Determination method of scaling laws based on least square method and applied to rectangular thin plates and rotor-bearing systems

References

• Adams, C., J. Bös, and E M. Slomski. 2018a. Scaling laws obtained from a sensitivity analysis and applied to thin vibrating structures. Mechanical Systems and Signal Processing 110:590–610. doi:10.1016/j.ymssp.2018.03.032.
   Web of Science ®Google Scholar
• Adams, C., J. Bs, and T. Melz. 2018b. An experimental investigation of vibrating plates in similitude and the possibility to replicate the responses using sensitivity-based scaling laws. In INTER-NOISE and NOISE-CON congress and conference proceedings, Vol. 257, No. 1, 799–810. Institute of Noise Control Engineering.
   Google Scholar
• Ambrus, A., H. J. Skadsem, and R. G. Mihai. 2018. Similarity analysis for downscaling a full size drill string to a laboratory scale test drilling rig. In ASME 2018 37th International Conference on Ocean, Offshore and Arctic Engineering (V008T11A005). American Society of Mechanical Engineers. doi:10.1115/OMAE2018-77202.
   Google Scholar
• Balawi, S., O. Shahid, and M. Al Mulla. 2015. Similitude and scaling laws-static and dynamic behavior beams and plates. Procedia Engineering 114:330–7. doi:10.1016/j.proeng.2015.08.076.
   Google Scholar
• Baxi, C. B., A. Telengator, and J. Razvi. 2012. Rotor scale model tests for power conversion unit of GT-MHR. Nuclear Engineering and Design 251:344–8. doi:10.1016/j.nucengdes.2011.09.060.
   Web of Science ®Google Scholar
• Buckingham, E. 1914. On physically similar systems: Illustrations of the use of dimensional equations. Physical Review 4 (4):345–76. doi:10.1103/PhysRev.4.345.
   Google Scholar
• Cho, U., and K. Wood. 1997. Empirical similitude method for the functional test with rapid prototypes. In 1997 International Solid Freeform Fabrication Symposium, University of Texas, Austin, Texas.
   Google Scholar
• Cho, U., K. L. Wood, and R. H. Crawford. 1998. Online functional testing with rapid prototypes: a novel empirical similarity method. Rapid Prototyping Journal, 4 (3):128–38.
   Google Scholar
• Coutinho, C P., A J. Baptista, and J D. Rodrigues. 2016. Reduced scale models based on similitude theory: A review up to 2015. Engineering Structures 2016 (119):81–94. doi:10.1016/j.engstruct.2016.04.016.
   Google Scholar
• Coutinho, C P., A J. Baptista, and J D. Rodriges. 2018. Modular approach to structural similitude. International Journal of Mechanical Sciences 135:294–312. doi:10.1016/j.ijmecsci.2017.11.005.
   Web of Science ®Google Scholar
• De Rosa, S., F. Franco, and V. Meruane. 2016. Similitudes for the structural response of flexural plates. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230 (2):174–88. doi:10.1177/0954406215572436.
   Web of Science ®Google Scholar
• De Rosa, S., F. Franco, and T. Polito. 2015. Partial scaling of finite element models for the analysis of the coupling between short and long structural wavelengths. Mechanical Systems and Signal Processing 52:722–40. doi:10.1016/j.ymssp.2014.06.007.
   Web of Science ®Google Scholar
• Dutson, A. J., and K. L. Wood. 2002. Foundations and Applications of the Empirical Similitude Method (Esm). Singapore University of Technology and Design.
   Google Scholar
• Ghannadiasl, A., and M. Mofid. 2016. Free vibration analysis of general stepped circular plates with internal elastic ring support resting on Winkler foundation by Green function method. Mechanics Based Design of Structures and Machines 44 (3):212–30. doi:10.1080/15397734.2015.1051228.
   Web of Science ®Google Scholar
• Guo, H., H. Zheng, and X. Zhuang. 2019. Numerical manifold method for vibration analysis of Kirchhoff's plates of arbitrary geometry. Applied Mathematical Modelling 66:695–727. doi:10.1016/j.apm.2018.10.006.
   Web of Science ®Google Scholar
• Kline, SJ. 1965. Similitude and Approximation Theory. New York: Springer-Verlag.
   Google Scholar
• Li, X. 2013. A scaling approach for high-frequency vibration analysis of line-coupled plates. Journal of Sound and Vibration 332 (18):4054–8. doi:10.1016/j.jsv.2013.03.037.
   Web of Science ®Google Scholar
• Li, J., Y. Xue, F. Li, and Y. Narita. 2019b. Active vibration control of functionally graded piezoelectric material plate. Composite Structures 207:509–18. doi:10.1016/j.compstruct.2018.09.053.
   Web of Science ®Google Scholar
• Li, B., H. Ma, X. Yu, J. Zeng, X. Guo, and B. Wen. 2019a. Nonlinear vibration and dynamic stability analysis of rotor-blade system with nonlinear supports. Archive of Applied Mechanics 89 (7):1375–402. doi:10.1007/s00419-019-01509-0.
   Web of Science ®Google Scholar
• Luo, Z., H L. Shi, and X B. Chen. 2015. Dynamic similarity design method of distortion experimental model for multiaxial rotor system. Journal of Northeastern University 36 (4):542–5 and 6.
   Google Scholar
• Luo, Z., Y. Wang, J. Zhai, Y. Zhu, and D. Wang. 2019. Prediction of vibration characteristics of blisks using similitude models. Mechanics Based Design of Structures and Machines 47 (2):121–35. doi:10.1080/15397734.2018.1481427.
   Web of Science ®Google Scholar
• Luo, Z., Y. Wang, Y. Zhu, X. Zhao, and D. Wang. 2016. The similitude design method of thin-walled annular plates and determination of structural size intervals. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 230 (13):2158–68. doi:10.1177/0954406215592055.
   Web of Science ®Google Scholar
• Luo, Z., Y. Zhu, X. Zhao, and D. Wang. 2015a. Determining dynamic scaling laws of geometrically distorted scaled models of a cantilever plate. Journal of Engineering Mechanics 142 (4):04015108. doi:10.1061/(ASCE)EM.1943-7889.0001028.
   Web of Science ®Google Scholar
• Luo, Z., Y. P. Zhu, X. Y. Zhao, and D. Y. Wang. 2015b. High-order vibrations’ dynamic scaling laws of distorted scaled models of thin-walled short cylindrical shells. Mechanics Based Design of Structures and Machines 43 (4):514–34. doi:10.1080/15397734.2015.1044610.
   Web of Science ®Google Scholar
• Miao, H., C. Zang, and M. I. Friswell. 2016. Dynamic similarity design method for an aero-engine dual rotor test rig. Journal of Physics: Conference Series 744 (1):012109. doi:10.1088/1742-6596/744/1/012109.
   Google Scholar
• Qin, Z., X. Pang, B. Safaei, and F. Chu. 2019. Free vibration analysis of rotating functionally graded CNT reinforced composite cylindrical shells with arbitrary boundary conditions. Composite Structures 220:847–60.
   Web of Science ®Google Scholar
• Ramu, M., V. Prabhu Raja, and P. R. Thyla. 2013. Establishment of structural similitude for elastic models and validation of scaling laws. KSCE Journal of Civil Engineering 17 (1):139–44. doi:10.1007/s12205-013-1216-x.
   Web of Science ®Google Scholar
• Rezaeepazhand, J., and G. J. Simitses. 1997. Structural similitude for vibration response of laminated cylindrical shells with double curvature. Composites Part B: Engineering 28 (3):195–200. doi:10.1016/S1359-8368(96)00046-7.
   Web of Science ®Google Scholar
• Rezaeepazhand, J., G.J. Simitses, J. Rezaeepazhand, and G.J. Simitses. 1995. Use of scaled-down models for predicting vibration response of laminated plates. Composite Structures 30 (4):419–26. doi:10.1016/0263-8223(94)00064-6.
   Web of Science ®Google Scholar
• Saltelli, A., K. Chan, and E. M. Scott. 2008. Sensitivity analysis. Chichester: Wiley.
   Google Scholar
• Sun, D. L., and X. F. Li. 2019. Initial value method for free vibration of axially loaded functionally graded Timoshenko beams with nonuniform cross section. Mechanics Based Design of Structures and Machines 47 (1):102–20. doi:10.1080/15397734.2018.1526690.
   Web of Science ®Google Scholar
• Wu, J J. 2003. 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 268 (5):1041–53. doi:10.1016/S0022-460X(03)00303-1.
   Web of Science ®Google Scholar
• Wu, J J. 2004. Vibration of a rectangular plate undergoing forces moving along a circular path. Finite Elements in Analysis and Design 40 (1):41–60. doi:10.1016/S0168-874X(02)00178-6.
   Web of Science ®Google Scholar
• 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. Computers & Structures 84 (3):102–14. doi:10.1016/j.compstruc.2005.09.033.
   Web of Science ®Google Scholar
• Wu, J J. 2007. Prediction of lateral vibration characteristics of a full-size rotor-bearing system by using those of its scale models. Finite Elements in Analysis and Design 43 (10):803–16. doi:10.1016/j.finel.2007.05.001.
   Web of Science ®Google Scholar
• Wu, J. J. 2015. Prediction of the torsional vibration characteristics of a rotor-shaft system using its scale model and scaling laws. World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering 9 (2):229–34.
   Google Scholar
• Wang, Y., and K. H. Chang. 2015. Continuum-based shape sensitivity analysis for 2D coupled atomistic/continuum simulations using bridging scale decomposition. Mechanics Based Design of Structures and Machines 43 (2):232–64. doi:10.1080/15397734.2014.942817.
   Web of Science ®Google Scholar
• Ye, R., L. Wang, X. Hou, Z. Luo, and Q. Han. 2018. Balancing method without trial weights for rotor systems based on similitude scale model. Frontiers of Mechanical Engineering 13 (4):571–80. doi:10.1007/s11465-018-0478-x.
   Web of Science ®Google Scholar
• Young, Y. L. 2010. Dynamic hydroelastic scaling of self-adaptive composite marine rotors. Composite Structures 92 (1):97–106. doi:10.1016/j.compstruct.2009.07.001.
   Web of Science ®Google Scholar
• Zhang, S., L. Xu, and R. Li. 2019. New exact series solutions for transverse vibration of rotationally-restrained orthotropic plates. Applied Mathematical Modelling 65:348–60. doi:10.1016/j.apm.2018.08.033.
   Web of Science ®Google Scholar
• Zhao, J., Q. Wang, X. Deng, K. Choe, R. Zhong, and C. Shuai. 2019. Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions. Composites Part B: Engineering 168:106–20. doi:10.1016/j.compositesb.2018.12.044.
   Web of Science ®Google Scholar
• Zeng, J., K. Chen, H. Ma, T. Duan, and B. Wen. 2019. Vibration response analysis of a cracked rotating compressor blade during run-up process. Mechanical Systems and Signal Processing 118:568–83. doi:10.1016/j.ymssp.2018.09.008.
   Web of Science ®Google Scholar
• Żur, K. K. 2016. Green's function for frequency analysis of thin annular plates with nonlinear variable thickness. Applied Mathematical Modelling 40 (5-6):3601–19. doi:10.1016/j.apm.2015.10.014.
   Web of Science ®Google Scholar
• Żur, K. K. 2018. Quasi-Green’s function approach to free vibration analysis of elastically supported functionally graded circular plates. Composite Structures 183:600–10. doi:10.1016/j.compstruct.2017.07.012.
   Web of Science ®Google Scholar