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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 한국계산역학회 Computers and Concrete, An International Journal Computers and Concrete, An International Journal Vol.23 No.5
- 발행연도
- 2019.1
- 수록면
- 303 - 309 (7page)
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This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy’s stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.
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참고문헌 (35)
참고문헌 신청
Akinola, A. P. / 1999 / An energy function for transversely isotropic elastic material and Ponyting effect / J. Appl. Math. Comput 6(3):639~649
Akinola, A. P. / 2001 / An application of nonlinear fundamental problems of a transversely isotropic layer in finite elastic deformation / Int. J. Nonlin. Mech 36(2):307~321
Bashmal, S. / 2010 / Frequency equations for the in-plane vibration of circular annular disks / Adv. Acoust. Vib
Batra, R. C. / 2008 / Exact solutions for radial deformations of a functionally-graded isotropic and incompressible second order elastic cylinder / Int. J. Nonlin. Mech 43(5):383~398
Benferhat, R. / 2016 / Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations / Earthq. Struct 10(6):1429~1449
Akinola, A. P. / 2001 / An application of nonlinear fundamental problems of a transversely isotropic layer in finite elastic deformation / Int. J. Nonlin. Mech 36(2):307~321
Bashmal, S. / 2010 / Frequency equations for the in-plane vibration of circular annular disks / Adv. Acoust. Vib
Batra, R. C. / 2008 / Exact solutions for radial deformations of a functionally-graded isotropic and incompressible second order elastic cylinder / Int. J. Nonlin. Mech 43(5):383~398
Benferhat, R. / 2016 / Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations / Earthq. Struct 10(6):1429~1449
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