Simplified equivalent SDOF system for predicting complex dynamic response of 1D and 2D elements under nonuniform dynamic load

The dynamic response of blast-loaded structural elements includes multiple modes of vibrations. An equivalent Single Degree of Freedom (SDOF) system is a popular fast-running engineering tool for design to capture the global behavior of the structural element, assuming a single and dominant Mode of Vibration (MOV). Typical models include a nonuniform load or a concentrated load at the midspan. In a close-in detonation scenario, the dominant mode of vibration differs from uniform loading. This paper develops an equivalent SDOF system to account for a nonuniform dynamic load. A literature review on the characteristics of the dynamic load from close-in detonation is provided. The non-uniform load is used to develop transformation factors based on the uniformity of the load. Next, a simplified approach is analytically developed, where the load is assumed to be uniform, allowing for a simpler system to be solved (similar to common practices in design manuals and commercial software). An equivalent uniform load is applied to achieve the same peak displacement. The method has also been developed for the noncentral detonation of 1D members. The method presented in the paper is validated with detailed Multi-Degree-of-Freedom (MDOF) models of one and 2D elements.