Element for Beam Dynamic Analysis Based on Analytical Deflection Trial Function
Table 1
Base frequency of beam free vibration and its comparison (rad/s).
Beam type
Theoretical solution
Dynamic stiffness matrix method
Interpolation trial function element
Analytical trial function element
Absolute value
Relative error (%)
Absolute value
Relative error (%)
Absolute value
Relative error (%)
Cantilever beam
43.8875389
43.8875390
44.0740
0.423
43.8875391
Simply supported beam
123.1941891
123.1941888
136.5902
10.874
123.1941889
One end clamped and another simply supported beam
192.4528355
192.4528348
255.4366
32.727
192.4528349
Clamped-clamped beam
279.2673996
279.2673991
283.4156
1.485
279.2673992
Note: calculation of eigenvalue and eigenvector cannot be conducted due to all DOFs of two ends of clamped-clamped beam being restrained. If the beam is divided into one element, semistructure is used for vibration simulation of clamped-clamped beam.
