弹性基础简支梁的动态分析

摘要

分析了弹性支撑梁固有频率随支撑刚度的变化规律,通过理论计算和有限元计算方法相结合,提出了弹性支撑梁初阶固有频率的简化计算方法。当支撑刚度很低时,系统的第一阶固有频率可以近似按照弹簧质量系统来计算,而初阶弯曲频率接近自由边界条件下梁的弯曲频率。另外对弹性基础梁在瞬态振动条件下的动力响应进行研究;同时随着弹性支撑刚度的变化计算了梁的减振效果,并通过有限元法对计算结果进行验证。%Natural frequency of a supported beam on an elastic foundation is studied,and the variation rules of stiffness with support condition was investigated.By theoretical calculation and the finite element method,the first-order natural frequency calculation method is proposed under elastic supporting condition.When support stiffness is too low,the first-order natural frequency can be approximately calculated according to spring-mass system,while the elementary bending frequency is near the free boundary conditions.We studied dynamic response of elastic foundation beam under transient vibration,calculated the damping effect of the beam with the elastic support stiffness changing,and verified the calculation results through the finite element method.