A double pendulum model with bi-lateral rigid constraint is constructed under harmonic excitation. The impact periodic solution of a nonlinear dynamic system under harmonic excitation and its existence conditions are studied. Adopting the modal analysis and matrix theory，an invertible transformation is introduced to obtain the parameter conditions for the existence of the impact periodic solution of the system. On the basis of the theoretical calculation results，applying Matlab software，numerical simulation is carried out to obtain the impact periodic solution of the system with small angle motion，which verifies that the theoretical research results have certain theoretical guidance in engineering practice.