Abstract 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.

中文翻译：

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用标度技术表征受爆炸载荷影响的单自由度系统的响应能量

摘要 针对爆炸加载所做的功，提出了一种表征简化质量弹簧单自由度（SDOF）系统响应能量的能量方法。对单自由度系统的研究包括完全弹性、弹性完全塑性和刚性完全塑性情况。使用缩放技术，响应能量的特征尺度由受到爆炸载荷的自由刚体的响应动能定义，并研究了单自由度系统的无量纲最大能量比（ER）的响应谱。最大 ER = 1 的简单而保守的标准被提议用于损坏评估。分析受三角爆炸载荷影响的完美弹性单自由度系统的派生封闭形式 ER 产生最大 ER 的响应谱。能量法的推导结果得到了现有数据和两种PI图和最大位移响应谱的验证。能量法的显着优势可以确保在开发响应谱和 PI 图时变量之间的一对一关系。对于弹性完美塑性情况，尽管不再提供封闭形式的解决方案，但观察到的最大 ER = 1 得到了广泛接受的数据的验证。对于刚性完美塑性情况，最大 ER = 1 的观察可以通过解析导出。此外，以与最大位移响应谱和PI图的主包络边界相似的概念，引入了次要包络边界用于损伤评估。