Abstract
Rotating structural components are omnipresent in engineering structures and natural world. This work investigates the effects of the centrifugal and Coriolis forces on the free vibrational characteristics of soft cylinders rotating with respect to the axis of symmetry based on the nonlinear elasticity and linear incremental theories. The formulations indicate that the biasing deformation, instantaneous elastic moduli, and incremental equations of motion strongly depend on the rotating speed. The characteristic equation for the natural frequency is derived using the state-space method and approximate laminate technique. The numerical examples included in this work demonstrate that the centrifugal and Coriolis forces might have significant effects on the vibrational characteristics of the cylinder. Results of this work will benefit the design and control of novel engineering systems with rotating soft cylinders or shafts.
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References
P. Zhang, and Z. Wu, Asian J. Water Environ. Pollut. 2, 27 (2005).
R. J. Mair, Géotechnique 58, 695 (2008).
H. Zhao, L. Shao, and J. F. Chen, Chem. Eng. J. 156, 588 (2010).
G. Clément, npj Microgr. 3, 29 (2017).
W. Yang, H. T. Wang, T. F. Li, and S. X. Qu, Sci. China-Phys. Mech. Astron. 62, 14601 (2019).
D. Wu, Y. J. Yin, H. M. Xie, Y. F. Shang, C. W. Li, L. F. Wu, and X. L. Dai, Sci. China-Phys. Mech. Astron. 57, 637 (2014).
S. Mora, and F. Richard, Int. J. Solids Struct. 167, 142 (2019).
D. Galic, and C. O. Horgan, J. Appl. Mech. 70, 426 (2003).
W. Q. Chen, and K. Y. Lee, J. Strain Anal. Eng. Des. 39, 437 (2004).
D. Guo, Z. Zheng, and F. Chu, Int. J. Solids Struct. 39, 725 (2002).
S. Sun, D. Cao, and Q. Han, Int. J. Mech. Sci. 68, 180 (2013).
S. Hosseini-Hashemi, M. R. Ilkhani, and M. Fadaee, Int. J. Mech. Sci. 76, 9 (2013).
Y. H. Dong, Y. H. Li, D. Chen, and J. Yang, Compos. Part B-Eng. 145, 1 (2018).
H. Y. Fang, J. S. Yang, and Q. Jiang, Int. J. Solids Struct. 39, 5241 (2002).
P. Chadwick, C. F. M. Creasy, and V. G. Hart, J. Aust. Math. Soc. Ser. B Appl. Math. 20, 62 (1977).
D. M. Haughton, and R. W. Ogden, J. Mech. Phys. Solids 28, 59 (1980).
D. M. Haughton, and R. W. Ogden, Q. J. Mech. Appl. Math. 33, 251 (1980).
J. Wang, A. Althobaiti, and Y. Fu, J. Mech. Mater. Struct. 12, 545 (2017).
A. Dorfmann, R. W. Ogden, and G. Saccomandi, Int. J. Solids Struct. 42, 3700 (2005).
Y. Anani, and G. H. Rahimi, Int. J. Mech. Sci. 108–109, 122 (2016).
F. Richard, A. Chakrabarti, B. Audoly, Y. Pomeau, and S. Mora, Proc. R. Soc. A 474, 20180242 (2018).
S. Mora, Nonlin. Dyn. 100, 2089 (2020).
A. Ertepinar, J. Sound Vib. 86, 343 (1983).
A. Ertepinar, J. Sound Vib. 93, 457 (1984).
D. M. Haughton, J. Sound Vib. 97, 107 (1984).
A. Dorfmann, and R. W. Ogden, J. Elast. 82, 99 (2006).
A. Dorfmann, and R. W. Ogden, IMA J. Appl. Math. 75, 603 (2010).
L. Dorfmann, and R. W. Ogden, Phil. Trans. R. Soc. A. 377, 20180077 (2019).
B. Wu, Y. Su, W. Chen, and C. Zhang, J. Mech. Phys. Solids 99, 116 (2017).
H. J. Ding, and W. Q. Chen, Three Dimensional Problems of Piezoelasticity (Nova Science Publishers, New York, 2001). p. 58.
W. Q. Chen, and H. J. Ding, The state-space method and its application in analyses of FGM structures, in Mechanics of Functionally Graded Materials and Structures, edited by Z. Zhong, L. Wu, and W. Q. Chen, (Nova Science Publishers, New York, 2012). pp. 139–178.
B. Wu, Y. Su, D. Liu, W. Chen, and C. Zhang, J. Sound Vib. 421, 17 (2018).
C. Moler, and C. van Loan, SIAM Rev. 45, 3 (2003).
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 51988101, 11925206, and 11772295).
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Li, K., Zhang, Y., Zhan, H. et al. Vibrational characteristics of rotating soft cylinders. Sci. China Phys. Mech. Astron. 64, 254611 (2021). https://doi.org/10.1007/s11433-020-1665-9
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DOI: https://doi.org/10.1007/s11433-020-1665-9