动边界约束梁在低速冲击下的动力响应

摘要

The dynamic responses of beams with specific constrained condition under low velocity im-pact is analyzed.The mechanical models of beams with flexible boundary constrains are established in this paper.A new method for solving the mode shapes is applied to express the displacement of beams under dif-ferent boundary constrains.Based on formulae for the relationship between contact force and embedding depth,the dynamic equations of beams with flexible boundary constrains under low velocity impact are pro-posed by using Lagrange method.The results indicate that the mode shapes that are solved by the new func-tion are the same as the traditional ones.Vertical elastic constrains have notable influence on displacement and impact forces under low velocity impact.%研究了特定约束条件下梁受低速冲击的动力响应,建立了具有动边界梁的力学模型. 运用一种新的求解振型的方法表示不同边界约束下梁的位移,并根据冲击局部区域的、准静态的接触理论,利用拉格朗日方程建立了低速冲击下动边界梁的动力方程. 研究表明:这种新的表达振型的方法求得的结果与传统方法求得的振型一致;低速冲击条件下,竖向弹性约束对结构位移和撞击力都有显著影响.