NUMERICAL PROBLEMS IN DYNAMIC STIFFNESS ANALYSIS OF CONTINUOUS BEAM

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.