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Research Papers

Extensional Waves in a Sandwich Plate With Interface Slip

[+] Author and Article Information
Peng Li

School of Human Settlements and Civil
Engineering,
Xi'an Jiaotong University,
Xi'an, Shaanxi 710049, China

Feng Jin

State Key Laboratory for Strength and Vibration
of Mechanical Structures,
Xi'an Jiaotong University,
Xi'an, Shaanxi 710049, China
e-mail: jinfengzhao@263.net

Weiqiu Chen

Department of Engineering Mechanics,
Zhejiang University,
Hangzhou, Zhejiang 310027, China

Jiashi Yang

Department of Mechanical and Materials
Engineering,
University of Nebraska-Lincoln,
Lincoln, NE 68588

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 18, 2012; final manuscript received December 5, 2014; published online January 27, 2015. Assoc. Editor: Walter Lacarbonara.

J. Vib. Acoust 137(3), 031001 (Jun 01, 2015) (7 pages) Paper No: VIB-12-1354; doi: 10.1115/1.4029334 History: Received December 18, 2012; Revised December 05, 2014; Online January 27, 2015

The two-dimensional (2D) equations for thin elastic plates are used to study extensional motions of a sandwich plate with weak interfaces. The interfaces are governed by the shear-slip model that possesses interface elasticity and allows for a discontinuity of the tangential displacements at the interfaces. Equations for the individual layers of the sandwich plate are coupled by the interface conditions. Through a procedure initiated by Mindlin, the layer equations can be written into equations for the collective motion of the layers representing the extensional motion of the sandwich plate, and equations for the relative motions of the layers with respect to each other representing the symmetric thickness-shear motion of the sandwich plate. The use of plate equations results in relatively simpler models compared to the equations of three-dimensional (3D) elasticity. Solutions to a few useful problems are presented. These include the propagation of straight-crested waves in an unbounded plate with weak interfaces, the reflection of extensional waves at the joint between a perfectly bonded sandwich plate and a sandwich plate with weak interfaces, and the vibration of a finite sandwich plate with weak interfaces.

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Figures

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Fig. 1

A sandwich plate with weak interfaces

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Fig. 2

Dispersion curves determined by Eq. (32)

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Fig. 3

Joint between two semi-infinite sandwich plates

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Fig. 4

Reflection coefficient versus Γ (α=0.1, β=2, and η=4.5)

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Fig. 5

Shear stress distribution under the upper film (Γ = 2): (a) essentially extensional mode and (b) essentially thickness-shear mode

Grahic Jump Location
Fig. 6

Effect of interface stiffness on the interface shear stress of the thickness-shear mode

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