Free Vibration Analysis of a Rotating Composite Shaft Using the 𝑝-Version of the Finite Element Method

Table 3

The critical speed of the graphite-epoxy composite shaft.

𝐿=2.47m, 𝐷=12.69cm, 𝑒=1.321mm, 10 layers of equal thickness (90^∘, 45^∘, −45^∘, 0^∘6, 90^∘), 𝑘𝑠=0.503
	Theory or method	First critical
		speed (rpm)
Bert and Kim [22]	Sanders shell theory	5349
	Donnell shallow shell theory	5805
	Bernoulli-Euler beam theory	5302
	Bresse-Timoshenko beam theory	5113
M.-Y. Chang et al. [6]	Continuum-based Timoshenko beam theory	5197
Present	Timoshenko beam theory by the 𝑝-version	5200
	of the finite element method