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Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration

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Abstract

In this paper, the large-amplitude (geometrically nonlinear) vibrations of rotating, laminated composite circular cylindrical shells subjected to radial harmonic excitation in the neighborhood of the lowest resonances are investigated. Nonlinearities due to large-amplitude shell motion are considered using the Donnell’s nonlinear shallow-shell theory, with account taken of the effect of viscous structure damping. The dynamic Young’s modulus which varies with vibrational frequency of the laminated composite shell is considered. An improved nonlinear model, which needs not to introduce the Airy stress function, is employed to study the nonlinear forced vibrations of the present shells. The system is discretized by Galerkin’s method while a model involving two degrees of freedom, allowing for the traveling wave response of the shell, is adopted. The method of harmonic balance is applied to study the forced vibration responses of the two-degrees-of-freedom system. The stability of analytical steady-state solutions is analyzed. Results obtained with analytical method are compared with numerical simulation. The agreement between them bespeaks the validity of the method developed in this paper. The effects of rotating speed and some other parameters on the nonlinear dynamic response of the system are also investigated.

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Abbreviations

\(c\) :

The coefficient of damping of the shell

\(A_{ij} \) :

Tensile stiffness

\(B_{ij} \) :

Coupling stiffness

\(D_{ij} \) :

Bending stiffness

\(E_k (\omega )\) :

The Young’s modulus of each lamina of the shell

\(F(t)\) :

External excitation

\(h\) :

The wall thickness of the shell

\(L\) :

The length of the shell

\(m \) :

The number of axial half-waves

\(n\) :

The number of circumferential waves

\(R\) :

The middle-surface radius of the shell

\(t \) :

Time

\(\delta \) :

The Dirac delta function

\(\mu _k \) :

The Poisson’s ratio of each lamina of the shell

\(\rho _k \) :

The mass density of each lamina of the shell

\(\omega \) :

The radian frequency of external excitation

\(\omega _{m,n} \) :

The linear radian frequency corresponding to the mode (\(m,\,n\))

\(\omega _n \) :

The angular velocity of the shell

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (Project no. 11302046 and 11172063).

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  1. Institute of Applied Mechanics, Northeastern University, Shenyang, 110819, China

    Yan Qing Wang

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  1. Yan Qing Wang
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Correspondence to Yan Qing Wang.

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Wang, Y.Q. Nonlinear vibration of a rotating laminated composite circular cylindrical shell: traveling wave vibration. Nonlinear Dyn 77, 1693–1707 (2014). https://doi.org/10.1007/s11071-014-1410-5

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