation of the single unit indicated that the lowest mode,
Mode 1, was a predominantly bending mode, whereas Modes 2 and 3 were most likely
representing twisting of the L-shaped unit (successfully depicted in the FE analysis later) and,
perhaps to a lesser extent, the result of not perfectly rigid and symmetric support conditions.
Modes 4 and 5 could be regarded as the second and third ‘beam-like’ modes of bending
vibration in the vertical plane.
Modal parameter results of the double terrace unit for the first six vertical modes of vibration
were also obtained. As it was noted from the mode shapes, the first mode of vibration excited
only the lower unit, which moved in a ‘rigid-body’ manner and engaged only one support. This
indicated that the first mode was actually caused by a relatively ‘elastic’ (tuneful) support under
the lower unit. The second mode was principally a ‘flexural’ mode where the units behaved like
simply supported beams undergoing bending. Both units moved in-phase and no moving was
detected over the supports this time. The dynamic behaviour in general, and the frequencies of
the higher modes seemed to be as expected and compared well with the corresponding behaviour
of the single terrace unit. However, bearing in mind that all accelerometers were positioned
vertically and that the structure under test was only represented by a series of lumped masses in a
straight line (that is, approximated as one dimensional structure), it is probably reasonable to
assume that the particular testing procedure missed certain complex modes of vibration. These
were depicted in the finite element analysis.
The dynamic model was in effect an extension of the existing static model, developed earlier.
The Block Lanczos eigenvalue extraction method for large, symmetric problems was utilised.
This method is especially powerful when searching for eigen-frequencies in a specific part of an
eigenvalue spectrum of a system. It performs particularly well when the model consists of a
combination of 3D and 2D or 1D elements, using the sparse matrix solver and overriding any
other solver specified previously. The adoption of the Block Lanczos method has significantly
reduced the CPU-time in this study and has added to the accuracy of the results over the initial
choice of the subspace method.
The steel reinforcement was introduced to the model in stages and a modal analysis was
performed every time, in order to study its effect on the natural frequencies of the unit. Previous
studies at MSc level have revealed no specific or conventional pattern. The same studies have
demonstrated the change in dynamic behaviour of a simply supported, singly reinforced concrete
beam of rectangular section, undergoing vibrations. Briefly, it was shown that an increase in the
amount of reinforcement is likely to increase certain modal frequencies and decrease others. For
example, introducing the tension reinforcement, resulted in marginally increasing the first two
natural frequencies associated with bending modes but had no effect on the next two modes
associated with predominantly torsional vibrations. In fact, reinforcing and therefore increasing
the specific stiffness of a particular structural element or structure could result in “forcing” this
structure into a different mode of vibration and somehow introducing lower corresponding
frequencies.
Initially, a number of degrees of freedom, (DOF) both translational and rotational were
restrained at the appropriate directions in an effort to depict realistic support conditions. Plane
symmetry was used very consciously, due to its effect on the mode shapes, to reduce the number
of elements in the FE-model and minimise effort and CPU-time. The FE-model was set to free
vibration. Two important properties, its natural frequencies and the corresponding mode shapes
were recorded and compared with those obtained experimentally. It was found that both natural
frequencies and mode shapes are extremely sensitive to support conditions. It was also
concluded that support conditions ‘built-in’ the FE-program were not adequate to model the
behaviour of the real supports satisfactorily. Correlation between experimental and computer
predicted natural frequencies and mode shapes improved with the introduction of more complex
(advanced) modelling techniques and gradual lifting of the limitations of the model. Best results
were achieved when the stiffness of the supports was modelled using the ANSYS dedicated
stiffness matrix element (MATRIX27).
Finally, it may be reasonable to conclude that predicted natural frequencies and mode shapes
may be more accurate and “realistic” than those obtained in the laboratory. This is more evident
in complex modes (eg: coupled, bending + torsion) as, among other (structural) parameters, they
greatly depend on the number, position, direction and quality of the transducers and data logging
equipment used. Also, it is well known that the higher the mode shape number the more difficult
it is to be accurately captured.
The paper includes a discussion of the results aided by a number of tables, figures, graphs
diagrams and sketches. Emphasis is given to the experience built up in interpreting modal
analysis results in order to be used for similar, or further work.