  The analysis of sound and vibrations is often performed in the frequency
domain, implying the assumption of steady-state behaviour and time-harmonic
excitation. External excitations, however, may be transient rather than
time-harmonic, requiring time-domain analysis. Some material properties, e.g.\
often used to represent for damping treatments, are still described in the
frequency domain, which complicates simulation in time. In this paper, we
present a method for the linearization of finite element models with nonlinear
frequency dependencies. The linearization relies on the rational approximation
of the finite element matrices by the AAA method. We introduce the Extended AAA
method, which is classical AAA combined with a degree two polynomial term to
capture the second order behaviour of the models. A filtering step is added for
removing unstable poles.
