Symmetric matrix-valued frequency to time transformation for unbounded domains applied to infinite beams

In structural dynamics coupled systems with unbounded deformable members are characterized by radiation damping. Typically, the unbounded subsystem is described in the frequency domain; either numerically or analytically by means of dynamical stiffness matrices. Recent papers describe a matrix-valued rational interpolation of the dynamical stiffness and straightforward transformation into the time-domain. In addition, the asymptotic behaviour has been considered, too, by adding fractional derivatives. However, the matrices involved in this process are unsymmetric even if the original dynamical stiffnesses are symmetric. The approach presented in this paper maintains the symmetry a priori without any numerical operations by simply using a rational approximation with a matrix-valued numerator but a scalar-valued denominator and contains some further numerical advantages. The method is demonstrated by treating an infinite beam on an elastic foundation.