We present results from investigations of periodic (sinusoidal) and burst signal (colliding travelling wave) configurations of axion strings, performed using adaptive mesh refinement simulations. We model the dependence of the massless axion and massive particle radiation on the amplitude and radius of curvature of the string $R$. We conclude that the Kalb-Ramond thin-string approximation is valid in the linear regime for sinusoidal strings, and that massive radiation is exponentially suppressed in this regime by parameters that determine the string curvaturem i.e. the amplitude $A$ and width of the travelling wave $\sim \sigma_\mathrm{d}$. In the nonlinear regime, massless and massive radiation are power-law suppressed with the power law index determined by the `regime' of behaviour, related to the relationship between $R, A, \delta$ and $\sigma_\mathrm{d}$ as defined in [1]. For burst signals, in the regime where $R < \sigma_\mathrm{d}$ but $R$ is not so low as to form coherent loops, massive particle radiation comprises up to 50% of the total signal. We postulate that this modelling could be usefully incorporated into gravitational wave burst signal predictions and axion spectrum measurements for string networks.