2109. Accurate prediction approach of dynamic characteristics for a rotating thin walled annular plate considering the centrifugal stress requirement

Zhong Luo1, You Wang2, Jingyu Zhai3, Yunpeng Zhu4

1, 2School of Mechanical Engineering and Automation, Northeastern University, Shenyang, P. R. China

3School of Mechanical Engineering, Dalian University of Technology, Dalian, P. R. China

4Department of Automatic Control and System Engineering, Sheffield University, Sheffield, UK

1Corresponding author

E-mail: 1zhluo@mail.neu.edu.cn, 2wy515077587@163.com, 3zhaijy@dlut.edu.cn, 4yzhu53@sheffield.ac.uk

Received 17 January 2016; received in revised form 15 April 2016; accepted 23 April 2016

Abstract. In allusion to the problem that experimental results of similitude models of a rotating turbine disc predict dynamic characteristics of the prototype, the accurate design method of dynamic similitude models of a rotating thin walled annular plate is investigated by considering the centrifugal stress requirement. The vibration differential equation is employed to deduce geometrically complete scaling laws of dynamic frequency and centrifugal stress. In order to determine accurate distorted scaling laws of dynamic frequency, the sensitivity analysis and determination principle are used. For distorted scaling laws of centrifugal stress, the average approach of candidate distorted scaling laws is proposed, and its mathematical form is simple. Furthermore, the numerical validation indicates that distorted scaling laws can predict dynamic characteristics of the prototype and reflect the strength conditions or even failures of a prototype with good accuracy, and applicable intervals of the distorted scaling law are calculated. Finally, an acceptable procedure of the similitude design method of a rotating thin walled annular plate is provided, which guides to the design of test models considering centrifugal stress requirement.

Keywords: rotating, annular plates, scaling laws, centrifugal stress, sensitivity.

References

[1]        Qin Z. Y., Yan S. Z., Chu F. L. Influence of clamp band joint on dynamic behavior of launching system in ascent flight. Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, Vol. 228, Issue 1, 2014, p. 97‑114.

[2]        Yao M. H., Chen Y. P., Zhang W. Nonlinear vibrations of blade with varying rotating speed. Nonlinear Dynamics, Vol. 68, Issue 4, 2012, p. 487‑504.

[3]        Yao M. H., Zhang W. Using the extended Melnikov method to study multi-pulse chaotic motions of a rectangular thin plate. International Journal of Dynamics and Control, Vol. 2, Issue 3, 2014, p. 365‑385.

[4]        Wang X., Striz A. G., Bert C. W. Free vibration analysis of annular plates by the DQ method. Journal of Sound and Vibration, Vol. 164, Issue 1, 1993, p. 173‑175.

[5]        Wang H. J., Chen Y. R., Chen L. W. Finite element dynamic analysis of rotating orthotropic sandwich annular plates. Composite Structures, Vol. 62, Issue 2, 2003, p. 205‑212.

[6]        Qian Y., Swanson S. R. Experimental measurement of impact response in carbon/epoxy plates. AIAA Journal, Vol. 28, Issue 6, 1990, p. 1069‑1074.

[7]        Simitses G. J., Rezaeepazhand J. Structural similitude and scaling laws for buckling of cross‑ply laminated plates. Journal of Thermoplastic Composite Materials, Vol. 8, Issue 3, 1995, p. 240‑251.

[8]        Rezaeepazhand J., Simitses G. J. Use of scaled-down models for predicting vibration response of laminated plates. Composite Structures, Vol. 30, Issue 4, 1995, p. 419‑426.

[9]        Rezaeepazhand J., Simitses G. J. Design of scaled down models for predicting shell vibration response. Journal of Sound and Vibration, Vol. 195, Issue 2, 1996, p. 301‑311.

[10]     Wu J. J., Cartmell M. P., Whittaker A. R. Prediction of the vibration characteristics of a full-size structure from those of a scale model. Computers and Structures, Vol. 80, Issue 18, 2002, p. 1461‑1472.

[11]     Wu J. J. The complete-similitude scale models for predicting the vibration characteristics of the elastically restrained flat plates subjected to dynamic loads. Journal of Sound and Vibration, Vol. 268, Issue 5, 2003, p. 1041‑1053.

[12]     Singhatanadgid P., Ungbhakorn V. Scaling laws for buckling of polar orthotropic annular plates subjected to compressive and torsional loading. Thin-Walled Structures, Vol. 43, Issue 7, 2005, p. 1115‑1129.

[13]     Singhatanadgid P., Songkhla A. N. An experimental investigation into the use of scaling laws for predicting vibration responses of rectangular thin plates. Journal of Sound and Vibration, Vol. 311, Issue 1, 2008, p. 314‑327.

[14]     Alves M., Oshiro R. E. Scaling impacted structures when the prototype and the model are made of different materials. International Journal of Solids and Structures, Vol. 43, Issue 9, 2006, p. 2744‑2760.

[15]     Oshiro R. E., Alves M. Predicting the behavior of structures under impact loads using geometrically distorted scaled models. Journal of the Mechanics and Physics of Solids, Vol. 60, Issue 7, 2012, p. 1330‑1349.

[16]     Raja V. P., Ramu M., Thyla P. R. Analytical and numerical validation of the developed structural similitude for elastic models. Indian Journal of Engineering and Materials Sciences, Vol. 20, 2013, p. 492‑496.

[17]     Ramu M., Raja V. P., Thyla P. R. Establishment of structural similitude for elastic models and validation of scaling laws. KSCE Journal of Civil Engineering, Vol. 17, Issue 1, 2013, p. 139-144.

[18]     Yazdi A. A., Rezaeepazhand J. Accuracy of scale models for flutter prediction of cross-ply laminated plates. Journal of Reinforced Plastics and Composites, Vol. 30, Issue 1, 2011, p. 45‑52.

[19]     Yazdi A. A. Study nonlinear vibration of cross-ply laminated plates using scale models. Polymer Composites, Vol. 35, Issue 4, 2014, p. 752‑758.

[20]     De Rosa S., Franco F., Meruane V. Similitudes for the structural response of flexural plates. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2015, (in Press).

[21]     Zhu Y. P., Luo Z., Zhao X. Y., Han Q. K. 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: Journal of Mechanical Engineering Science, Vol. 229, Issue 1, 2014, p. 59‑68.

[22]     Luo Z., Zhao X. Y., Zhu Y. P., Li J. Z. Determination method of the structure size interval of dynamic similar models for predicting vibration characteristics of the isotropic sandwich plates. Journal of Vibroengineering, Vol. 16, Issue 2, 2014, p. 608‑622.

[23]     Luo Z., Wang Y., Zhu Y. P., Wang D. Y. The dynamic similitude design method of thin walled structures and experimental validation. Shock and Vibration, 2016, p. 6836183.

[24]     Soedel W. Vibrations of Shells and Plates. Second Edition. Marcel Dekker Inc., New York, 1993.

[25]     Lee I. W., Jung G. H. An efficient algebraic method for the computation of natural frequency and mode shape sensitivities – Part I. Distinct natural frequencies. Computers and Structures, Vol. 62, Issue 3, 1997, p. 429‑435.

[26]     Lee I. W., Jung G. H. An efficient algebraic method for the computation of natural frequency and mode shape sensitivities – Part II. Multiple natural frequencies. Computers and Structures, Vol. 62, Issue 3, 1997, p. 437‑443.