Surrogate impulse ground motion for practical simulation of critical nonlinear structural responses

Impulse-based representations of earthquake ground motions provide an efficient framework for evaluating critical nonlinear structural responses. However, the direct use of ideal impulse ground motions expressed by Dirac’s delta function may excite all eigenmodes with identical amplitude and phase, thereby producing unrealistically amplified floor acceleration and velocity responses and leading to numerical difficulties in nonlinear time-history response analyses. This paper proposes a surrogate impulse ground motion with finite duration for the practical simulation of critical elastic–plastic responses. The surrogate impulse is constructed as a weighted sum of Chebyshev polynomials, and its coefficients are determined by minimizing response discrepancies at the termination of excitation for many models with diverse dynamic characteristics. The proposed formulation preserves the essential characteristics of impulse-based critical excitation while suppressing super-high-frequency components. Numerical investigations demonstrate that the surrogate impulse accurately reproduces displacement responses obtained from conventional impulse inputs while substantially reducing unrealistic acceleration and velocity amplification. Applications to a multi-story elastic–plastic building model under surrogate double and multi impulse inputs confirm that maximum displacement responses are well captured without inducing excessive floor responses. The proposed method provides a practical and robust framework for critical nonlinear response evaluation under pulse-type and long-duration ground motions.