참고문헌
- Ahouel, M., Houari, M.S.A., Bedia, E. and Tounsi, A. (2016), "Size-dependent mechanical behavior of functionally graded trigonometric shear deformable nanobeams including neutral surface position concept", Steel Compos. Struct., 20(5), 963-981. https://doi.org/10.12989/scs.2016.20.5.963
- Amirian, B., Hosseini-ara, R. and Moosavi, H. (2014), "Surface and thermal effects on vibration of embedded alumina nanobeams based on novel Timoshenko beam model", Appl. Math. Mech., 35(7), 875-886. https://doi.org/10.1007/s10483-014-1835-9
- Anne, G., Vanmeensel, K., Vleugels, J. and Van der biest, O. (2005), "Electrophoretic deposition as a novel near net shaping technique for functionally graded biomaterials", Mater. Sci. Forum, 492-493,213-218. https://doi.org/10.4028/www.scientific.net/MSF.492-493.213
- Ansari, R., Pourashraf, T. and Gholami, R. (2015), "An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory", Thin Wall. Struct., 93, 169-176. https://doi.org/10.1016/j.tws.2015.03.013
- Belkorissat, I., Houari, M.S.A., Tounsi, A., Bedia, E. and Mahmoud, S. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
- Berrabah, H., Tounsu, A., Semmah, A. and Adda, B. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351
- De pietro, G., Hui, Y., Giunta, G., Belouettar, S., Carrera, E. and Hu, H. (2016), "Hierarchical one-dimensional finite elements for the thermal stress analysis of three-dimensional functionally graded beams", Compos. Struct., 153, 514-528. https://doi.org/10.1016/j.compstruct.2016.06.012
- Della, C. and Shu, D.W. (2015), "Vibration of porous beams with embedded piezoelectric sensors and actuators.
- Ebrahimi, F. and SALARI, E. (2015), "Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments", Compos. Struct., 128, 363-380. https://doi.org/10.1016/j.compstruct.2015.03.023
- Elsibai K.A. and Youssef, H.M. (2011), "State-space approach to vibration of gold nano-beam induced by ramp type heating without energy dissipation in femtoseconds scale", J. Therm. Stresses, 34(3), 244-263. https://doi.org/10.1080/01495739.2010.545737
- Eltaher, M., Alshorbagy, A.E. and Mahmoud, F. (2013a), "Vibration analysis of Euler-Bernoulli nanobeams by using finite element method", Appl. Math. Model., 37(7), 4787-4797. https://doi.org/10.1016/j.apm.2012.10.016
- Eltaher, M., Mahmoud, F., Assie, A. and Meletis, E. (2013b), "Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams", Appl. Math. Comput., 224, 760-774.
- Eringen, A.C. and Edelen, D. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10(3), 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
- Hassanin, H. and Jiang, K. (2010), "Infiltration-processed, functionally graded materials for microceramic componenets", Proceedings of the Micro Electro Mechanical Systems (MEMS), 2010 IEEE 23rd International Conference on, 2010. IEEE.
- Hayati, H., Hosseini, S.A. and Rahmani, O. (2017), "Coupled twist-bending static and dynamic behavior of a curved singlewalled carbon nanotube based on nonlocal theory", Microsyst. Technol., 23(7), 2393-2401. https://doi.org/10.1007/s00542-016-2933-0
- Hosseini-hashemi, S., Nahas, I., Fakher, M. and Nazemnezhad, R. (2014), "Surface effects on free vibration of piezoelectric functionally graded nanobeams using nonlocal elasticity", Acta Mechanica, 225(6), 1555-1564. https://doi.org/10.1007/s00707-013-1014-z
- Hosseini, S. and Rahmani, O. (2017), "Exact solution for axial and transverse dynamic response of functionally graded nanobeam under moving constant load based on nonlocal elasticity theory", Meccanica, 52(6), 1441-1457. https://doi.org/10.1007/s11012-016-0491-2
- Juntarasaid, C., Pulngern, T. and Chucheepsakul, S. (2012), "Bending and buckling of nanowires including the effects of surface stress and nonlocal elasticity", Physica E: Lowdimensional Syst. Nanostruct., 46, 68-76. https://doi.org/10.1016/j.physe.2012.08.005
- Kato, K., Kurimoto, M., Shumiya, H., Adachi, H., Sakuma, S. and Okubo, H. (2006), "Application of functionally graded material for solid insulator in gaseous insulation system", IEEE T. Dielect. El. In., 13(2), 362-372. https://doi.org/10.1109/TDEI.2006.1624281
- Ke, L.L. and Wang, Y.S. (2012), "Thermoelectric-mechanical vibration of piezoelectric nanobeams based on the nonlocal theory", Smart Mater. Struct., 21(2), 025018. https://doi.org/10.1088/0964-1726/21/2/025018
- Leclaire, P., Horoshenkov, K., Swift, M. and Hothersall, D. (2001), "The vibrational response of a clamped rectangular porous plate", J. Sound Vib., 247(1), 19-31. https://doi.org/10.1006/jsvi.2000.3657
- Lee, H.L. and Chang, W.J. (2011), "Surface effects on axial buckling of nonuniform nanowires using non-local elasticity theory", IET Micro & Nano Lett., 6(1), 19-21. https://doi.org/10.1049/mnl.2010.0191
- Lee, W.Y., Stinton, D.P., Berndt, C.C., Erdogan, F., Lee, Y.D. and Mutasim, Z. (1996), "Concept of functionally graded materials for advanced thermal barrier coating applications", J. Am. Ceram. Soc., 79(12), 3003-3012. https://doi.org/10.1111/j.1151-2916.1996.tb08070.x
- Lei, Y., Adhikari, S. and Friswell, M. (2013), "Vibration of nonlocal Kelvin-Voigt viscoelastic damped Timoshenko beams", Int. J. Eng. Sci., 66-67, 1-13. https://doi.org/10.1016/j.ijengsci.2013.02.004
- Li, C. (2013), "Size-dependent thermal behaviors of axially traveling nanobeams based on a strain gradient theory", Struct. Eng. Mech., 48, 415-434. https://doi.org/10.12989/sem.2013.48.3.415
- Li, C., Lim, C.W., Yu, J. and Zeng, Q. (2011), "Analytical solutions for vibration of simply supported nonlocal nanobeams with an axial force", Int. J. Struct. Stab. Dynam., 11(2), 257-271. https://doi.org/10.1142/S0219455411004087
- Malekzadeh, P. and Shojaee, M. (2013), "Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams", Composites Part B: Eng., 52, 84-92. https://doi.org/10.1016/j.compositesb.2013.03.046
- Mirjavadi, S.S., Matin, A., Shafiei, N., Rabby, S. and Mohasel afshari, B. (2017), "Thermal buckling behavior of twodimensional imperfect functionally graded microscale-tapered porous beam", J. Therm. Stresses, 40(10), 1201-1214. Doi: 10.1080/01495739.2017.1332962.
- Muller, E., DraSar, C., Schilz, J. and Kaysser, W. (2003), "Functionally graded materials for sensor and energy applications", Mater. Sci. Eng., 362(1-2), 17-39. https://doi.org/10.1016/S0921-5093(03)00581-1
- Murmu, T. and Adhikari, S. (2010), "Nonlocal transverse vibration of double-nanobeam-systems", J. Appl. Phys., 108(8), 083514. https://doi.org/10.1063/1.3496627
- Natarajan, S., Chakraborty, S., Thangavel, M., Bordas, S. and Rabczuk, T. (2012), "Size-dependent free flexural vibration behavior of functionally graded nanoplates", Comput. Mater. Sci., 65, 74-80. https://doi.org/10.1016/j.commatsci.2012.06.031
- Nazemnezhad, R. and Hosseini-hashemi, S. (2014), "Nonlocal nonlinear free vibration of functionally graded nanobeams", Compos. Struct., 110, 192-199. https://doi.org/10.1016/j.compstruct.2013.12.006
- Nemat-alla, M. (2003), "Reduction of thermal stresses by developing two-dimensional functionally graded materials", Int. J. Solids Struct., 40(26), 7339-7356. https://doi.org/10.1016/j.ijsolstr.2003.08.017
- Nemat-alla, M., Ahmed, K.I. and Hassab-allah, I. (2009), "Elastic-plastic analysis of two-dimensional functionally graded materials under thermal loading", Int. J. Solids Struct., 46(14-15), 2774-2786. https://doi.org/10.1016/j.ijsolstr.2009.03.008
- Olevsky, E., Wang, X., Maximenko, A. and Meyers, M. (2007), "Fabrication of net-shape functionally graded composites by electrophoretic deposition and sintering: modeling and experimentation", J. Am.Ceram. Soc., 90(10), 3047-3056. https://doi.org/10.1111/j.1551-2916.2007.01838.x
- Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M., Greil, P., Hempel, U., Scharnweber, D. and Schulte, K. (2003), "Functionally graded materials for biomedical applications", Mater. Sci. Eng., 362(1-2), 40-60. https://doi.org/10.1016/S0921-5093(03)00580-X
- Rafiee, M., Yang, J. and Kitipornchai, S. (2013), "Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers", Compos. Struct., 96, 716-725. https://doi.org/10.1016/j.compstruct.2012.10.005
- Rahmani, O., Hosseini, S., Ghoytasi, I. and Golmohammadi, H. (2017a), "Buckling and free vibration of shallow curved micro/nano-beam based on strain gradient theory under thermal loading with temperature-dependent properties", Appl. Phys. A, 123, 4.
- Rahmani, O., Niaei, A.M., Hosseini, S. and Shojaei, M. (2017b), "In-plane vibration of FG micro/nano-mass sensor based on nonlocal theory under various thermal loading via differential transformation method", Superlattices Microstruct., 101, 23-39. https://doi.org/10.1016/j.spmi.2016.11.018
- Rahmani, O. and Pedram, O. (2014), "Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory", Int. J. Eng. Sci., 77, 55-70. https://doi.org/10.1016/j.ijengsci.2013.12.003
- Renault, A., Jaouen, L. and Sgard, F. (2011), "Characterization of elastic parameters of acoustical porous materials from beam bending vibrations", J. Sound Vib., 330(9), 1950-1963. https://doi.org/10.1016/j.jsv.2010.11.013
- Shafiei, N., Kazemi, M. and Ghadiri, M. (2016a), "Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler-Bernoulli microbeams", Physica E: Low-dimensional Syst. Nanost., 83, 74-87. https://doi.org/10.1016/j.physe.2016.04.011
- Shafiei, N., Kazemi, M. Safi, M. and Ghadiri, M. (2016b), "Nonlinear vibration of axially functionally graded non-uniform nanobeams", Int. J. Eng. Sci., 106, 77-94. https://doi.org/10.1016/j.ijengsci.2016.05.009
- Simsek, M. (2014), "Large amplitude free vibration of nanobeams with various boundary conditions based on the nonlocal elasticity theory", Composites Part B: Eng., 56, 621-628. https://doi.org/10.1016/j.compositesb.2013.08.082
- Simsek, M. (2016), "Buckling of Timoshenko beams composed of two-dimensional functionally graded material (2D-FGM) having different boundary conditions", Compos. Struct., 149, 304-314. https://doi.org/10.1016/j.compstruct.2016.04.034
- Simsek, M. and Yurtcu, H. (2013a), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
- Simsek, M. and Yurtcu, H.H. (2013b), "Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory", Compos. Struct., 97, 378-386. https://doi.org/10.1016/j.compstruct.2012.10.038
- Thau, H.T. and VO, T.P. (2012), "A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 54, 58-66. https://doi.org/10.1016/j.ijengsci.2012.01.009
-
Touloukian, Y.S. and Ho, C. (1970), "Thermal expansion. Nonmetallic solids", Thermophysical properties of matter-The TPRC Data Series, New York: IFI/Plenum, 1970-, (Eds., Touloukian, Y.S.), (series ed.); Ho, CY
${\mid}e$ (series tech. ed.), 1. - Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007), "Vibration of nonlocal Timoshenko beams", Nanotechnology, 18(10), 105401. https://doi.org/10.1088/0957-4484/18/10/105401
- Watari, F., Yokoyama, A., Omori, M., Hirai, T., Kondo, H., Uo, M. and Kawasaki, T. (2004), "Biocompatibility of materials and development to functionally graded implant for bio-medical application", Compos. Sci. Technol., 64(6), 893-908. https://doi.org/10.1016/j.compscitech.2003.09.005
- Wattanasakulpong, N. and Chaikittiratana, A. (2015), "Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method", Meccanica, 50(5), 1331-1342. https://doi.org/10.1007/s11012-014-0094-8
- Wosko, M., Paszkiewicz, B., Piasecki, T., Szyszka, A., Paszkiewicz, R. and Tlaczala, M. (2005), "Applications of functionally graded materials in optoelectronic devices", Optica Applicata, 35(3), 663-667.
- Yang, J. and Shen, H.S. (2002), "Vibration characteristics and transient response of shear-deformable functionally graded plates in thermal environments", J. Sound Vib., 255(3), 579-602. https://doi.org/10.1006/jsvi.2001.4161
- Youssef, H.M. and Elsibai, K.A. (2011), "Vibration of gold nanobeam induced by different types of thermal loading-a state-space approach", Nanosc. Microsc. Therm., 15(1), 48-69. https://doi.org/10.1080/15567265.2010.549929
- Zhang, Y., Wang, C. and Challamel, N. (2009), "Bending, buckling, and vibration of micro/nanobeams by hybrid nonlocal beam model", J. Eng. Mech., 136(5),, 562-574.
- Zhou, F.X. and Ma, Q. (2014), "Dynamic response of twodimensional fluid-saturated porous beam", Appl. Mech. Mater., 580-583, 169-174. https://doi.org/10.4028/www.scientific.net/AMM.580-583.169
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