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.

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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

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Fig. 3

Amplitude–frequency curve without particles

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Fig. 4

Phase–frequency curve without particles

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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

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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)

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Fig. 10

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

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Fig. 11

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




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