Analytical Dynamic Analysis under Impulse Loadings Using Laplace Transform

Articles in Press

Document Type : Research Article

Authors

1 Department of Civil Engineering, Bu-Ali Sina University, Hamedan, Iran

2 University of Genoa, Savona compose, Genoa, Italy

Abstract

The application of impulse loading is commonly observed in practice, and accurately estimating the corresponding response through numerical techniques poses significant challenges. This study introduces an analytical formulation to assess the dynamic responses of multi-degree-of-freedom (MDF) beams subjected to impact loading, utilizing the Laplace transform. By focusing on simple beam configurations, this research aims to illuminate previously unexplored aspects of the system's dynamic behavior under impulse loading. Throughout the investigation, any arbitrary or irregular impact loading in the time domain was transformed into the Heaviside step function using the Laplace transform technique. Initially, analytical forced-vibration responses corresponding to the impact loading were mathematically derived. Subsequently, the proposed forced-vibration formulation was validated through laboratory-scale experimental tests. The experimental data were also used to update the finite element model (FEM) for evaluating numerical responses using the Newmark HHT-alpha method under short-time loading. The results indicate that unconditionally stable schemes, such as Newmark HHT-alpha, encounter challenges related to numerical damping, amplitude decay, period elongation, and spurious frequency errors when subjected to impulse loading; however, the proposed method effectively mitigates these errors. The robustness of the proposed method was examined for unusual shock-type loads, and the results demonstrate that the error associated with traditional methods, such as the Newark HHT method is significantly high, with some cases exceeding 300 %.

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AUT Journal of Civil Engineering

Articles in Press, Accepted Manuscript
Available Online from 18 September 2025

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