Dynamicity is one of the critical characteristics and a major challenge in designing communication protocols in wireless networks. Most of the previous works had focused on the internal node changes (e.g., mobility, arrival, or departure) and not considered the effect of external environmental change. However, the external environmental change, in general, is a more complex phenomenon that can impede nodes from successful communication, implying the protocols of the previous dynamic models do not work well in practice. In this paper, we give an algorithm for distributed broadcasting in a more general model with fully dynamic wireless networks, called FD-Broadcast. Specifically, we present a fully dynamic model which allows node mobility and churns (due to node arrivals/departure) and external environmental change. In contrast to the previous works on dynamic networks, our model defines the full dynamicity in terms of localized topological changes of each node and can tolerate some external environmental change. The external environment changes are captured by the random jamming method. We show that FD-Broadcast can achieve broadcasting in $O(D_{S})$ rounds with a high probability guarantee under the assumption of constant dynamic rate in the SINR model, where $D_{S}$ is the dynamic diameter, a parameter proposed to depict the complexity of dynamic broadcasting. Moreover, the lower bound of dynamic broadcasting is proved to be $\Omega(D_{S})$, thus, FD-Broadcast is asymptotically optimal with high probability.