Abstract
A non-local solution for a functionally graded piezoelectric nano-rod is presented by accounting the surface effect. This solution is used to evaluate the characteristics of the wave propagation in the rod structure. The model is loaded under a two-dimensional (2D) electric potential and an initially applied voltage at the top of the rod. The mechanical and electrical properties are assumed to be variable along the thickness direction of the rod according to the power law. The Hamilton principle is used to derive the governing differential equations of the electromechanical system. The effects of some important parameters such as the applied voltage and gradation of the material properties on the wave characteristics of the rod are studied.
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Abbreviations
- u,v,w :
-
displacement components
- x 1,x 2,x 3 :
-
Cartesian coordinates
- T ij :
-
stress components
- Ɛ ij :
-
strain components
- B i :
-
body force components
- a i :
-
acceleration components
- ρ :
-
density
- μ,λ :
-
Lame’s constants
- E :
-
modulus of elasticity
- ν :
-
Poisson’s ratio
- E k :
-
electric field
- e ijk :
-
piezoelectric constants
- ∇2 :
-
Laplacian operator
- l m ,l s :
-
non-local parameters
- ϕ :
-
electric potential
- V 0 :
-
applied voltage
- b,h :
-
dimensions of rod
- τ αβ :
-
surface stress
- τ 0 :
-
residual surface tension
- μ 0,λ 0 :
-
surface Lame’s constants
- U :
-
total energies
- U s :
-
surface energies
- E ek :
-
kinetic energy
- D i :
-
electric displacement
- c :
-
phase velocity
- k :
-
wave number
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Project supported by the University of Kashan (No. 463865/13) and the Iranian Nanotechnology Development Committee
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Arefi, M. Surface effect and non-local elasticity in wave propagation of functionally graded piezoelectric nano-rod excited to applied voltage. Appl. Math. Mech.-Engl. Ed. 37, 289–302 (2016). https://doi.org/10.1007/s10483-016-2039-6
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DOI: https://doi.org/10.1007/s10483-016-2039-6