Analytical Expressions for Frequency and Buckling of Large Amplitude Vibration of Multilayered Composite Beams

Table 1

Comparison of the frequency ratio of the isotropic single layer beam with simple end conditions for different amplitude ratio.

𝑊max	For Slender beams without considering shear deformation and rotary inertia			𝜂=𝐿/𝑟
	Ref. [1]	Ref. [13]	Ref. [14]	10		25		50		100
				Ref. [15]	Present	Ref. [15]	Present	Ref. [15]	Present	Ref. [15]	Present
1	1.0892	1.0891	1.0897	1.11162 (7)^a	1.1121	1.09253 (5)	1.0940	1.08971 (5)	1.0908	1.08900 (5)	1.0900
2	1.3178	1.3177	1.3229	1.37006 (16)	1.3721	1.32130 (8)	1.3268	1.31425 (7)	1.3264	1.31249 (7)	1.3230
3	1.6257	1.6256	1.6394	1.68839 (47)	1.6981	1.61464 (14)	1.6245	1.60520 (11)	1.6057	1.60295 (11)	1.6399
4	1.9761	—	—	—	2.2190	—	2.0366	—	2.0092	—	2.0023

^aNumbers in the parentheses indicate the number of iterations required to achieve an accuracy of 10⁻⁶ in the evaluation of non-dimensional nonlinear frequency.