NUMERICAL PROBLEMS IN DYNAMIC STIFFNESS ANALYSIS OF CONTINUOUS BEAM
连续梁单元动态刚度矩阵数值问题的研究

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.