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对爆炸荷载作用下的单自由度系统运动微分方程进行求解,推导了弹塑性各阶段运动微分方程的通解,由此得到位移、速度、加速度的时程轨迹表达式。通过对表达式进行分析,得到弹性结构系统产生的最大位移及对应时刻的变化规律,以及弹塑性结构系统在塑性阶段及回弹阶段位移及抗力的变化规律。最后将通解法应用于单层抗爆控制室的设计,并与等效静力方法和动力数值积分方法的计算结果进行比较,验证了该方法的准确性和实用性。
The differential equations of motion of a single degree of freedom system under the action of explosion loads are solved. The general solutions of the differential equations of motion and elasticity at each stage are deduced, and the expressions of time-course trajectories of displacement, velocity and acceleration are obtained. Through the analysis of the expression, the maximum displacement produced by the elastic structure system and the variation law corresponding to the moment are obtained, and the displacement and resistance changes of the elastoplastic structural system in the plastic phase and the rebound phase are obtained. Finally, the general solution is applied to the design of single-layer explosion-proof control room, and compared with the equivalent static method and dynamic numerical method, the accuracy and practicability of the method are verified.