Exact axisymmetric solutions for laminated transversely isotropic piezoelectric circular plate (I)

Ding, Hu; Xu, Rongqiao; Guo, Fenglin

doi:10.1007/bf02916748

Cited by 5 publications

(6 citation statements)

References 6 publications

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“…The finite Hankel transform is an effective method to handle the axisymmetric bending problems of a circular plate which is defined as follows [40]: Jμfalse[f(rfalse¯,zfalse¯)false]=∫01r¯f(rfalse¯,zfalse¯)Jμfalse(kr¯false)drfalse¯, where Jμfalse(kr¯false) is the Bessel function of the first kind of order μ . Then, the state space vector related to the Hankel transform domain takes the form as follows: boldRjfalse(k,z¯false)=[4pt1emUrfalse(k,z¯false)Sfalse(k,z¯false)Hfalse(k,z¯false)Dfalse(k,z¯false)T...…”

Section: State Equations and Hankel Transformmentioning

confidence: 99%

“…According to boundary conditions of circular plate presented by Ding et al . [40], the elastic simply supported condition can be extended to the 1D piezoelectric QC circular plate: ufalse¯zfalse(1,z¯false)=0,wfalse¯zfalse(1,z¯false)=0,ϕfalse¯false(1,z¯false)=0,false[(C¯11−C¯12)sufalse¯r(1,zfalse¯)+σfalse¯rr(1,zfalse¯)false]=0 and J0false(kfalse)=0. …”

Section: State Equations and Hankel Transformmentioning

confidence: 99%

“…According to boundary conditions of circular plate presented by Ding et al [40], the elastic simply supported condition can be extended to the 1D piezoelectric QC circular plate:…”

Section: State Equations and Hankel Transformmentioning

confidence: 99%

“…The finite Hankel transform is an effective method to handle the axisymmetric bending problems of a circular plate which is defined as follows [40]: where J μ (kr) is the Bessel function of the first kind of order μ. Then, the state space vector related to the Hankel transform domain takes the form as follows:…”

Section: State Equations and Hankel Transformmentioning

confidence: 99%

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Axisymmetric bending analysis of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate

Qin

et al. 2020

Proc. R. Soc. A.

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Within a framework of the state space method, an axisymmetric solution for functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate is presented in this paper. Applying the finite Hankel transform onto the state space vector, an ordinary differential equation with constant coefficients is obtained for the circular plate provided that the free boundary terms are zero and an exponential function distribution of material properties is assumed. The ordinary differential equation is then used to obtain the stress, displacement and electric components in the physical domain of the elastic simply supported circular plate through the use of the propagator matrix method and the inverse Hankel transform. The numerical studies are carried out to show the validity of the present solution and reveal the influence of material inhomogeneity on the axisymmetric bending of the circular plate with different layers and loadings, which provides guidance for the design and manufacture of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate.

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Section: State Equations and Hankel Transformmentioning

confidence: 99%

Section: State Equations and Hankel Transformmentioning

confidence: 99%

“…According to boundary conditions of circular plate presented by Ding et al [40], the elastic simply supported condition can be extended to the 1D piezoelectric QC circular plate:…”

Section: State Equations and Hankel Transformmentioning

confidence: 99%

Section: State Equations and Hankel Transformmentioning

confidence: 99%

See 2 more Smart Citations

Axisymmetric bending analysis of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate

Qin

et al. 2020

Proc. R. Soc. A.

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“…Wang et al (2001) discussed the vibration problem of a piezoelectric circular laminate under simply supported and clamped boundary conditions based on the Kirchhoff thin plate theory. Ding et al (1999aDing et al ( , 1999bDing et al ( , 1999c derived the exact solution for a piezoelectric circular plate under static and vibration conditions employing the state vector approach, finite Hankel transformation and propagating matrix method.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for a multilayered magneto-electro-elastic circular plate under simply supported lateral boundary conditions

Wang

Han

Pan

2010

Smart Mater. Struct.

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We derive, in this paper, the analytical solution for a three-dimensional transversely isotropic axisymmetric multilayered magneto-electro-elastic (MEE) circular plate under simply supported boundary conditions. The state space vector, the finite Hankel transform and propagating matrix methods are utilized together to obtain the full-field solutions for the MEE plate made of piezoelectric (PE) and piezomagnetic (PM) layers. Numerical examples for three-layered and five-layered PE/PM composites with different stacking sequences and under different loading conditions are presented and discussed. These results can serve as benchmark solutions for future numerical analyses of layered MEE plates.

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Free Vibrations of Functionally Graded Piezoceramic Hollow Spheres With Radial Polarization

Chen¹,

Wang²,

2002

Journal of Sound and Vibration

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Exact axisymmetric solutions for laminated transversely isotropic piezoelectric circular plate (I)

Cited by 5 publications

References 6 publications

Axisymmetric bending analysis of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate

Axisymmetric bending analysis of functionally graded one-dimensional hexagonal piezoelectric quasi-crystal circular plate

An analytical solution for a multilayered magneto-electro-elastic circular plate under simply supported lateral boundary conditions

Free Vibrations of Functionally Graded Piezoceramic Hollow Spheres With Radial Polarization

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