This study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. Linearization assumptions which have already been used by Hounser and other researchers cannot be valid for all rocking blocks with various slenderness ra More
This study proposes a new linear approximation for solving the dynamic response equations of a rocking rigid block. Linearization assumptions which have already been used by Hounser and other researchers cannot be valid for all rocking blocks with various slenderness ratios and dimensions; hence, developing new methods which can result in better approximation of governing equations while keeping simplicity is necessary. In this paper, a new linear approximation is derived for solving the deferential equations of a rocking block in order to include wider range of blocks with various slenderness. The proposed method is verified by numerical solutions of the governing equations utilizing two methods of: average acceleration and fourth order Runge-Kutta. Verifications revealed more reasonable accuracy of the proposed method in comparison with the current linearization assumptions
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