The purpose of this paper is to prove that any dynamic response of a multi-degree of freedom system with an arbitrary type of non-linear property can be solved with required accuracy by application of the incremental perturbation method. Namely it will be theoretically shown that a set of explicit formula for calculating all the perturbation coefficients up to any order can be derived from the equations of motion through the proposed general procedure. This solution method is shown applicable to any dynamic problem, in which generalized forces can be expressed by analytical functions of generalized displacements, velocities and accelerations. The effectiveness of the proposed incremental perturbation method will be demonstrated by a successful result of dynamic response simulation of a multistory building model with high viscosity fluid damper.
