Determining Dynamic Scaling Laws of Geometrically Distorted Scaled Models of a Cantilever Plate
Publication: Journal of Engineering Mechanics
Volume 142, Issue 4
Abstract
This study investigates new dynamic scaling laws of geometrically distorted models in predicting the dynamic characteristics of a cantilever plate. The significance of this study is to provide new scaling laws and rules for selecting dynamic scaling laws, which guide the design of distorted models. By considering the size effect of different orders’ vibration, a governing equation and the method of sensitivity analysis are employed to establish dynamic scaling laws between the model and the prototype. Both approximate and accurate scaling laws are investigated and the processes for determining these scaling laws are summarized. After that, a commonly used titanium alloy plate is analyzed as a prototype to compare the accuracy of the approximate scaling laws and the accurate scaling laws. Finally, the applicability of these new scaling laws is validated by experimental data. The results indicate that, by using the new scaling laws, the distorted models can predict the characteristics of the titanium alloy plate prototype with good accuracy.
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Acknowledgments
The authors gratefully acknowledge the financial support from the Fundamental Research Funds for the Central Universities of China (Grants N130503001 and N140301001); the Key Laboratory for Precision & Non-traditional Machining of Ministry of Education, Dalian University of Technology (Grant JMTZ201602); and the Excellent Talents Support Program in Institutions of Higher Learning in Liaoning Province of China (Grant LJQ2015038).
References
De Rosa, S., and Franco, F. (2008). “A scaling procedure for the response of an isolated system with high modal overlap factor.” Mech. Syst. Sig. Process., 22(7), 1549–1565.
De Rosa, S., Franco, F., and Meruane, V. (2015). “Similitudes for the structural response of flexural plates.” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., in press.
Krayterman, B., and Sabnis, G. M. (1984). “Similitude theory: Plates and shells analysis.” J. Eng. Mech., 1247–1263.
Lee, W., and Jung, G. H. (1997a). “An efficient algebraic method for the computation of natural frequency and mode shape sensitivities: Part I, distinct natural frequencies.” Comput. Struct., 62(3), 429–435.
Lee, W., and Jung, G. H. (1997b). “An efficient algebraic method for the computation of natural frequency and mode shape sensitivities: Part II, multiple natural frequencies.” Comput. Struct., 62(3), 437–443.
Luo, Z., Zhao, X. Y., Zhu, Y. P., and Li, J. Z. (2014a). “Determination method of the structure size interval of dynamic similar models for predicting vibration characteristics of the isotropic sandwich plates.” J Vibroeng, 16(2), 608–622.
Luo, Z., et al. (2015). “Determination method of dynamic distorted scaling laws and applicable structure size intervals of a rotating thin-wall short cylindrical shell.” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 229(5), 806–817.
Oshiro, R. E., and Alves, M. (2004). “Scaling impacted structures.” Arch. Appl. Mech., 74(1–2), 130–145.
Oshiro, R. E., and Alves, M. (2006). “Scaling impacted structures when the prototype and the model are made of different materials.” Int. J. Solids. Struct., 43(9), 2744–2760.
Oshiro, R. E., and Alves, M. (2007). “Scaling of cylindrical shells under axial impact.” Int. J. Impact. Eng., 34(1), 89–103.
Oshiro, R. E., and Alves, M. (2009). “Scaling of structures subject to impact loads when using a power law constitutive equation.” Int. J. Solids. Struct., 46(18–19), 3412–3421.
Oshiro, R. E., and Alves, M. (2012). “Predicting the behaviour of structures under impact loads using geometrically distorted scaled models.” J. Mech. Phys. Solids., 60(7), 1330–1349.
Qian, Y., and Swanson, S. R. (1990). “Experimental measurement of impact response in carbon/epoxy plates.” AIAA J., 28(6), 1069–1074.
Qian, Y., Swanson, S. R., Nuismer, R. J., and Bucinell, R. B. (1990). “An experimental study of scaling rules for impact damage in fiber composites.” J. Compos. Mater., 24(5), 559–570.
Ramu, M., Raja, V. P., and Thyla, P. R. (2013). “Establishment of structural similitude for elastic models and validation of scaling laws.” KSCE J. Civ. Eng., 17(1), 139–144.
Rezaeepazhand, J., Simitses, G. J., and Starnes, J. H. (1996a). “Design of scaled down models for predicting shell vibration response.” J. Sound. Vib., 195(2), 301–311.
Rezaeepazhand, J., Simitses, G. J., and Starnes, J. H. (1996b). “Scale models for laminated cylindrical shells subjected to axial compression.” Compos. Struct., 34(4), 371–379.
Rezaeepazhand, J., and Yazdi, A. A. (2011). “Similitude requirements and scaling laws for flutter prediction of angle-ply composite plates.” Compos. Part B: Eng., 42(1), 51–56.
Simitses, G. J., and Rezaeepazhand, J. (1992). “Structural similitude and scaling laws for laminated beam-plates.” Proc., Sessions, ASME Summer Mechanics and Materials Conf., ASME, New York.
Simitses, G. J., and Rezaeepazhand, J. (1995). “Structural similitude and scaling laws for buckling of cross-ply laminated plates.” J. Thermoplast. Compos., 8(3), 240–251.
Simitses, G. J., Starnes, J. H., and Rezaeepazhand, J. (2002). “Structural similitude and scaling laws for plates and shells: A review.” Advances in the mechanics of plates and shells, Springer, Netherlands, 295–310.
Singhatanadgid, P., and Ungbhakorn, V. (2002). “Scaling laws for vibration response of anti-symmetrically isotropic laminated plates.” Struct. Eng. Mech., 14(3), 345–364.
Soedel, W. (2004). Vibrations of shells and plates, CRC Press, London.
Sun, J., Arteaga, I. L., and Kari, L. (2013). “Dynamic modeling of a multilayer rotating blade via quadratic layerwise theory.” Compos. Struct., 99(1), 276–287.
Ungbhakorn, V., and Singhatanadgid, P. (2003). “Similitude invariants and scaling laws for buckling experiments on anti-symmetrically isotropic laminated plates subjected to biaxial loading.” Compos. Struct., 59(4), 455–465.
Wilson, J. F. (2014). “Similitude laws and small-scale model experiments characterizing dynamic failures of flawed utility poles.” ASME J. Mech. Des., 136(9), 091401.
Wu, J. J. (2005). “Dynamic analysis of a rectangular plate under a moving line load using scale beams and scaling laws.” Compos. Struct., 83(19), 1646–1658.
Wu, J. J. (2006). “Prediction of the dynamic characteristics of an elastically supported full-size flat plate from those of its complete-similitude scale model.” Compos. Struct., 84(3), 102–114.
Yoo, H. H., and Kim, S. K. (2002). “Free vibration analysis of rotating cantilever plates.” AIAA J., 40(11), 2188–2196.
Zhu, Y. P., Luo, Z., Zhao, X. Y., and Han, Q. K. (2014). “Determination method of the structure size interval of dynamically similar models for predicting vibration characteristics of the coated thin plates.” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 229(1), 59–68.
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Published In
Journal of Engineering Mechanics
Volume 142 • Issue 4 • April 2016
Copyright
© 2015 American Society of Civil Engineers.
History
Received: May 3, 2015
Accepted: Sep 14, 2015
Published online: Dec 17, 2015
Published in print: Apr 1, 2016
Discussion open until: May 17, 2016
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