用线性振动比拟法研究不同模量梁的冲击问题

Study on impact problem of different modulus beam by linear vibration analogy

把被冲击的拉压弹性模量不同的梁简化为集中质量与轻质弹簧相连接的单自由度弹性系统,使重物对梁的冲击问题转化为重物对具有集中质量单自由度弹性系统的冲击问题,然后采用动力学方程推导出了重物对梁的冲击时间、动载荷系数的函数表达式,克服了能量法仅能给出最大动载荷系数的不足.通过算例分析指出,有关材料力学教材及专著给出的最大动载荷系数公式,仅是动力学方程推导出的动载荷系数函数式的特例.当拉压弹性模量相差较大时,不能把重物对拉压弹性模量不同梁的冲击问题简单地作为重物对单弹性模量梁的冲击问题处理,必须考虑拉压弹性模量不同的因素对梁冲击的影响.

The impact of heavy weight on tensile and compressive elastic modulus of different beams is studied in this paper. By simplifying these different beams as single degree of freedom elastic system of concentrated mass connected with no spring, the impact on the beams is converted to the impact on the single degree of freedom elastic system with concentrated mass. And then by dynamic equation, the impact time and the function expression of dynamic load coefficient is derived and the defects of energy method, which can only give the factor of dynamic load, is conquered as well. Through the analysis of numerical examples, the paper shows that the maximum dynamic load coefficient formula given by the textbooks of related mechanics and monographs is only a special case of dynamic load coefficient function derived by dynamic equation. When the difference of elastic modulus in tension and compression is large, the impact of heavy weight on that of different beams cannot be simply considered as the impact of weight on beams of single elastic modulus, but different factors affecting the impact of tensile and compressive elastic modulus on beams must be taken into account.