Lower bound of performance index of anti-sway control of a pendulum using on-off damping radial spring-damper

La Duc Viet, Nguyen Trong Kien
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Coriolis damping, anti-sway control, analytical optimization, on-off damping, optimal bound


An on-off damping radial spring-damper can be attached to a pendulum to suppress its nonlinear sway motion. This paper studies the class of on-off damping controller, which switches the damping level from high to low and back at fixed times every quarter of period. Among this class, this paper shows the solution of the lower bound controller producing the lowest amplitude-frequency curve. The lower bound curve shows some fundamental natures of the system and gives some useful directions for a good on-off damping controller.


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D. H. Bich and N. X. Nguyen. Nonlinear vibration of functionally graded circular cylindrical shells based on improved Donnell equations. Journal of Sound and Vibration, 331, (25), (2012), pp. 5488–5501. https://doi.org/10.1016/j.jsv.2012.07.024. https://doi.org/10.1016/j.jsv.2012.07.024.">

Y. W. Kim. Free vibration analysis of FGM cylindrical shell partially resting on Pasternak elastic foundation with an oblique edge. Composites Part B: Engineering, 70, (2015), pp. 263–276. https://doi.org/10.1016/j.compositesb.2014.11.024. https://doi.org/10.1016/j.compositesb.2014.11.024.">

N. D. Duc and P. T. Thang. Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations. Aerospace Science and Technology, 40, (2015), pp. 115–127. https://doi.org/10.1016/j.ast.2014.11.005. https://doi.org/10.1016/j.ast.2014.11.005.">

N. D. Duc, N. D. Tuan, P. Tran, N. T. Dao, and N. T. Dat. Nonlinear dynamic analysis of Sigmoid functionally graded circular cylindrical shells on elastic foundations using the third order shear deformation theory in thermal environments. International Journal of Mechanical Sciences, 101, (2015), pp. 338–348. https://doi.org/10.1016/j.ijmecsci.2015.08.018. https://doi.org/10.1016/j.ijmecsci.2015.08.018.">

R. Bahadori and M. M. Najafizadeh. Free vibration analysis of two-dimensional functionally graded axisymmetric cylindrical shell on Winkler–Pasternak elastic foundation by First-order Shear Deformation Theory and using Navier-differential quadrature solution methods. Applied Mathematical Modelling, 39, (16), (2015), pp. 4877–4894. https://doi.org/10.1016/j.apm.2015.04.012. https://doi.org/10.1016/j.apm.2015.04.012.">

D. H. Bich, D. V. Dung, and V. H. Nam. Nonlinear dynamical analysis of eccentrically stiffened functionally graded cylindrical panels. Composite Structures, 94, (8), (2012), pp. 2465–2473. https://doi.org/10.1016/j.compstruct.2012.03.012. https://doi.org/10.1016/j.compstruct.2012.03.012.">

D. H. Bich, D. V. Dung, V. H. Nam, and N. T. Phuong. Nonlinear static and dynamic buckling analysis of imperfect eccentrically stiffened functionally graded circular cylindrical thin shells under axial compression. International Journal of Mechanical Sciences, 74, (2013), pp. 190–200. https://doi.org/10.1016/j.ijmecsci.2013.06.002. https://doi.org/10.1016/j.ijmecsci.2013.06.002.">

B. Mirzavand, M. R. Eslami, and J. N. Reddy. Dynamic thermal postbuckling analysis of shear deformable piezoelectric-FGM cylindrical shells. Journal of Thermal Stresses, 36, (3), (2013), pp. 189–206. https://doi.org/10.1080/01495739.2013.768443. https://doi.org/10.1080/01495739.2013.768443.">

N. D. Duc and P. T. Thang. Nonlinear response of imperfect eccentrically stiffened ceramic–metal–ceramic FGM thin circular cylindrical shells surrounded on elastic foundations and subjected to axial compression. Composite Structures, 110, (2014), pp. 200–206. https://doi.org/10.1016/j.compstruct.2013.11.015. https://doi.org/10.1016/j.compstruct.2013.11.015.">

N. D. Duc, P. T. Thang, N. T. Dao, and H. V. Tac. Nonlinear buckling of higher deformable S-FGM thick circular cylindrical shells with metal–ceramic–metal layers surrounded on elastic foundations in thermal environment. Composite Structures, 121, (2015), pp. 134–141. https://doi.org/10.1016/j.compstruct.2014.11.009. https://doi.org/10.1016/j.compstruct.2014.11.009.">

D. H. Bich, N. X. Nguyen, and H. V. Tung. Postbuckling of functionally graded cylindrical shells based on improved Donnell equations. Vietnam Journal of Mechanics, 35, (1), (2013), pp. 1–15. https://doi.org/10.15625/0866-7136/35/1/2894. https://doi.org/10.15625/0866-7136/35/1/2894.">

V. H. Nam, N. T. Phuong, D. H. Bich, and D. V. Dung. Nonlinear static and dynamic buckling of eccentrically stiffened functionally graded cylindrical shells under axial compression surrounded by an elastic foundation. Vietnam Journal of Mechanics, 36, (1), (2014), pp. 27–47. https://doi.org/10.15625/0866-7136/36/1/3470. https://doi.org/10.15625/0866-7136/36/1/3470.">

G. G. Sheng and X. Wang. Thermomechanical vibration analysis of a functionally graded shell with flowing fluid. European Journal of Mechanics-A/Solids, 27, (6), (2008), pp. 1075–1087. https://doi.org/10.1016/j.euromechsol.2008.02.003. https://doi.org/10.1016/j.euromechsol.2008.02.003.">

G. G. Sheng and X. Wang. Dynamic characteristics of fluid-conveying functionally graded cylindrical shells under mechanical and thermal loads. Composite Structures, 93, (1), (2010), pp. 162–170. https://doi.org/10.1016/j.compstruct.2010.06.004. https://doi.org/10.1016/j.compstruct.2010.06.004.">

Z. Iqbal, M. N. Naeem, N. Sultana, S. H. Arshad, and A. G. Shah. Vibration characteristics of FGM circular cylindrical shells filled with fluid using wave propagation approach. Applied Mathematics and Mechanics, 30, (11), (2009), pp. 1393–1404. https://doi.org/10.1007/s10483-009-1105-x. https://doi.org/10.1007/s10483-009-1105-x.">

A. G. Shah, T. Mahmood, M. N. Naeem, and S. H. Arshad. Vibrational study of fluid-filled functionally graded cylindrical shells resting on elastic foundations. ISRN Mechanical Engineering, 2011, (2011), pp. 1–13. https://doi.org/10.5402/2011/892460. https://doi.org/10.5402/2011/892460.">

F. M. A. da Silva, R. O. P. Montes, P. B. Goncalves, and Z. J. G. N. Del Prado. Nonlinear vibrations of fluid-filled functionally graded cylindrical shell considering a time-dependent lateral load and static preload. Journal of Mechanical Engineering Science, 230, (1), (2016), pp. 102–119. https://doi.org/10.1177/0954406215587729. https://doi.org/10.1177/0954406215587729.">

H. L. Dai, W. F. Luo, T. Dai, and W. F. Luo. Exact solution of thermoelectroelastic behavior of a fluid-filled FGPM cylindrical thin-shell. Composite Structures, 162, (2017), pp. 411–423. https://doi.org/10.1016/j.compstruct.2016.12.002. https://doi.org/10.1016/j.compstruct.2016.12.002.">

P. V. Khuc, B. H. Dao, and D. X. Le. Analysis of nonlinear thermal dynamic responses of sandwich functionally graded cylindrical shells containing fluid. Journal of Sandwich Structures & Materials, (2017), pp. 1–22. https://doi.org/10.1177/1099636217737235. https://doi.org/10.1177/1099636217737235.">

D. O. Brush and B. O. Almroth. Buckling of bars, plates, and shells. McGraw-Hill, New York, (1975).

A. S. Volmir. The nonlinear dynamics of plates and shells. Science edition, Moscow, (1975).

B. Budiansky and R. S. Roth. Axisymmetric dynamic buckling of clamped shallow spherical shells. NASA Technical Note, 510, (1962), pp. 597–606.

H. Huang and Q. Han. Nonlinear dynamic buckling of functionally graded cylindrical shells subjected to time-dependent axial load. Composite Structures, 92, (2), (2010), pp. 593–598. https://doi.org/10.1016/j.compstruct.2009.09.011. https://doi.org/10.1016/j.compstruct.2009.09.011.">




How to Cite

L. D. Viet and N. T. Kien, Lower bound of performance index of anti-sway control of a pendulum using on-off damping radial spring-damper, Vietnam J. Mech. 41 (2019) 193–201. DOI: https://doi.org/10.15625/0866-7136/13625.



Research Article