ENHANCEMENT OF THE IMPULSE METHOD FOR THE ANALYSIS OF SINGLE-DEGREE-OF-FREEDOM SYSTEMS UNDER DYNAMIC LOADS

Abstract

The article presents an improved impulse-based method for analyzing single-degree-of-freedom systems subjected to short-term dynamic actions, such as impact or explosion. The classical impulse method is widely used in engineering practice for simplified assessment of instantaneous loads, where the impulse energy is transmitted to the structure as an increment of velocity. However, this approach provides accurate results only when the duration of the impulse is very short compared to the system’s natural period. When the load duration is comparable to or longer than the natural vibration period, the computational method requires refinement. The study proposes an enhanced impulse approach that allows the evaluation of the dynamic response of the system without performing numerical time integration. The loading is considered in the form of a decaying triangular pulse, representing a typical time history of pressure generated by an impact or blast wave. Analytical analysis of an undamped single-mass system is carried out, and a correction coefficient is introduced to account for the influence of the impulse duration on the maximum displacement amplitude. It is shown that the proposed methodology provides a smooth transition between instantaneous impulse action and quasi-static loading, producing accurate results over a wide range of ratios between the impulse duration and the natural vibration period. A comparative analysis for a simply supported beam was conducted, demonstrating that the use of the correction coefficient significantly improves the agreement between the analytical estimate of maximum displacement and results obtained from numerical integration. The analysis revealed that the classical impulse method underestimates peak displacements for moderate impulse durations, whereas the proposed methodology ensures consistency with exact solutions across the entire range of ratios. The results of the comparison confirmed the efficiency of the approach for practical structural design, particularly when evaluating the effects of short-term impact and blast loads on beams with various support conditions. The proposed method simplifies the engineering analysis of the dynamic behavior of structural elements, reduces the volume of numerical calculations, and provides high accuracy in determining maximum deformations and displacements. Its use is suitable for assessing the safety and dynamic stability of structures under short-duration loads and can be further extended to multi-modal systems and more complex structural configurations. The study results can serve as a basis for developing standardized engineering guidelines and methodological approaches to the design of building elements considering dynamic effects of impulse loads.