摘要
首先运用广义函数建立了轴向力作用下含任意不连续点的弹性基础Euler(欧拉)梁的自由振动的统一微分方程.不连续点的影响由广义函数(Dirac delta函数)引入梁的振动方程.微分方程运用Laplace变换方法求解;与传统方法不同的是,该文方法求得的模态函数为整个不连续梁的一般解.由于模态函数的统一化以及连续条件的退化,特征值的求解得到了极大地简化.最后,以梁-质量块模型和轴向力作用下弹性基础裂纹梁模型为例验证了该文方法的正确性与有效性.
The general governing differential equations for the vibration of elastic foundation EulerBernoulli beams with different discontinuities subject to axial forces were established based on generalized functions. For each discontinuity at a given location, a basic modal dis placement function （ Dirac delta function） starting at that location was introduced. The differen tial equations were then solved by means of Laplace transformation. Unlike the classical vibra tion solutions to problems of beams with discontinuities, the generalized solution was in a sin gle unified expression for the whole beam. Due to unification of the modal function and degen eration of the compatibility conditions, solution of the eigenvalues was greatly simplified. Final ly, the free vibration problems of （a） an elastic foundation beam with multiple masses and cor responding rotary inertias, and （ b ） an elastic foundation beam with multiple cracks under axial force, were solved with the proposed method. Results show that the present method is accurate and effecient for free vibration analysis of beams with different discontinuities.
出处
《应用数学和力学》
CSCD
北大核心
2014年第1期81-91,共11页
Applied Mathematics and Mechanics
基金
国家自然科学基金(51265037)
教育部留学回国人员科研启动基金
江西省高校科技落地计划项目(KJLD12075)
江西省教育厅科技项目(GJJ13524)~~
关键词
自由振动
广义函数
轴向力
弹性基础
不连续梁
free vibration
generalized function
axial force
elastic foundation
beam withdiscontinuity
