Dynamic response analysis of rocking rigid blocks subjected to half-sine pulse type base excitations

Abstract

The motion of a rocking block subjected to half-sine pulse base excitation is analyzed by the mathematical model of lumped-mass approximation. The governing equation of the motion of the rocking block is derived as a second order ODE. The solutions of the derived equation for different size of rocking blocks are illustrated by mat lab figures in terms of displacement, velocity and acceleration responses. The coefficients of the equation of the minimum required overturning acceleration of rocking blocks are obtained, and the overturning instant of the rocking block is investigated through force vibration and free vibration. parameter studies are also performed. to verify the results accordingly to the Housner's (1963) postulation and to the report of N. Makris (1998) about dynamic response of rocking blocks.