  The resistive response of Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ to AC
mechanical deformation is considered in the multi-domain state. This resistance
change depends both upon the anelastic relaxation of domain walls and upon the
relation between resistance and the domain wall configuration. Samples are
adhered to the surface of a piezoelectric stack, which is driven by an AC
voltage while the AC modulation of the sample resistance is measured. As the
response time of electrons is faster than that of the lattice, the phase
difference $\phi$ between the AC resistance modulation and the AC deformation
of the piezoelectric is entirely due to anelastic relaxation effects in the
sample. An expression is derived for relating $\phi$ to a sample's complex
compliance, $J(\omega)$, in this experimental configuration. Measurements of
Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ for x= (0.025, 0.052) reveal a peak in the
out-of-phase resistivity modulation in the orthorhombic antiferromagnetic state
well below the Ne\'el temperature $T_N$ and structural transition $T_S$.
Meanwhile, for a composition that is tetragonal at all temperatures, x=0.07,
the resistance modulation remains entirely in phase over the same temperatures,
establishing domain motion as a probable cause of the observed effects in the
samples that do undergo the tetragonal-to-orthorhombic transition. Fits are
provided of $\tan\phi$ for a sample with x=0.025 for various amplitude
excitations on the piezoelectric stack, from which the apparent activation
energy $E_a$ for domain wall motion is found to decreases with increasing
amplitude of the deformation along the $[110]_T$ axis. We find
$\frac{dE_a}{d\varepsilon^0_{[110,110]_T}} = -1115\pm 196$ eV with $E_a = 9.09
\pm 0.74 \times 10^{-3}$ eV in the zero strain limit if we assume linearity
over the entire range of strain amplitudes.
