A Hybrid Finite Element-Fourier Spectral Method for Vibration Analysis of Structures with Elastic Boundary Conditions

Table 2

Comparison of computing time of the hybrid method with pure FEM and FEM with different truncated Fourier terms and/or FEM element numbers, in which a completely free-free beam structure is used.

Method	FSM truncated; term,	FEM element; number,	The 20th modal frequency	Degrees of freedom	Computing time (s)
Analytical	—	—	19.50000000	—	—
FSM	80	—	19.50000044	85	0.016
FEM	—	600	19.50000073	1202	9.235
Hybrid	40	300	19.49999961	647	7.66
FSM	60	—	19.5000032	65	0.016
FEM	—	500	19.50000153	1002	5.133
Hybrid	30	250	19.50000005	537	3.947
FSM	50	—	19.5000114	55	0.015
FEM	—	250	19.50002436	502	0.64
Hybrid	25	125	19.50001615	282	0.499
FSM	30	—	19.50046727	35	<0.01
FEM	—	100	19.50094026	202	0.047
Hybrid	15	50	19.50069514	122	0.031