Maximum response of SDOF systems under consecutive triangular pulses

This study investigates the dynamic response of linear-elastic and elastic–plastic Single Degree of Freedom (SDOF) systems subjected to two consecutive triangular pulse loads, a scenario relevant to blast-resistant design yet often neglected in conventional analysis. The concept of an amplification factor (AMF) is introduced to quantify the increase in maximum displacement relative to a single load. The response is analyzed across three classical regimes—impulsive, dynamic, and quasi-static—highlighting the dominant role of delay time between pulses in shaping the structural response. Closed-form expressions are derived for AMF in both impulsive and quasi-static limits, and analytical relationships are established between the amplification factor and the asymptotic bounds of Pressure-Impulse (P-I) diagrams. Parametric studies show that while the impulse and peak pressure ratios ( η and κ ) set the amplification bounds, the delay time t h critically governs the maximum response. In the elastic–plastic case, three distinct regimes are identified based on the yielding state at the time of the second load, and closed-form expressions for the asymptotes are derived. The findings offer both fundamental insight and practical tools for constructing conservative failure envelopes without the need for extensive numerical simulations.