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

Table 2

The critical speed of the boron-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)
Zinberg and Symonds [1]	Measured experimentally	6000
	EMBT	5780
dos Reis et al. [2]	Bernoulli-Euler beam theory with stiffness	4942
	determined by shell finite elements
Kim and Bert [4]	Sanders shell theory	5872
Bert [23]	Donnell shallow shell theory	6399
Bert and Kim [22]	Bernoulli-Euler beam theory	5919
	Bresse-Timoshenko beam theory	5788
Gupta and Singh [3]	EMBT	5747
	LBT	5620
M.-Y. Chang et al. [6]	Continuum-based Timoshenko beam theory	5762
Present	Timoshenko beam theory by the 𝑝-version	5760
	of the finite element method