Experimental Methods in Earthquake Engineering - Dynamic Behavior of Concrete and Seismic Engineering - page 166

With the development of numerical methods, a new method has evolved: the
pseudo-dynamic method, which is complementary to shaking table tests.

In principle, it involves numerically integrating, in the course of time, the
equations of dynamics, written for the structure into a relative motion reference
frame:

M a t C v t F ª d t º M a t

¬ ¼

r r int r e

where M and C represent the viscous damping and mass operators, F int the inner
forces (apart from viscous effects), a r (t), v r (t) and d r (t) the accelerations, speeds and
displacements related to the structure with regard to its base considered as fixed, and
a e (t) the driving acceleration of the same base.

At a given time, the equation is numerically integrated over a short period of
time, giving an approximation of the displacement d(t). The displacement is then
applied to the model, fixed at its base, through a few wisely located jacks that allow
an estimation of the internal forces (F int ) which will be used for the numerical
integration on the next interval.

The main features of the method are the fact that it is possible to work on models
that are much larger than shaking tables, and that we can proceed slowly.
Nevertheless, rate effects are only taken into account through the viscous damping
operator, and the displacements are only imposed on the structure at a small number
of points, which is not well adapted to real structures with a well-distributed mass.

As we may note, the theoretical concepts on which both experimental methods
are based are rather simple. The actual difficulty lies in the interpretation of the
results and their transposition to real structures, as has been demonstrated in
numerous model tests; it also lies in the implementation aspects, which
fundamentally condition the quality of the results. Thus, in the case of shaking tables
for example, it is essential to control the electro-mechanical system that drives the
table. In the same way, for the pseudo-dynamic method, the splitting into time
periods as well as the integration algorithm of the dynamics equations have a
considerable influence on the final quality of the results.

This is the reason why, in this chapter, the stress is deliberately laid on these
aspects that may at first seem to be more “technological” (numerical as well as
experimental), yet which remain linked to the dynamic behavior of the structures.
The test examples given, obtained from the ELSA and TAMARIS European
facilities, illustrate our remarks explicitly and concretely.