Characterization with scaling techniques on response energy of a single degree of freedom system subject to blast loading

摘要

In terms of work done by blast loading, an energy method to characterize response energy of a simplified mass spring single-degree-of-freedom (SDOF) system is proposed. The study on the SDOF system includes perfectly elastic, elastic perfectly-plastic, and rigid perfectly-plastic cases. With scaling techniques, a characteristic scale of response energy is defined by the response kinetic energy of a free rigid body subject to blast loading, and response spectra of a dimensionless maximum energy ratio (ER) are investigated for the SDOF system. A simple and conservative criterion of maximum ER = 1 is proposed for damage assessment. Analyzing the derived closed form ER for the perfectly elastic SDOF system subject to triangular blast loading yields the response spectra of maximum ER. The derived results with the energy method are validated by available data and two methods of P-I diagrams and the response spectra of the maximum displacements. The distinct advantage of the energy method can ensure the one-to-one relationship between variables in developing the response spectra and P-I diagrams. For the elastic perfectly-plastic case, the observation of maximum ER = 1 is validated with well-accepted data, although closed-form solutions are no longer available. For the rigid perfectly-plastic case, the observation of maximum ER =1 can be derived analytically. In addition, with a similar concept to primary envelope boundaries of the response spectra of the maximum displacements and P-I diagrams, the secondary envelope boundary is introduced for damage assessment.