The issue of noise generated by filter capacitors in high-voltage direct current (HVDC) transmission converter stations has become increasingly prevalent. In order to study the noise problem of filter capacitors, it is necessary to begin with an analysis of the vibration mechanism that causes the noise. The primary cause of capacitor vibration is the generation of an alternating electric field in the insulating medium by the application of an AC voltage to the plates. This electric field exerts a force on the conductor, resulting in irregular vibrations and the production of noise. Current research does not consider the influence of the residual charge of the dielectric film and the internal insulating material on its internal vibration. This article therefore first conducts a theoretical analysis of the internal force of the filter capacitor, and then uses COMSOL simulation software to establish the multilayer structure of the capacitor core. The stress calculation model for the dielectric and aluminum foil layers explores and summarizes the influence of uneven residual charges and internal insulating materials on the stress of the capacitor core when it is in the alternating current (AC) and direct current (DC) mixed excitation state, by setting different residual charge distributions. The findings indicate that the residual charge of the dielectric film within the filter capacitor and the internal insulating material exerts a significant influence on its force under the influence of the electric field. These results provide valuable theoretical guidance for the development of capacitor vibration reduction and noise reduction measures.