×
Wei, Kexiang; Zhang, Wenming; Xia, Ping; Liu, Yingchun

Nonlinear dynamics of an electrorheological sandwich beam with rotary oscillation. (English) Zbl 1264.74146

J. Appl. Math. 2012, Article ID 659872, 17 p. (2012).
Summary: The dynamic characteristics and parametric instability of a rotating electrorheological (ER) sandwich beam with rotary oscillation are numerically analyzed. Assuming that the angular velocity of an ER sandwich beam varies harmonically, the dynamic equation of the rotating beam is first derived based on Hamilton’s principle. Then the coupling and nonlinear equation is discretized and solved by the finite element method. The multiple scales method is employed to determine the parametric instability of the structures. The effects of electric field on the natural frequencies, loss factor, and regions of parametric instability are presented. The results obtained indicate that the ER material layer has a significant effect on the vibration characteristics and parametric instability regions, and the ER material can be used to adjust the dynamic characteristics and stability of the rotating flexible beams.

Cited in 1 Document

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H55 Stability of dynamical problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
PDF BibTeX XML Cite
\textit{K. Wei} et al., J. Appl. Math. 2012, Article ID 659872, 17 p. (2012; Zbl 1264.74146)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] J. Chung and H. H. Yoo, “Dynamic analysis of a rotating cantilever beam by using the finite element method,” Journal of Sound and Vibration, vol. 249, no. 1, pp. 147-164, 2002.
[2] A. A. Al-Qaisia, “Dynamics of a rotating beam with flexible root and flexible hub,” Structural Engineering and Mechanics, vol. 30, no. 4, pp. 427-444, 2008.
[3] S. Y. Lee, S. M. Lin, and Y. S. Lin, “Instability and vibration of a rotating Timoshenko beam with precone,” International Journal of Mechanical Sciences, vol. 51, no. 2, pp. 114-121, 2009. · Zbl 1264.74092
[4] H. Arvin and F. Bakhtiari-Nejad, “Non-linear modal analysis of a rotating beam,” International Journal of Non-Linear Mechanics, vol. 46, no. 6, pp. 877-897, 2011.
[5] B. A. H. Abbas, “Dynamic stability of a rotating Timoshenko beam with a flexible root,” Journal of Sound and Vibration, vol. 108, no. 1, pp. 25-32, 1986.
[6] T. H. Young and T. M. Lin, “Stability of rotating pretwisted, tapered beams with randomly varying speeds,” Journal of Vibration and Acoustics, Transactions of the ASME, vol. 120, no. 3, pp. 784-790, 1998.
[7] S. C. Sinha, D. B. Marghitu, and D. Boghiu, “Stability and control of a parametrically excited rotating beam,” Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME, vol. 120, no. 4, pp. 462-469, 1998. · Zbl 0899.93021
[8] J. Chung, D. Jung, and H. H. Yoo, “Stability analysis for the flapwise motion of a cantilever beam with rotary oscillation,” Journal of Sound and Vibration, vol. 273, no. 4-5, pp. 1047-1062, 2004.
[9] O. Turhan and G. Bulut, “Dynamic stability of rotating blades (beams) eccentrically clamped to a shaft with fluctuating speed,” Journal of Sound and Vibration, vol. 280, no. 3-5, pp. 945-964, 2005.
[10] D. Younesian and E. Esmailzadeh, “Non-linear vibration of variable speed rotating viscoelastic beams,” Nonlinear Dynamics, vol. 60, no. 1-2, pp. 193-205, 2010. · Zbl 1189.74049
[11] K. Wei, G. Meng, W. Zhang, and S. Zhou, “Vibration characteristics of rotating sandwich beams filled with electrorheological fluids,” Journal of Intelligent Material Systems and Structures, vol. 18, no. 11, pp. 1165-1173, 2007.
[12] M. V. Gandhi, B. S. Thompson, and S. B. Choi, “A new generation of innovative ultra-advanced intelligent composite materials featuring electro-rheological fluids: an experimental investigation,” Journal of Composite Materials, vol. 23, no. 12, pp. 1232-1255, 1989.
[13] C. Y. Lee and C. C. Cheng, “Dynamic characteristics of sandwich beam with embedded electro-rheological fluid,” Journal of Intelligent Material Systems and Structures, vol. 9, no. 1, pp. 60-68, 1998.
[14] T. Fukuda, T. Takawa, and K. Nakashima, “Optimum vibration control of CFRP sandwich beam using electro-rheological fluids and piezoceramic actuators,” Smart Materials and Structures, vol. 9, no. 1, pp. 121-125, 2000.
[15] S. B. Choi, “Electric field-dependent vibration characteristics of a plate featuring an electrorheological fluid,” Journal of Sound and Vibration, vol. 234, no. 4, pp. 705-712, 2000.
[16] J. Y. Yeh, L. W. Chen, and C. C. Wang, “Dynamic stability of a sandwich beam with a constrained layer and electrorheological fluid core,” Composite Structures, vol. 64, no. 1, pp. 47-54, 2004.
[17] Z. F. Yeh and Y. S. Shih, “Critical load, dynamic characteristics and parametric instability of electrorheological material-based adaptive beams,” Computers and Structures, vol. 83, no. 25-26, pp. 2162-2174, 2005.
[18] K. X. Wei, G. Meng, S. Zhou, and J. Liu, “Vibration control of variable speed/acceleration rotating beams using smart materials,” Journal of Sound and Vibration, vol. 298, no. 4-5, pp. 1150-1158, 2006.
[19] M. Yalcintas and J. P. Coulter, “Electrorheological material based adaptive beams subjected to various boundary conditions,” Journal of Intelligent Material Systems and Structures, vol. 6, no. 5, pp. 700-717, 1995.
[20] M. Yalcintas and J. P. Coulter, “Electrorheological material based non-homogeneous adaptive beams,” Smart Materials and Structures, vol. 7, no. 1, pp. 128-143, 1998.
[21] E. H. K. Fung and D. T. W. Yau, “Vibration characteristics of a rotating flexible arm with ACLD treatment,” Journal of Sound and Vibration, vol. 269, no. 1-2, pp. 165-182, 2004.
[22] H. Saito and K. Otomi, “Parametric response of viscoelastically supported beams,” Journal of Sound and Vibration, vol. 63, no. 2, pp. 169-178, 1979. · Zbl 0395.73058
[23] H. H. Yoo and S. H. Shin, “Vibration analysis of rotating cantilever beams,” Journal of Sound and Vibration, vol. 212, no. 5, pp. 807-808, 1998.
[24] H. Y. Hu, Applied Nonlinear Dynamics, Press of Aeronautical Industries, Beijing, China, 2000.
[25] T. H. Tan, H. P. Lee, and G. S. B. Leng, “Parametric instability of spinning pretwisted beams subjected to spin speed perturbation,” Computer Methods in Applied Mechanics and Engineering, vol. 148, no. 1-2, pp. 139-163, 1997. · Zbl 0924.73097
[26] C. Y. Lin and L. W. Chen, “Dynamic stability of a rotating beam with a constrained damping layer,” Journal of Sound and Vibration, vol. 267, no. 2, pp. 209-225, 2003.
[27] D. L. Don, An investigation of electrorheological material adaptive structure [M.S. thesis], Lehigh University, Bethlehem, Pa, USA, 1993.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.