摘要
针对连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵,分析了在使用连续梁单元进行结构动态特性分析中的数值问题,基于连续梁单元的运动方程,导出了连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵,分析了影响动态刚度矩阵中双曲函数自变量的各个独立变量及其产生的影响,并给出了初估连续梁单元合理长度的方法,使用单一连续Bernoulli-Euler和Timoshenko梁单元的动态刚度矩阵分别进行了悬臂梁频响曲线的数值求解,研究表明,在合理选择连续梁单元的长度时,大多数工程结构的动态特性分析中都不会产生数值问题.
The numerical difficulties in dealing with dynamic stiffness matrices for continuous Bernoulli-Euler beam and continuous Timoshenko beam are analyzed. The dynamic stiffness matrices of these two beam elements are obtained from their flexural vibration governing partial differential equations. The independent variables of hyperbolic functions in these dynamic stiffness matrices are expressed in several variables. A method for estimating the reasonable lengths of continuous beams is proposed. A cantilever beam is used as a numerical example. It is modeled with a single continuous Bernoulli-Euler beam element and a single continuous Timoshenko beam element, respectively. Dynamic responses of this beam are analyzed. It is found that when the reasonable sizes of continuous beams are adopted, the required natural frequencies of engineering structures may be obtained without numerical problems in dealing with dynamic stiffness matrices for continuous beams. This research may provide a theoretical reference for constructing engineering models by using continuous beam elements.
出处
《力学与实践》
CSCD
北大核心
2009年第4期32-36,共5页
Mechanics in Engineering
基金
大连理工大学青年教师培养基金资助项目(20070020)
