modified linear approximation for assessment of rigid block dynamics

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