Computer molecular dynamics (MD) simulations of dynamically driven twin structures reveal the main results of resonance ultrasonic spectroscopy (RUS) and dynamic mechanical analysis (DMA), namely the high-friction damping at low frequencies, and underdamped oscillations at high frequencies. High-frequency spectra show absorption, which relates to phonon heating of the sample and phase shifts between the applied dynamical strain field and the geometrical movements inside the microstructure. Two main excitations have been identified to describe this behavior. The first is the progression and retraction of needle twins, the second is the movement of kinks inside twin boundaries. The dynamical response of these excitations has been simulated over large frequency and amplitude regions. It is shown that propagations of needle twins and kinks have a propensity to irreversibility when needles completely retract and destroy themselves and when kinks disappear at the sample surface. These movements lead to macroscopic “jerks” or spikes in the heat content of the sample. At higher frequencies, all movements become oscillatory with very small amplitudes, which, below a cut-off of one lattice unit, are simple phonon vibrations. These movements are continuous and do not contribute to the jerk-spectra. The connection between the simulated microstructures and the dynamical elastic measurements are discussed.