引用本文: 唐斌. 连续梁单元动态刚度矩阵数值问题的研究[J]. 力学与实践, 2009, 31(4): 32-36.
TANG Bin. NUMERICAL PROBLEMS IN DYNAMIC STIFFNESS ANALYSIS OF CONTINUOUS BEAM$[J]. MECHANICS IN ENGINEERING, 2009, 31(4): 32-36.  Citation: TANG Bin. NUMERICAL PROBLEMS IN DYNAMIC STIFFNESS ANALYSIS OF CONTINUOUS BEAM$[J]. MECHANICS IN ENGINEERING, 2009, 31(4): 32-36.

## NUMERICAL PROBLEMS IN DYNAMIC STIFFNESS ANALYSIS OF CONTINUOUS BEAM

• 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.

Abstract: The numerical difficulties in dealing with dynamic stiffness matricesfor continuous Bernoulli-Euler beam and continuous Timoshenko beam areanalyzed. The dynamic stiffness matrices of these two beam elements areobtained from their flexural vibration governing partial differentialequations. The independent variables of hyperbolic functions in thesedynamic stiffness matrices are expressed in several variables. Amethod for estimating the reasonable lengths of continuous beams isproposed. A cantilever beam is used as a numerical example. It is modeledwith a single continuous Bernoulli-Euler beam element and a singlecontinuous Timoshenko beam element, respectively. Dynamic responses of thisbeam are analyzed. It is found that when the reasonable sizes of continuousbeams are adopted, the required natural frequencies of engineeringstructures may be obtained without numerical problems in dealing with dynamicstiffness matrices for continuous beams. This researchmay provide a theoretical reference for constructing engineering models byusing continuous beam elements.

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