Year 2019,
, 118 - 124, 20.09.2019
İbrahim Keles
,
Vedat Suat Erturk
References
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a problem on elastic vibrations, Philosophical Magazine,vol. 33, no
223, p.614–22, DOI: 10.1080/14786444208520820.
- [2] Mirsky I. (1964). Axisymmetric vibrations of orthotropic cylinders,
Journal of the Acoustical Society of America, vol. 36, no 11, p. 2106–
12, DOI: 10.1121/1.1919329.
- [3] Klosner JM, Dym CL.(1966). Axisymmetric plane-strain dynamic
response of a thick orthotropic shell, Journal of the Acoustical Society of America, vol. 39, no 1, p. 1-7, DOI: 10.1121/1.1909869
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jsvi.1995.0484.
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of functionally graded annular fin, Journal of Thermal Stresses, vol.
42, no. 4, p. 440-451, DOI: 10.1080/01495739.2018.1469963.
- [7] Aslan T.A ., Noori A .R., Temel B.(2018) A unified approach for
out-of-plane forced vi- bration of axially functionally graded circular rods, European Mechanical Science vol.2, no. 2,p. 37–45, DOI:
10.26701/ems.374524 .
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method, Karaelmas Science and Engineering Journal, vol. 8, no. 4, p.
496-504, DOI: 10.7212%2Fzkufbd.v8i2.1159.
- [9] Celebi K., Yarimpabuc D., and Baran T. (2018). Forced vibration
analysis of inhomogeneous rods with non-uniform cross-section, Journal of Engineering Research, vol. 6, no. 3, p. 189-202, DOI:
10.21605/cukurovaummfd.316746
- [10] Celebi K., Yarımpabuç D., Tutuncu N. (2018). Free vibration analysis
of functionally graded beams using complementary functions method, Archive of Applied Mechanics, vol. 88, no. 5, p. 729-739, DOI:
10.1007/s00419-017-1338-6.
- [11] Güven U., Baykara C. (2001). On stress distributions in functionally
graded isotropic spheres subjected to internal pressure, Mechanic
Research Communications, vol. 28, no. 3, p. 277-281, DOI:10.1016/
s0093-6413(01)00174-4.
- [12] Tütüncü, N., Öztürk, M. (2001). Exact solutions for stresses in functionally graded pressure vessels, Composites Part B: Engineering, vol.
32, no. 8, p. 683-686, DOI: 10.1016/s1359-8368(01)00041-5.
- [13] Horgan C.O., Chan A.M. (1999). The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials, Journal of Elasticity, vol. 55, p. 43-59, DOI: 10.1023/A:1007625401963.
- [14] Obata Y, Noda N. (1994). Steady thermal stressesin a hollow circular cylinder and a hollow sphere of a functionally gradient
material, Journal of Thermal Stresses vol. 17, p. 471-87, DOI:
10.1080/01495739408946273.
- [15] Tutuncu, N., Temel, B. (2009). A novel approach to stress analysis of
pressurized FGM cylinders, disks and spheres, Composite Structures, vol. 91, no. 3, p. 385-390, DOI: 10.1016/j.compstruct.2009.06.009.
- [16] Zhou J.K. (1986), Differential Transformation and Its Applications
for Electrical Circuits, Huazhong University Press, Wuhan, China.
- [17] Arikoglu A., Ozkol I. (2005). Solution of boundary value problems
for integrodifferential equations by using differential transform
method, Applied Mathematics and Computation, vol. 168, no. 2. p.
1145–1158, DOI: 10.1016/j.amc.2004.10.009.
- [18] Chen C. K., Ho S. H. (1998). Application of differential transformation to eigenvalue problems, Applied Mathematics and Computation, vol. 79, no. 2-3, p. 173–188,DOI: 10.1016/0096-3003(95)00253-7.
- [19] Malik M., Dang H. H. (1998). Vibration analysis of continuous
systems by differential transformation, Applied Mathematics
and Computation, vol. 96, no. 1, p. 17–26, DOI: 10.1016/S0096-
3003(97)10076-5.
- [20] Hassan I.H.A-H. (2002). On solving some eigenvalue problems
by using a differential transformation”, Applied Mathematics
and Computation, vol. 127, no. 1, p. 1– 22, DOI: 10.1016/S0096-
3003(00)00123-5.
- [21] Yeh Y. L., Jang M. J., Wang C. C. (2006). Analyzing the free vibrations of a plate using finite difference and differential transformation
method, Applied Mathematics and Computation, vol. 178, no. 2, p.
493–501, DOI: 10.1016/j.amc.2005.11.068 (2006).
- [22] Yeh Y. L., Wang C. C., Jang M. J. (2007). Using finite difference and
differential transformation method to analyze of large deflections
of orthotropic rectangular plate problem, Applied Mathematics
and Computation, vol. 190, no. 2, p. 1146–1156, DOI: 10.1016/j.
amc.2007.01.099.
- [23] Shin Y. J., Kwon K. M., Yun J. H. Vibration analysis of a circular arch
with variable cross-section using differential transformation and generalized differential quadrature, Journal of Sound and Vibration,
vol. 309, no. 1-2, p. 9–19, DOI: 10.1016/j.jsv.2006.08.020.
- [24] Chen C.J., Wu W.J. (1996). Application of the Taylor differential
transformation method to viscous damped vibration of hard and
soft spring system. Computers & Structures, vol. 59, no. 4, p. 631-
639, DOI: 10.1016/0045-7949(95)00304-5.
- [25] Chen C.K., Ho S.H.(1999). Solving partial differential equations
by two-dimensional differential transform method, Applied Mathematics and Computation, vol. 106, no. 2-3, p. 171-179, DOI:
10.1016/S0096-3003(98)10115-7.
- [26] Hassan I.H.A-H. (2002). Different applications for the differential
transformation in the differential equations, Applied Mathematics and Computation, vol. 129, no. 2-3, p. 183 – 201, DOI: 10.1016/
S0096-3003(01)00037-6.
- [27] Erturk V. S., Momani S. (2007). A reliable algorithm for solving
tenth-order boundary value problems, Numerical Algorithms, vol.44, no.2, p. 147-158, DOI: 10.1007/s11075-007-9093-3.
- [28] Arikoglu A., Ozkol I. (2006), Solution of difference equations by using
differential transform method, Applied Mathematics and Computation, vo. 174, no. 2, p. 1216-1228, DOI: 10.1016/j.amc.2005.06.013.
- [29] Rashidi M.M., Erfani E. (2011). A new analytical study of MHD stagnation-point flow in porous media with heat transfer, Computres
& Fluids, vol. 40, p. 172-178, DOI: 10.1016/j.compfluid.2010.08.021.
- [30] Ni Q., Zhang Z.L., Wang L. (2011). Application of the differential
transformation method to vibration analysis of pipes conveying
fluid, Applied Mathematics and Computation, vol. 217, no. 16, p.
7028-7038, DOI: 10.1016/j.amc.2011.01.116.
- [31] ANSYS Swanson Analysis System, Inc., 201 Johnson Road, Houston,
PA 15342-1300, USA.
A practical Jointed Approach to Functionally Graded Structures by Differential Transform Method
Year 2019,
, 118 - 124, 20.09.2019
İbrahim Keles
,
Vedat Suat Erturk
Abstract
In this study, a practical jointed approach in the static vibration investigation of functionally graded material
(FGM) structures under internal pressure is applied by differential transform method (DTM). The FGM material
consist of isotropic material that show exponential variation in the thickness. The ratio of Poisson is taken
as a constant. Displacement and stress distributions due to non-homogeneous constant are intended. Stress
distribution dependent on the homogeneity parameter is computed and the results obtained for cylindrical
and spherical structures were compared with finite element method (FEM). The inhomogeneity parameter
is empirically regulated, with a continuously varying volume fraction of the constituents. The parameters for
homogeneity were randomly selected to show displacement and stress distributions.
References
- [1] Tranter, C.J. (1942). The application of the Laplace transformation to
a problem on elastic vibrations, Philosophical Magazine,vol. 33, no
223, p.614–22, DOI: 10.1080/14786444208520820.
- [2] Mirsky I. (1964). Axisymmetric vibrations of orthotropic cylinders,
Journal of the Acoustical Society of America, vol. 36, no 11, p. 2106–
12, DOI: 10.1121/1.1919329.
- [3] Klosner JM, Dym CL.(1966). Axisymmetric plane-strain dynamic
response of a thick orthotropic shell, Journal of the Acoustical Society of America, vol. 39, no 1, p. 1-7, DOI: 10.1121/1.1909869
- [4] Ahmed N. (1966). Axisymmetric plane-strain vibrations of a thick-layered orthotropic cylindrical shell, Journal of the Acoustical Society of America, vol. 40, no 6, p. 1509–16, DOI: 10.1121/1.1910256
- [5] Ghosh A.K. (1995). Axisymmetric vibration of a long cylinder, Journal of Sound Vibration, vol. 186, no. 5, p. 711–21, DOI: 10.1006/
jsvi.1995.0484.
- [6] Yıldırım A., Yarımpabuç D., Celebi K. (2019). Thermal stress analysis
of functionally graded annular fin, Journal of Thermal Stresses, vol.
42, no. 4, p. 440-451, DOI: 10.1080/01495739.2018.1469963.
- [7] Aslan T.A ., Noori A .R., Temel B.(2018) A unified approach for
out-of-plane forced vi- bration of axially functionally graded circular rods, European Mechanical Science vol.2, no. 2,p. 37–45, DOI:
10.26701/ems.374524 .
- [8] Yarımpabuç D., Eker M., Çelebi K. (2018). Forced vibration analysis of non-uniform piezoelectric rod by complementary functions
method, Karaelmas Science and Engineering Journal, vol. 8, no. 4, p.
496-504, DOI: 10.7212%2Fzkufbd.v8i2.1159.
- [9] Celebi K., Yarimpabuc D., and Baran T. (2018). Forced vibration
analysis of inhomogeneous rods with non-uniform cross-section, Journal of Engineering Research, vol. 6, no. 3, p. 189-202, DOI:
10.21605/cukurovaummfd.316746
- [10] Celebi K., Yarımpabuç D., Tutuncu N. (2018). Free vibration analysis
of functionally graded beams using complementary functions method, Archive of Applied Mechanics, vol. 88, no. 5, p. 729-739, DOI:
10.1007/s00419-017-1338-6.
- [11] Güven U., Baykara C. (2001). On stress distributions in functionally
graded isotropic spheres subjected to internal pressure, Mechanic
Research Communications, vol. 28, no. 3, p. 277-281, DOI:10.1016/
s0093-6413(01)00174-4.
- [12] Tütüncü, N., Öztürk, M. (2001). Exact solutions for stresses in functionally graded pressure vessels, Composites Part B: Engineering, vol.
32, no. 8, p. 683-686, DOI: 10.1016/s1359-8368(01)00041-5.
- [13] Horgan C.O., Chan A.M. (1999). The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials, Journal of Elasticity, vol. 55, p. 43-59, DOI: 10.1023/A:1007625401963.
- [14] Obata Y, Noda N. (1994). Steady thermal stressesin a hollow circular cylinder and a hollow sphere of a functionally gradient
material, Journal of Thermal Stresses vol. 17, p. 471-87, DOI:
10.1080/01495739408946273.
- [15] Tutuncu, N., Temel, B. (2009). A novel approach to stress analysis of
pressurized FGM cylinders, disks and spheres, Composite Structures, vol. 91, no. 3, p. 385-390, DOI: 10.1016/j.compstruct.2009.06.009.
- [16] Zhou J.K. (1986), Differential Transformation and Its Applications
for Electrical Circuits, Huazhong University Press, Wuhan, China.
- [17] Arikoglu A., Ozkol I. (2005). Solution of boundary value problems
for integrodifferential equations by using differential transform
method, Applied Mathematics and Computation, vol. 168, no. 2. p.
1145–1158, DOI: 10.1016/j.amc.2004.10.009.
- [18] Chen C. K., Ho S. H. (1998). Application of differential transformation to eigenvalue problems, Applied Mathematics and Computation, vol. 79, no. 2-3, p. 173–188,DOI: 10.1016/0096-3003(95)00253-7.
- [19] Malik M., Dang H. H. (1998). Vibration analysis of continuous
systems by differential transformation, Applied Mathematics
and Computation, vol. 96, no. 1, p. 17–26, DOI: 10.1016/S0096-
3003(97)10076-5.
- [20] Hassan I.H.A-H. (2002). On solving some eigenvalue problems
by using a differential transformation”, Applied Mathematics
and Computation, vol. 127, no. 1, p. 1– 22, DOI: 10.1016/S0096-
3003(00)00123-5.
- [21] Yeh Y. L., Jang M. J., Wang C. C. (2006). Analyzing the free vibrations of a plate using finite difference and differential transformation
method, Applied Mathematics and Computation, vol. 178, no. 2, p.
493–501, DOI: 10.1016/j.amc.2005.11.068 (2006).
- [22] Yeh Y. L., Wang C. C., Jang M. J. (2007). Using finite difference and
differential transformation method to analyze of large deflections
of orthotropic rectangular plate problem, Applied Mathematics
and Computation, vol. 190, no. 2, p. 1146–1156, DOI: 10.1016/j.
amc.2007.01.099.
- [23] Shin Y. J., Kwon K. M., Yun J. H. Vibration analysis of a circular arch
with variable cross-section using differential transformation and generalized differential quadrature, Journal of Sound and Vibration,
vol. 309, no. 1-2, p. 9–19, DOI: 10.1016/j.jsv.2006.08.020.
- [24] Chen C.J., Wu W.J. (1996). Application of the Taylor differential
transformation method to viscous damped vibration of hard and
soft spring system. Computers & Structures, vol. 59, no. 4, p. 631-
639, DOI: 10.1016/0045-7949(95)00304-5.
- [25] Chen C.K., Ho S.H.(1999). Solving partial differential equations
by two-dimensional differential transform method, Applied Mathematics and Computation, vol. 106, no. 2-3, p. 171-179, DOI:
10.1016/S0096-3003(98)10115-7.
- [26] Hassan I.H.A-H. (2002). Different applications for the differential
transformation in the differential equations, Applied Mathematics and Computation, vol. 129, no. 2-3, p. 183 – 201, DOI: 10.1016/
S0096-3003(01)00037-6.
- [27] Erturk V. S., Momani S. (2007). A reliable algorithm for solving
tenth-order boundary value problems, Numerical Algorithms, vol.44, no.2, p. 147-158, DOI: 10.1007/s11075-007-9093-3.
- [28] Arikoglu A., Ozkol I. (2006), Solution of difference equations by using
differential transform method, Applied Mathematics and Computation, vo. 174, no. 2, p. 1216-1228, DOI: 10.1016/j.amc.2005.06.013.
- [29] Rashidi M.M., Erfani E. (2011). A new analytical study of MHD stagnation-point flow in porous media with heat transfer, Computres
& Fluids, vol. 40, p. 172-178, DOI: 10.1016/j.compfluid.2010.08.021.
- [30] Ni Q., Zhang Z.L., Wang L. (2011). Application of the differential
transformation method to vibration analysis of pipes conveying
fluid, Applied Mathematics and Computation, vol. 217, no. 16, p.
7028-7038, DOI: 10.1016/j.amc.2011.01.116.
- [31] ANSYS Swanson Analysis System, Inc., 201 Johnson Road, Houston,
PA 15342-1300, USA.