A Semianalytical Method for Nonlinear Vibration of Euler-Bernoulli Beams with General Boundary Conditions

Table 1

Normalized frequency ratio ${\omega }_n/{\omega }_L$ for a simply supported beam.

$A$	$N=9$	$N=11$	$N=13$	Woinowsky-Krieger [1]	Mei [28]
0.1	1.0009	1.0009	1.0009	1.0008	1.0009
0.2	1.0037	1.0037	1.0037	1.0038	1.0037
0.4	1.0149	1.0149	1.0149	1.0150	1.0148
0.6	1.0331	1.0331	1.0334	1.0380	1.0339
0.8	1.0580	1.0581	1.0588	1.0580	1.0578
1.0	1.0891	1.0893	1.0908	1.0890	1.0889
1.5	1.1893	1.1910	1.1932	1.1900	1.1902
2.0	1.3140	1.3201	1.3300	1.3160	1.3022