Elsevier

Applied Mathematical Modelling

Volume 95, July 2021, Pages 593-611
Applied Mathematical Modelling

Buckling and free vibration of eccentric rotating CFRP cylindrical shell base on FSDT

https://doi.org/10.1016/j.apm.2021.02.029Get rights and content

Highlights

  • The dynamic model of an eccentric rotating CFRP cylindrical shell using FSDT is established for the first time.

  • The buckling and free vibration analyses of the eccentric rotating CFRP cylindrical shell are presented.

  • Taking into account the influences of coriolis and centrifugal forces caused by eccentric rotation.

  • The critical bucking mode of the shell alters from (1, 1) to (2, 1) with the increase of rotating speed.

Abstract

In this paper, the dynamic model of an eccentric rotating carbon fiber reinforced polymer (CFRP) laminated cylindrical shell based on the first-order shear deformation theory is established for the first time. The buckling and free vibration analyses of the eccentric rotating CFRP laminated cylindrical shell under the axial excitation are presented. Taking into account the influences of Coriolis force and centrifugal force caused by eccentric rotation. By utilizing the Hamilton principle, the first-order shear deformation theory and the von-Karman type nonlinear geometric relationship, a system of the partial differential governing equations for the eccentric rotating CFRP laminated cylindrical shell is derived. Then, the ordinary differential equations of the eccentric rotating CFRP laminated cylindrical shell are obtained according to Galerkin method. The present method are validated by carrying out some comparisons with the existing results in the published literatures. The natural frequencies and critical buckling loads of the system are solved numerically. In this study, the influences of the eccentric distance, ratio of radius to length, rotating speed as well as the number of layers of the eccentric rotating CFRP laminated cylindrical shell on the buckling and free vibration behaviors are discussed.

Introduction

Due to the ultra-high material properties, e.g., strong corrosion resistance, light weight, high strength and high heat resistance, carbon fiber reinforced polymer structures have been widely used in the aerospace, automobile, ship and other engineering fields. Recently, the superduper mechanical properties of the CFRP structures had attracted many scholars widely attention to ensure their reliability and expand their applications [1], [2], [3]. As we all know that the rotating cylindrical shell structure is a kind of important structural unit in many engineering communities, such as space annular antenna, aircraft, centrifugal separator and missile [4,5]. But the eccentric rotation is unavoidable in practical engineering. And the cylindrical shell structure is often used in the middle part of actual machinery. At this point, the two ends of the cylindrical shell will be compressed by the two end parts. Therefore, it is necessary to study the buckling and vibration behaviors of the eccentrically rotating shell under the axial compression.

More and more researchers paid attention to the carbon fiber reinforced polymer structures because of their superduper mechanical properties. Kolanua et al. [6] investigated the stability and failure behavior of composite panels subject to bonded blade stiffener which reinforced with carbon fiber under the compression load. The critical loads of the delamination behavior and an approximate displacement curve of a CFRP plate subjected to low-velocity impacts are investigated by Salvetti et al. [7]. Using DIC and SEM, Cui et al. [8] investigated fracture mechanism and failure process of the electromagnetic riveted joints which reinforced with carbon fiber subject to the high speed load.

Combining experimental test, theoretical method and finite element simulation, the stress capacity and deformation of the CFRP cloud picture were investigated by Zhang et al. [9]. Bambach et al. [10,11] presented plastic mechanism and experiment researches on the post-buckling behaviors of the SHS tubes with bonded CFRP under the axial load. Liu et al. [12] investigated the mechanical characteristics and failure modes of the aluminum honeycomb filled square tube reinforced with carbon fiber. Poul et al. [13] performed the experimental tests to explore the shear strengthening of a steel plate strengthened with CFRP which subject to the quasi-static load. Juntanalikit et al. [14] investigated the strengthening of the CFRP jacketing, numerically and experimentally. Reuter et al. [15] presented numerical and experimental researches on the shear strength of the GFRP tube structure. The fire stability was studied by Timme et al. [16] on the CFRP shell structure with the test setup of intermediate-scale.

There are amounts of literatures investigating the free vibration and buckling of the rotating circular cylindrical shell structures. The influences of the magnetic field, electrical potential, rotation speed, thickness to radios ratio, axial and circumferential wave numbers on free vibration of the rotating FGP-FRP cylindrical shell were investigated by Meskini and Ghasemi [17]. Ghasemi and Meskini [18,19] investigated the free vibration characteristics of the rotating porous laminated cylindrical shell and metal-fiber thin laminate cylindrical shell with the simply-supported boundary condition based on the Love's shell theory. Qin et al. [20] provided an approach to study the free vibrations of the rotating cylindrical shell reinforced with the carbon nanotube subject to the arbitrary boundary conditions. They evaluated the effects of boundary conditions, the volume fractions of carbon nanotube and the geometric parameters on the free vibration. The free vibrations of rotating cylindrical shells by using the theoretical method were investigated by Karroubi and Irani-Rahaghi [21].

SafarPour et al. [22] investigated free vibration and buckling of the rotating piezoelectric cylindrical shell reinforced with carbon nanotube. Wagner et al. [23] presented the numerical and experimental studies for the thin cylindrical shells under the axial compression load with two kinds of loading imperfections. Zaczynska et al. [24] investigated the buckling behavior of the composite cylindrical reinforced by carbon-fiber shell subject to the impulsive axial compression loading. Kiani et al. [25], [26], [27], [28] made a lot of important researches on the free vibration and thermal buckling of the conical shells and cylindrical shells. These studies are very meaningful for the theoretical research and engineering application. The static and free vibration analysis and the buckling analyses of the sandwich cylindrical shell and panel with functionally graded (FG) core and viscoelastic interface had been presented by Alibeigloo et al. [29], [30].

There are amounts of literatures and references investigating the dynamic characteristic of the rotating cylindrical shell structures. Liew et al. [31] investigated the stability of the rotating cylindrical shell subject to the static and the periodic axial loads by using the Ritz method and the Bolotin first approximation. Han et al. [32] investigated the dynamic instability of a cylindrical shell with periodic axial load and time varying rotating speeds by utilizing the Donnell shell theory. The nonlinear dynamic model and the amplitude-frequency responses were studied by Sun and Liu [33] for a thin rotating cylindrical shell. Using the first-order shear theory, Yao et al. [34] established the model of the persisted cylindrical shells with the presetting angle for of the aero-engine compressor blade, investigated the nonlinear dynamic responses of the shell. Sheng and Wang [35] investigated the nonlinear vibration of the rotating FG cylindrical shell under the thermal environment by using Hamilton principle.

Considering the influences of the Coriolis force and the centrifugal force, Sun et al. [36] studied the nonlinear travelling wave vibrations of a thin rotating cylindrical shell. Han et al. [37] studied the dynamic instability of the thin cylindrical shells with the time varying periodical rotating speed. By using the approximate analytical solution and numerical method, Wang et al. [38,39] studied the nonlinear vibrations of the rotating circular cylindrical shells subjected to the harmonic excitation. Then, Wang [40] investigated the nonlinear vibrations in the neighborhood of the lowest resonances for the rotating laminated cylindrical shells under the radial excitation. Shen et al. [41,42] studied the nonlinear vibrations of a FGM cylindrical shell under the elastic medium.

At present, a large number of scholars have analyzed the free vibration, buckling and dynamics of rotating circular cylindrical shell structures. Nevertheless, few scholars had paid attention to the eccentric rotating cylindrical shell structures. Based on Hamilton principle and Flügge's thin shell theory, Wu et al. [43] analyzed the free vibration of the eccentric rotating thin cylindrical shells with the simply-supported boundary condition. For further study, we present the buckling and free vibration analyses of the eccentric rotating CFRP laminated cylindrical shell with axial excitation. The effects of the centrifugal force and Coriolis force caused by eccentric rotation are taken into account. Based on Hamilton principle, FSDT and von-Karman nonlinear relations, we establish the dynamic model of the eccentric rotating CFRP laminated cylindrical shell, which can be expressed as the ordinary differential equations via Galerkin method. In this study, the influences of the eccentric distance, rotating speed, ratio of radius to length as well as the number of layers of the eccentric rotating CFRP laminated cylindrical shell on the buckling and free vibration behaviors are discussed.

Section snippets

Formulation of eccentric rotating cylindrical shell model

An eccentric rotating CFRP laminated cylindrical shell is considered which include the middle surface radius R, uniform thickness h, length L, central axis X and axis of rotation X1, as shown in Fig. 1. Fig. 1(a) represent the model of the eccentric rotating CFRP laminated cylindrical shell, Fig. 1(b) is the sectional drawing on the plane (θ,  z) of the cylindrical shell. The distance between the centralaxis X (the red dotted line) and axis of rotation X1 (the blue dotted line) of the eccentric

Free vibration analysis

In this section, the natural frequency analyses of the eccentric rotating CFRP laminated cylindrical shell are investigated. For the free vibration, one set the axial excitation to zero and ignore the damping term in Eq. (30). We assume a set of periodic solution which can be expressed byumn(t)=umn0eiωt,vmn(t)=vmn0eiωt,wmn(t)=wmn0eiωt,φxmn(t)=φxmn0eiωt,φθmn(t)=φθmn0eiωt,where i=1, ω is the natural frequency of vibration and umn0, vmn0, wmn0, φxmn0 and φθmn0 are the amplitude of the system.

Buckling analysis

For buckling analysis, one assume all the inertia terms in Eq. (30) are zero. Thus, the algebraic equations are obtained as[s11s12s13s14s15s21s22s23s24s25s31s32s33+s^33s34s35s41s42s43s44s45s51s52s53s54s55]{umnvmnwmnφxmnφθmn}=0,where s^33=Γ3R3π4(30m3n36m3n24m3n5)p0, and Γ3=1LR3π(48mn560mn3+12mn). All other coefficients can be seen in Appendix B.

Setting the value of the determinant of the coefficient matrix in the above Eq. (33) to be 0, the buckling loads p0 of the eccentric rotating CFRP

Conclusions

This paper focuses on buckling and free vibration analyses of the eccentric rotating CFRP laminated cylindrical shell with the axial excitation. Taking into account the influences of Coriolis force and centrifugal force caused by eccentric rotation. By utilizing the Hamilton principle, the first-order shear deformation theory and the von-Karman type nonlinear geometric relationship, the system of the partial differential governing equations for the eccentric rotating CFRP laminated cylindrical

Acknowledgments

The authors gratefully acknowledge the supports of National Natural Science Foundation of China (NNSFC) through grant Nos. 12002057, 11872127 and 11832002, Scientific Research Project of Beijing Educational Committee No. KM202111232023, Qin Xin Talents Cultivation Program, Beijing Information Science & Technology University QXTCP A201901.

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