Skip Navigation Links
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland


C. Steve Suh (editor)

Texas A&M University, USA


Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China


A Similitude Design Method of Rotating Thin-wall Short Cylindrical Shell Considering Nonlinear Vibration Response

Journal of Vibration Testing and System Dynamics 2(1) (2018) 53--67 | DOI:10.5890/JVTSD.2018.03.006

Zhong Luo$^{1}$,$^{2}$, Yunpeng Zhu$^{3}$, YouWang$^{4}$, FeiWang$^{1}$,$^{2}$, Qingkai Han$^{5}$

$^{1}$ School of Mechanical Engineering & Automation, Northeastern University, Shenyang, China

$^{2}$ Key Laboratory of Vibration and Control of Aero-Propulsion Systems Ministry of Education of China, Northeastern University, Shenyang, Liaoning, China

$^{3}$ Department of Automation Control and System Engineering, University of Sheffield, Sheffield S13JD, UK

$^{4}$ Shenyang Institute of Automation Chinese Academy of Sciences, Shenyang, China

$^{5}$ School of Mechanical Engineering, Dalian University of Technology, Dalian, China

Download Full Text PDF



This study investigates the non-linear dynamic scaling laws for a rotating thin-wall short cylindrical shell. By introducing the geometric non-linear term, corresponding governing equations are employed to establish the non-linear scaling laws. Both the natural frequency and single-point excitation response of the rotating cylindrical shell are investigated. The applicability of the scaling laws of the rotating thin-wall short cylindrical shell is verified numerically. In addition, the scaling laws for linear and non-linear vibrations are compared. Analytical results indicate that the scaled model designed by the non-linear scaling laws are more restrictive than that of using the linear scaling laws. In addition, they predict the characteristics of the prototype with good accuracy.


This work was supported by the National Science Foundation of China under the grant number 11572082; the Fundamental Research Funds for the Central Universities of China under the grant numbers N160312001 and N150304004; and the Excellent Talents Support Program in Institutions of Higher Learning in Liaoning Province of China under the grant number LJQ2015038.


  1. [1]  Qin, Z.Y., Han, Q.K., and Chu, F.L. (2013), Analytical model of bolted disk-drum joints and its application to dynamic analysis of jointed rotor, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228, 646-663.
  2. [2]  Luo, Z., Sun, N., Wang, Y., et al. (2013), Study of vibration characteristics of the short thin cylindrical shells and its experiment, Journal of Vibroengineering, 15(3), 1270-1283.
  3. [3]  Yao, M.H., Chen, Y.P., and Zhang, W. (2012), Nonlinear vibrations of blade with varying rotating speed, Nonlinear Dynamics, 68, 487-504.
  4. [4]  Yao, M.H. and Zhang, W. (2014), Using the extended Melnikov method to study multi-pulse chaotic motions of a rectangular thin plate, International Journal of Dynamics and Control, 2, 365-385.
  5. [5]  Ungbhakorn, V. and Singhatanadgid, P. (2003), Similitude and physical modeling for buckling and vibration of symmetric cross-ply laminated circular cylindrical shells, Journal of Composite Materials, 37(19), 16971712.
  6. [6]  Rezaeepazhand, J., Simitses, G.J., and Starnes, J.H. (1996), Scale models for laminated cylindrical shells subjected to axial compression, Composite Structure, 34(4), 371-379.
  7. [7]  Bijan, D., Suong, H., and Mehdi, H. (2012), Similitude study on bending stiffness and behavior of composite tubes, Journal of Composite Materials, 46(21), 2695-2710.
  8. [8]  Torkamani, S., Navazi, H.M., Jafari, A.A., and et al. (2009), Structural similitude in free vibration of orthogonally stiffened cylindrical shells, Thin-Walled Structures, 47(11), 1316-1330.
  9. [9]  Oshiro, R.E. and Alves, M. (2004), Scaling impacted structures, Archive of applied mechanics, 74(1-2), 130-145.
  10. [10]  Oshiro, R.E. and Alves, M. (2012), Predicting the behaviour of structures under impact loads using geometrically distorted scaled models, Journal of the Mechanics and Physics of Solids, 60(7), 1330-1349.
  11. [11]  Wen, H.M. and Jones, N. (1993), Experimental investigation of the scaling laws for metal plates struck by large masses, International journal of impact engineering, 13(3), 485-505.
  12. [12]  Ungbhakorn, V. and Wattanasakulpong, N. (2007), Structural similitude and scaling laws of anti-symmetric cross-ply laminated cylindrical shells for buckling and vibration experiments, International Journal of Structural Stability and Dynamics, 7(4), 609-627.
  13. [13]  Rezaeepazhand, J., Simitses, G.J., and Starnes, J.H. (1996), Design of scaled down models for predicting shell vibration response, Journal of Sound and Vibration, 195(2), 301-311.
  14. [14]  Leissa, A.W. (1973), Vibration of shells, Scientific and Technical Information Office, National Aeronautics and Space Administration.
  15. [15]  Ganapathi, M. and Varadan, T.K. (1996), Large amplitude vibrations of circular cylindrical shells, Journal of sound and vibration, 192(1), 1-14.
  16. [16]  Li, H.Y., Guo, X.H., Xie, L.Y., and et al. (2009), Precession response analysis of thin rotating circular cylindrical shell considering geometric nonlinearity, Journal of Vibration Engineering, 5, 552-558.
  17. [17]  Liu, J., Li, Y.G., and Guo X.H. (2002), Study on the precession of vibrating shape for circular cylindrical shell, Journal of Vibration and Shock, 3, 61-63.
  18. [18]  Li, Y.Q., Yan, S.Y., and Guo X.H. (2001), Vibration response analysis of circular cylindrical shells, Chinese Journal of Applied Mechanics, 3, 85-90.
  19. [19]  Zhu, Y., Luo, Z., Zhao, X., and Han, Q.K. (2015), Determination method of the structure size interval of dynamically similar models for predicting vibration characteristics of the coated thin plates, Proceedings of the Institution of Mechanical Engineers, Part C:
  20. [20]  Cao, Z, Y. (1983), Theory of Plate and Shell Vibration, Chinese Railway Press. Beijing.
  21. [21]  De, Rosa, S. and Franco, F, A. (2008), Scaling procedure for the response of an isolated system with high modal overlap factor, Mechanical Systems and Signal Processing, 22(7), 1549-1565.
  22. [22]  Huang, S.C. and Soedel, W. (1988), On the forced vibration of simply supported rotating cylindrical shells, The Journal of the Acoustical Society of America, 84(1), 275-285.