0
Research Papers

Nonlinear Vibrations of Buried Rectangular Plate

[+] Author and Article Information
Guangyang Hong

Department of Mechanics,
Northeastern University,
Shenyang 110819, China
e-mail: 1113125092@qq.com

Jian Li

Department of Mechanics,
Northeastern University,
Shenyang 110819, China
e-mail: jianli@mail.neu.edu.cn

Zhicong Luo

Department of Mechanics,
Northeastern University,
Shenyang 110819, China
e-mail: luozhitiancai@163.com

Hongying Li

Department of Mechanics,
Northeastern University,
Shenyang 110819, China
e-mail: lihy@mail.neu.edu.cn

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 20, 2017; final manuscript received February 22, 2018; published online April 20, 2018. Assoc. Editor: Alper Erturk.

J. Vib. Acoust 140(5), 051010 (Apr 20, 2018) (7 pages) Paper No: VIB-17-1505; doi: 10.1115/1.4039538 History: Received November 20, 2017; Revised February 22, 2018

We perform an investigation on the vibration response of a simply supported plate buried in glass particles, focusing on the nonlinear dynamic behaviors of the plate. Various excitation strategies, including constant-amplitude variable-frequency sweep and constant-frequency variable-amplitude sweep are used during the testing process. We employ the analysis methods of power spectroscopy, phase diagramming, and Poincare mapping, which reveal many complicated nonlinear behaviors in the dynamic strain responses of an elastic plate in granular media, such as the jump phenomena, period-doubling bifurcation, and chaos. The results indicate that the added mass, damping, and stiffness effects of the granular medium on the plate are the source of the nonlinear dynamic behaviors in the oscillating plate. These nonlinear behaviors are related to the burial depth of the plate (the thickness of the granular layer above plate), force amplitude, and particle size. Smaller particles and a suitable burial depth cause more obvious jump and period-doubling bifurcation phenomena to occur. Jump phenomena show both soft and hard properties near various resonant frequencies. With an increase in the excitation frequency, the nonlinear added stiffness effect of the granular layer makes a transition from strong negative stiffness to weak positive stiffness.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Aranson, I. S. , and Tsimring, L. S. , 2005, “ Patterns and Collective Behavior in Granular Media: Theoretical Concepts,” Rev. Mod. Phys., 78(2), pp. 641–692. [CrossRef]
Gandhi, P. , Knobloch, E. , and Beaume, C. , 2015, “ Localized States in Periodically Forced Systems,” Phys. Rev. Lett., 114(3), p. 034102. [CrossRef] [PubMed]
Aoki, K. M. , Akiyama, T. , Yamamoto, K. , and Yoshikawa, T. , 1997, “ Experimental Study on the Mechanism of Convection Modes in Vibrated Granular Beds,” Europhys. Lett., 40(2), pp. 159–164. [CrossRef]
Lee, J. , 1998, “ Subharmonic Motion of Particles in a Vibrating Tube,” Phys. Rev. E, 58(2), pp. 1218–1221. [CrossRef]
Jiang, Z. H. , Wang, Y. Y. , and Wu, J. , 2007, “ Subharmonic Motion of Granular Particles Under Vertical Vibrations,” Europhys. Lett., 74(3), pp. 417–423.
Ji, S. Y. , and Shen, H. H. , 2008, “ Internal Parameters and Regime Map for Soft Poly-Dispersed Granular Materials,” J. Rheol., 52(1), pp. 87–103. [CrossRef]
Ji, S. Y. , 2013, “ Probability Analysis of Contact Forces in Quasi-Solid-Liquid Phase Transition of Granular Shear Flow,” Sci. China Phys. Mech. Astron., 56(2), pp. 395–403. [CrossRef]
Wang, Y. Q. , and Zu, J. W. , 2017, “ Analytical Analysis for Vibration of Longitudinally Moving Plate Submerged in Infinite Liquid Domain,” Appl. Math. Mech., 38(5), pp. 625–646. [CrossRef]
Wang, Y. Q. , Xue, S. W. , Huang, X. B. , and Du, W. , 2016, “ Vibrations of Axially Vertical Rectangular Plates in Contact With Fluid,” Int. J. Struct. Stability Dyn., 16(2), p. 1450092. [CrossRef]
Liao, C. Y. , Wu, Y. C. , Chang, C. Y. , and Ma, C. C. , 2017, “ Theoretical Analysis Based on Fundamental Functions of Thin Plate and Experimental Measurement for Vibration Characteristics of a Plate Coupled With Liquid,” J. Sound Vib., 394, pp. 545–574. [CrossRef]
Wang, Y. Q. , and Zu, J. W. , 2017, “ Nonlinear Steady-State Responses of Longitudinally Traveling Functionally Graded Material Plates in Contact With Liquid,” Compos. Struct., 164, pp. 130–144. [CrossRef]
Soni, S. , Jain, N. K. , and Joshi, P. V. , 2018, “ Vibration Analysis of Partially Cracked Plate Submerged in Fluid,” J. Sound Vib., 412, pp. 28–57. [CrossRef]
Wang, Y. Q. , and Zu, J. W. , 2016, “ Instability of Viscoelastic Plates With Longitudinally Variable Speed and Immersed in Ideal Liquid,” Int. J. Appl. Mech., 9(1), p. 1750005. [CrossRef]
Soni, S. , Jain, N. K. , and Joshi, P. V. , 2017, “ Analytical Modeling for Nonlinear Vibration Analysis of Partially Cracked Thin Magneto-Electro-Elastic Plate Coupled With Fluid,” Nonlinear Dyn., 90(1), pp. 137–170. [CrossRef]
Koch, S. , Duvigneau, F. , Orszulik, R. , Gabbert, U. , and Woschke, E. , 2017, “ Partial Filling of a Honeycomb Structure by Granular Materials for Vibration and Noise Reduction,” J. Sound Vib., 393, pp. 30–40. [CrossRef]
Xu, Z. W. , Wang, M. Y. , and Chen, T. N. , 2004, “ An Experimental Study of Particle Damping for Beams and Plates,” ASME J. Vib. Acoust., 126(1), pp. 141–148. [CrossRef]
Filipich, C. P. , and Rosales, M. B. , 2002, “ A Further Study about the Behavior of Foundation Piles and Beams in a Winkler–Pasternak Soil,” Int. J. Mech. Sci., 44(1), pp. 21–36. [CrossRef]
Morfidis, K. , 2010, “ Vibration of Timoshenko Beams on Three-Parameter Elastic Foundation,” Comput. Struct., 88(5–6), pp. 294–308. [CrossRef]
Donskoy, D. , Reznik, A. , Zagrai, A. , and Ekimov, A. , 2005, “ Nonlinear Vibrations of Buried Landmines,” J. Acoust. Soc. Am., 117(2), pp. 690–700. [CrossRef] [PubMed]
Zagrai, A. , Donskoy, D. , and Ekimov, A. , 2005, “ Structural Vibrations of Buried Land Mines,” J. Acoust. Soc. Am., 118(6), pp. 3619–3628. [CrossRef]
Kang, W. , Turner, J. A. , Bobaru, F. , Yang, L. , and Rattanadit, K. , 2007, “ Granular Layers on Vibrating Plates: Effective Bending Stiffness and Particle-Size Effects,” J. Acoust. Soc. Am., 121(2), pp. 888–896. [CrossRef] [PubMed]
Dorbolo, S. , Volfson, D. , Tsimring, L. , and Kudrolli, A. , 2005, “ Dynamics of a Bouncing Dimer,” Phys. Rev. Lett., 95(4), p. 044101. [CrossRef] [PubMed]
Dorbolo, S. , Ludewig, F. , and Vandewalle, N. , 2008, “ Bouncing Trimer: A Random Self-Propelled Particle, Chaos and Periodical Motions,” New J. Phys., 15(3), p. 033016.
Pachecovázquez, F. , Ludewig, F. , and Dorbolo, S. , 2014, “ Dynamics of a Grain-Filled Ball on a Vibrating Plate,” Phys. Rev. Lett., 113(11), p. 118001. [CrossRef] [PubMed]
Wang, Y. Q. , and Yang, Z. , 2017, “ Nonlinear Vibrations of Moving Functionally Graded Plates Containing Porosities and Contacting With Liquid: Internal Resonance,” Nonlinear Dyn., 90(2), pp. 1461–1480. [CrossRef]
Ho, C. , Lang, Z. Q. , and Billings, S. A. , 2014, “ A Frequency Domain Analysis of the Effects of Nonlinear Damping on the Duffing Equation,” Mech. Syst. Signal Process., 45(1), pp. 49–67. [CrossRef]
Josserand, C. , Tkachenko, A. V. , Mueth, D. M. , and Jaeger, H. M. , 2000, “ Memory Effects in Granular Materials,” Phys. Rev. Lett., 85(17), pp. 3632–3635. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Schematic of the experimental setup (1. vibration exciter, 2. force sensor, 3. vibrating table, 4. signal generator, 5. power amplifier, 6. data signal collecting device, 7. computer, and 8. elastic steel plate)

Grahic Jump Location
Fig. 2

Reliability verification of experimental system

Grahic Jump Location
Fig. 3

Amplitude–frequency curve without particles

Grahic Jump Location
Fig. 4

Phase–frequency curve without particles

Grahic Jump Location
Fig. 5

Amplitude–frequency curves for various depths and force amplitudes with a granular diameter of 1.0–1.5 mm: (a) 10 mm, (b) 15 mm, (c) 20 mm, (d) 25 mm, (e) 30 mm, and (f) summary figure

Grahic Jump Location
Fig. 6

Amplitude–frequency curves for various depths, force amplitudes, and measurement points with a granular diameter of 1.0–1.5 mm

Grahic Jump Location
Fig. 7

Amplitude–frequency curves and phase frequency curves for different force amplitudes and measurement points with a granular diameter of 4.0–4.5 mm and a burial depth of 30 mm: (a) amplitude–frequency curve and (b) phase-frequency curve

Grahic Jump Location
Fig. 8

Amplitude–frequency curves for various particle sizes, and measurement points with a burial depth of 30 mm. L–S means frequency changes from large to small; S–L means frequency changes from small to large: (a) small particles and (b) large particles.

Grahic Jump Location
Fig. 9

The complete process of period-doubling bifurcation (granular diameter is 1.2 mm, depth is 30 mm, and frequency is 280 Hz)

Grahic Jump Location
Fig. 10

General bifurcation with a granular diameter of 1.0–1.5 mm at depths of 15 mm and 30 mm

Grahic Jump Location
Fig. 11

General bifurcation with a granular diameter of 4.0–5.0 mm at depths of 25 mm and 50 mm

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In