A Chebyshev Spectral Method with Null Space Approach for Boundary-Value Problems of Euler-Bernoulli Beam

Table 4

The first three dimensionless natural frequencies of a cantilever cone beam with tip-mass, the rotatory inertia of mass, and its eccentricity at the left end (β₁=0, β₂=0, β₃→∞, β₄→∞, and μ_R = δ_R = γ_R = δ_L =0).

γL	α	μL
			Present	(Ref. [7])	Present	(Ref. [7])	Present	(Ref. [7])
0.0	1.2	0.2	1.805113	1.805116	4.531398	4.531399	7.682832	7.682833
		2.0	1.180606	1.180605	4.242896	4.242897	7.478641	7.478641
	2.0	0.2	2.392504	2.392498	5.375541	5.375538	8.914098	8.914100
		2.0	1.485717	1.485704	5.108411	5.108415	8.760282	8.760286
0.3	1.2	0.2	1.759466	1.759470	3.493511	3.493510	5.666955	5.666955
		2.0	1.122790	1.122787	2.228089	2.228088	5.079316	5.079316
	2.0	0.2	2.268671	2.268663	3.648412	3.648385	6.290178	6.290136
		2.0	1.363150	1.363162	2.253308	2.253207	5.818125	5.818075
0.6	1.2	0.2	1.634321	1.634324	2.779848	2.779846	5.472033	5.472032
		2.0	0.991768	0.991773	1.795564	1.795562	5.051224	5.051225
	2.0	0.2	1.954460	1.954460	3.049005	3.048977	6.199510	6.199473
		2.0	1.124889	1.124886	1.935342	1.935209	5.807056	5.807008