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Date of Publication:2009-01-01
Journal:力学与实践
Affiliation of Author(s):能源与动力学院
Volume:31
Issue:4
Page Number:32-36
ISSN No.:1000-0879
Abstract: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.
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