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The dynamic behavior of rigid‐block structures resting on a rigid foundation subjected to horizontal harmonic excitation is examined. For slender structures, the nonlinear equation of motion is approximated by a piecewise linear equation. Using this approximation for an initially quiescent structure, safe or no‐toppling and unsafe regions are identified in an excitation amplitude versus excitation frequency plane. Furthermore, several possible modes of steady‐state response are detected, and analytical procedures are developed for determining the amplitudes of the predominant modes and for performing stability analyses. It is shown that the produced stability diagrams can be beneficial to assessing the toppling potential of a rigid‐block structure under a given amplitude‐frequency combination of harmonic excitation; in this manner the integration of the equation of motion is circumvented.
Spanos et al. (Thu,) studied this question.
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