FE-Meshfree QUAD4 Element with Modified Radial Point Interpolation Function for Structural Dynamic Analysis

Table 8

First 12 natural frequencies (×10⁴ Hz) of a cantilever beam using irregular nodal distribution (50 × 5 elements).

Method						Reference (ABAQUS QUAD8)
FEM-QUAD4	0.0830	0.0831	0.0834	0.0835	0.0838	0.0822
	0.4989	0.4992	0.5016	0.5019	0.5036	0.4931
	1.2827	1.2827	1.2827	1.2827	1.2827	1.2823
	1.3168	1.3176	1.3243	1.3245	1.3297	1.2990
	2.3992	2.4007	2.4114	2.4139	2.4242	2.3607
	3.6701	3.6725	3.6914	3.6963	3.7096	3.6002
	3.8467	3.8468	3.8470	3.8470	3.8471	3.8442
	5.0697	5.0728	5.0974	5.1059	5.1249	4.9566
	6.4062	6.4063	6.4072	6.4072	6.4074	6.3897
	6.5590	6.5643	6.5999	6.6089	6.6360	6.3972
	8.1119	8.1186	8.1651	8.1733	8.2060	7.8719
	8.9562	8.9565	8.9528	8.9585	8.9606	8.9331
FE-Meshfree (QS, )	0.0823	0.0822	0.0822	0.0822	0.0822	0.0822
	0.4937	0.4937	0.4936	0.4936	0.4936	0.4931
	1.2826	1.2826	1.2825	1.2824	1.2822	1.2823
	1.3010	1.3010	1.3008	1.3009	1.3010	1.2990
	2.3655	2.3655	2.3655	2.3655	2.3661	2.3607
	3.6094	3.6092	3.6098	3.6095	3.6113	3.6002
	3.8450	3.8450	3.8445	3.8444	3.8441	3.8442
	4.9716	4.9715	4.9722	4.9728	4.9755	4.9566
	6.3984	6.3984	6.3978	6.3974	6.3966	6.3897
	6.4116	6.4114	6.4126	6.4142	6.4179	6.3972
	7.9019	7.9017	7.9043	7.9039	7.9110	7.8719
	8.9347	8.9346	8.9337	8.9333	8.9331	8.9331