An unusual amplitude growth property and its remedy for structure-dependent integration methods

An unusual amplitude growth in the steady-state response of a high frequency mode for a structure-dependent integration method is numerically and analytically identified. This is a brand new type of amplitude growth and it has never been found in the conventional integration methods. The root cause of this unusual amplitude growth can be revealed by examining the local truncation error constructed from a forced vibration error, where the dominant error term for high frequency modes plays the key role for this unusual amplitude growth. An effective remedy is proposed by introducing a load-dependent term into the difference equation for displacement and/or velocity increment to remove the dominant error term. As a result, this adverse amplitude growth can be automatically removed. Consequently, the inclusion of the load-dependent term in the formulation of the difference equation for displacement increment and/or velocity increment is inevitable for a general structure-dependent integration method.