We develop a reliable residual-based a posteriori error estimator for a nonconforming method with non-matching meshes for a harmonic elastodynamics equation and show that the approximation method converges with an optimal order to the exact solution. Moreover, we propose an adaptive strategy to reduce computational cost and derive better approximations for problems with singularities and with large approximating systems. Numerical experiments confirm theoretical conclusions. © 2018 Global-Science Press.