Free and Forced Vibration Analysis in Abaqus Based on the Polygonal Scaled Boundary Finite Element Method

Table 1

The first five natural frequencies (Hz) of a horizontal soil foundation.

Method	Element size (m)	Degrees of freedom	Natural frequencies (Hz)					Relative error (%)
			Mode 1	Mode 2	Mode 3	Mode 4	Mode 5
Analytical solution	—	—	0.3467	1.0401	1.7334	2.4268	3.1202	—
FEM	0.5	126	0.3466	1.0377	1.7223	2.3964	3.0556	1.623
	0.25	410	0.3467	1.0395	1.7307	2.4192	3.1040	0.407
	0.1	1458	0.3467	1.0400	1.7330	2.4256	3.1176	0.065
	0.05	8442	0.3467	1.0400	1.7333	2.4265	3.1195	0.017
PSBFEM	0.5	164	0.3468	1.0416	1.7406	2.4466	3.1623	1.057
	0.25	644	0.3467	1.0404	1.7349	2.4308	3.1286	0.212
	0.1	3998	0.3467	1.0401	1.7336	2.4273	3.1213	0.027
	0.05	15998	0.3467	1.0401	1.7334	2.4268	3.1205	0.007