Nonlinear Vibrations of Buried Rectangular Plate

[+] Author and Article Information
Guangyang Hong

Department of Mechanics, Northeastern University, Shenyang, China

Jian Li

Department of Mechanics, Northeastern University, Shenyang, China

Zhicong Luo

Department of Mechanics, Northeastern University, Shenyang, China

Hongying Li

Department of Mechanics, Northeastern University, Shenyang, China

1Corresponding author.

ASME 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 an elastic plate in granular media. 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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