Vibration systems with sliding friction are analyzed by using the Linear Accelerated Method based upon a new analytical logic which can study in detail the state of sliding motion within the constant time step. The logic was applied to linear single-mass systems with and without external force. The obtained numerical values are compared with the theoretical one and also the one without this logic. Then it was proved that the computing time is shortened greatly. In other words, much shorter time step is demanded, if the same computing accuracy is expected without the new logic.
It is also shown that the new logic is applicable to linear two-mass systems and non-linear vibration systems in which the upper part is a non-linear structure and the lower part is a sliding friction.