Nonlinear finite element analysis of maxillary molar vibration

The vibration of a maxillary molar was studied using the finite element method according to nonlinear behaviour of the human periodontal ligament (PDL). The effect of alveolar bone loss to the vibration of the tooth was also investigated to assess the condition of periodontium. Threedimensional finite element model of a maxillary molar was constructed using CT image reconstruction, and the elastic face foundation constraint was applied to the place where the PDL was attached to. Modal analysis was performed using the finite element method. The nonlinear behaviour of the PDL was approached by the piecewise linearised method. The results indicated that the vibration of the maxillary molar could be described by several modal frequencies and modes. The first four modes were dominant, which varied with the deformation of the PDL. The vibration frequency of the tooth decreased with the losing of the alveolar bone, but the ratio of decreasing had no significant correlation with the nonlinear behaviour of the human PDL. The vibration frequency of the tooth can be used to describe the loss of the alveolar bone, under physiological short-term loading.