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Research Papers: Heat and Mass Transfer

A Fractional-Order Generalized Thermoelastic Problem of a Bilayer Piezoelectric Plate for Vibration Control

[+] Author and Article Information
Yeshou Xu, Zhao-Dong Xu, Jinxiang Chen, Chao Xu

Key Laboratory of Concrete and Prestressed
Concrete Structures of Ministry of Education,
Southeast University,
Nanjing 210096, China

Tianhu He

School of Science,
Lanzhou University of Technology,
Lanzhou 730050, China

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 11, 2016; final manuscript received February 12, 2017; published online April 11, 2017. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 139(8), 082003 (Apr 11, 2017) (10 pages) Paper No: HT-16-1736; doi: 10.1115/1.4036092 History: Received November 11, 2016; Revised February 12, 2017

Multilayered piezoelectric structures have special applications for vibration control, and they often serve in a thermoelastic coupling environment. In this work, the fractional-order generalized thermoelasticity theory is used to investigate the dynamic thermal and elastic behavior of a bilayer piezoelectric–thermoelastic plate with temperature-dependent properties. The thermal contact resistance is implemented to describe the interfacial thermal wave propagation. The governing equations for the bilayer piezoelectric–thermoelastic plate with temperature-dependent properties are formulated and then solved by means of Laplace transformation and Riemann-sum approximation. The distributions of the nondimensional temperature, displacement, and stress are obtained and illustrated graphically. According to the numerical results, the effects of the thermal contact resistance, the ratio of the material properties between different layers, the temperature-dependent properties, and the fractional-order parameters on the distributions of the considered quantities are revealed in different cases and some remarkable conclusions are obtained. The investigation helps gain insights into the optimal design of actuators, sensors, which are made of piezoelectric materials.

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Figures

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Fig. 1

Schematic diagram of the bilayer pizeoelectric–thermoelastic plate

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Fig. 2

Distributions of the nondimensional temperature with different thermal contact resistance ζ, when t=0.75, υ=2.0,α=0.25, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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Fig. 3

Distributions of the nondimensional displacement with different thermal contact resistance ζ, when t=0.75, υ=2.0,α=0.25, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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Fig. 4

Distributions of the nondimensional stress with different thermal contact resistance ζ, when t=0.75, υ=2.0, α=0.25, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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Fig. 5

Distributions of the nondimensional temperature with different thermal conductivity ratio (density and heat capacity ratio), between medium I and medium II, when t=0.75, υ=2.0, α=0.95, ζ=10: (a) κ0II/κ0I( ρII/ρI, CEII/CEI)=0.5 and (b) κ0II/κ0I( ρII/ρI, CEII/CEI)=2.0

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Fig. 6

Distributions of the nondimensional displacement with different thermal conductivity ratio (density and heat capacity ratio), between medium I and medium II, when t=0.75, υ=2.0, α=0.95, ζ=10: (a) κ0II/κ0I( ρII/ρI, CEII/CEI)=0.5 and (b) κ0II/κ0I( ρII/ρI,CEII/CEI)=2.0

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Fig. 7

Distributions of the nondimensional stress with different thermal conductivity ratio (density and heat capacity ratio), between medium I and medium II, when t=0.75, υ=2.0, α=0.95, ζ=10: (a) κ0II/κ0I( ρII/ρI, CEII/CEI)=0.5 and (b) κ0II/κ0I( ρII/ρI, CEII/CEI)=2.0

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Fig. 8

Distributions of the nondimensional temperature with different temperature-dependent parameter υ, when t=0.75, α=0.25,ζ=10, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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Fig. 9

Distributions of the nondimensional displacement withdifferent temperature-dependent parameter υ, when t=0.75, α=0.25,ζ=10, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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Fig. 10

Distributions of the nondimensional stress with different temperature-dependent parameter υ, when t=0.75,α=0.25,ζ=10, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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Fig. 11

Distributions of the nondimensional temperature with different fractional-order parameter α, when t=0.75, υ=2.0,ζ=10, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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Fig. 12

Distributions of the nondimensional displacement withdifferent fractional-order parameter α,when t=0.75, υ=2.0,ζ=10, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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Fig. 13

Distributions of the nondimensional stress with different fractional-order parameter α, when t=0.75, υ=2.0,ζ=10, and κ0II/κ0I=0.5, ρII/ρI=0.5, CEII/CEI=0.5

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