  We investigate the exact dynamics of trace distance discord by considering
two qubits under dephasing whose states belong to a class of $X$ states beyond
Bell diagonal form. The necessary condition for the occurrence of freezing
trace distance discord is found and compared with that of entropic discord. For
an illustration, we consider two interacting qubits coupled to independent
reservoirs and demonstrate these dynamical properties of trace distance
discord. It is interesting to find that the freezing trace distance discord
exists even for $X$ states without maximally mixed marginals and can be tuned
by dipole-dipole coupling of two qubits. Moreover, we consider the initial
extended Werner-like states and investigate the differences between trace
distance discord and entanglement. The influences of initial state and the
dipole-dipole coupling of the two qubits on the dynamics of nonclassical
correlations are explored.
