双模量悬臂梁在线性分布荷载作用下的Kantorovich解

基于双模量悬臂梁在分布载荷作用下发生弯曲变形时,会形成各向同性的拉伸区和压缩区,为此,将双模量悬臂梁看成2种各向同性材料组成的层合梁,采用弹性理论建立双模量悬臂梁在均布载荷作用下的静力平衡方程,利用静力平衡方程确定双模量悬臂梁的中性面位置。在此基础上,利用Kantorovich法研究分布载荷作用下双模量悬臂梁的平面应力问题,推导出悬臂梁的应力公式,并将该应力公式计算结果与有限元法计算结果进行比较,以验证双模量悬臂梁的应力公式的可靠性。研究结果表明:在分布载荷作用下,双模量悬臂梁的平面应力问题不宜采用相同弹性模量弹性理论计算,而应该采用双模量弹性理论计算。     

The theoretical analysis of dynamic response on cantilever beam of variable stiffness

The paper presents the theoretical analysis of a variable stiffness beam. The bending stiffness EI varies continuously along the length of the beam. Dynamic equation yields differential equation with variable co- efficients based on the model of the Euler-Bernoulli beam. Then differential equation with variable coefficients becomes that with constant coefficients by variable substitution. At last, the study obtains the solution of dy- namic equation. The cantilever beam is an object for analysis. When the flexural rigidity at free end is a constant and that at clamped end is varied, the dynamic characteristics are analyzed under several cases. The results dem- onstrate that the natural angular frequency reduces as the fiexural rigidity reduces. When the rigidity of clamped end is higher than that of free end, low-level mode contributes the larger displacement response to the total re- sponse. On the contrary, the contribution of low-level mode is lesser than that of hi~h-level mode.     

悬臂梁质量摆杆结构一阶模态减振控制分析

为了分析悬挂小球和摆杆对悬臂梁一阶模态振动的减振效果,采用Hamilton原理建立了悬臂梁质量摆杆减振结构的动力学模型.小球通过摆杆与支架连接,支架放置在悬臂梁顶端,以小球和摆杆的质量为分析参数,进行了一阶模态的减振控制分析.理论分析表明,当悬臂梁作一阶模态振动时,质量摆杆结构起到了很好的减振效果,并且小球起主要的减振作用.     

网状结构PDO血管内支架的抗弯刚度及体外降解性能

以4种直径的聚对二氧杂环己酮(PDO)单丝为原料,采用手工编织法制备网状结构血管内支架.采用悬臂梁法对PDO血管内支架的抗弯刚度进行测试及分析,研究单丝直径及编织头数与支架抗弯刚度的关系.对PDO单丝及支架进行体外降解试验,研究单丝的力学性能及支架抗弯刚度在降解过程中的变化情况.试验结果表明:采用悬臂梁法可以有效测量支架的抗弯刚度;PDO支架的抗弯刚度随单丝直径及编织头数的增大而增大;PDO单丝降解10星期后基本丧失力学性能;PDO支架的抗弯刚度能保持10星期左右,随后发生断裂及解体,失去抗弯能力.     

悬臂梁在横向荷载下的力学响应分析

从能量的角度出发,考虑弹性梁轴线伸长的基础上,建立Euler-Bernoulli梁在横向机械载荷作用下的几何非线性数学模型。结合Hamilton变分原理和Kantorovich时间平均法得到了梁的非线性自由振动的无量纲常微分控制方程组。采用打靶法,求得了悬臂梁的弯曲变形和自由振动的数值解,并对数值结果进行了分析。