Year 2022,
, 32 - 45, 08.06.2022
Yusuf Ziya Yüksel
,
Şeref Doğuşcan Akbaş
References
- [1] Laura, P.A.A., Gutierrez, R.H., Carnicer and R., Sanzi, H.C. (1991). Free Vibrations of a Solid Circular Plate of Linearly Varying Thickness and Attached to a Winkler Foundation, Journal of Sound and Vibration, 144: 149–161, doi: 10.1016/0022-460X(91)90738-6.
- [2] Xiang, Y., Wang, C.M. and Kitipornchai, S. (1994). Exact Vibration Solution for Initially Stressed Mindlin Plates on Pasternak Foundations, International Journal of Mechanical Sciences, 36: 311–316, doi: 10.1016/0020-7403(94)90037-X.
- [3] Xiang, Y., Kitipornchai, S. and Liew, K.M. (1996). Buckling and Vibration of Thick Laminates on Pasternak Foundations, Journal of Engineering Mechanics, 122: 54–63, doi: 10.1061/(asce)0733-9399(1996)122:1(54).
- [4] Parida, S and Mohanty, S. C. (2018). Free vibration and buckling analysis of functionally graded plates resting on elastic foundation using higher order theory. International Journal of Structural Stability and Dynamics, 18(04), 1850049, doi: https://doi.org/10.1142/S0219455418500499
- [5] Manoj, T., Ayyappan, M., Krishnan, K.S. and Nageswara Rao, B. (2000). Nonlinear Vibration Analysis of Thin Laminated Rectangular Plates on Elastic Foundations, ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik, 80: 183–192, doi: 10.1002/(SICI)1521-4001(200003)80:3<183::AID-ZAMM183>3.0.CO;2-P.
- [6] Shen, H.S., Zheng, J.J. and Huang, X.L. (2003). Dynamic Response of Shear Deformable Laminated Plates Under Thermomechanical Loading and Resting on Elastic Foundatios, Composite Structures, 60: 57–66, doi: 10.1016/S0263-8223(02)00295-7.
- [7] Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004). Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation, International Journal for Numerical Methods in Engineering, 59: 1313–1334, doi: 10.1002/nme.915.
- [8] Hosseini-Hashemi, S., Rokni Damavandi Taher, H., Akhavan, H. and Omidi, M. (2010). Free Vibration of Functionally Graded Rectangular Plates Using First-Order Shear Deformation Plate Theory, Applied Mathematical Modelling, 34: 1276–1291, doi: 10.1016/j.apm.2009.08.008.
- [9] Civalek, Ö. andYavas, A. (2006). Large deflection static analysis of rectangular plates on two parameter elastic foundations. International journal of science and technology, 1(1), 43-50.
- [10] Dehghan, M. and Baradaran, G.H. (2011). Buckling and Free Vibration Analysis of Thick Rectangular Plates Resting on Elastic Foundation Using Mixed Finite Element And Differential Quadrature Method, Applied Mathematics and Computation, 218: 2772–2784, doi: 10.1016/j.amc.2011.08.020.
- [11] Akgöz, B. and Civalek, O. (2011). Nonlinear Vibration Analysis of Laminated Plates Resting on Nonlinear Two-Parameters Elastic Foundations, Steel and Composite Structures, 11(5), 403-421.
- [12] Zhu, P., Lei, Z.X. and Liew, K.M. (2012). Static and Free Vibration Analyses of Carbon Nanotube-Reinforced Composite Plates Using Finite Element Method with First Order Shear Deformation Plate Theory, Composite Structures, 94: 1450–1460, doi: 10.1016/j.compstruct.2011.11.010.
- [13] Long, R., Barry, O., and Oguamanam, D.C.D. (2012). Finite Element Free Vibration Analysis of Soft-Core Sandwich Beams, AIAA journal, 50(1), 235-238, doi: 10.2514/1.J050697.
- [14] Sharaf, T. and Fam, A. (2012). Numerical Modelling of Sandwich Panels with Soft Core and Different Rib Configurations, Journal of Reinforced Plastics and Composites, 31(11), 771-784, doi: 10.1177/0731684412445494.
- [15] Sobhy, M. (2012). Buckling and Free Vibration of Exponentially Graded Sandwich Plates Resting on Elastic Foundations under Various Boundary Conditions, Composite Structures, 99: 76–87, doi: 10.1016/j.compstruct.2012.11.018.
- [16] Nedri, K., El Meiche, N. and Tounsi, A. (2014). Free Vibration Analysis of Laminated Composite Plates Resting on Elastic Foundations by Using a Refined Hyperbolic Shear Deformation Theory, Mechanics of Composite Materials, 49: 629–640, doi: 10.1007/s11029-013-9379-6.
- [17] Mercan, K., Demir, Ç. and Civalek, Ö. (2016). Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique. Curved and Layered Structures, 3(1), doi: https://doi.org/10.1515/cls-2016-0007
- [18] Akbaş, Ş.D. (2014). Wave propagation analysis of edge cracked beams resting on elastic foundation, International Journal of Engineering & Applied Sciences (IJEAS), 6: 40–52. doi: 10.1371/journal.pone.0100496.
- [19] Akbaş, Ş.D. (2015). Free Vibration Analysis of Edge Cracked Functionally Graded Beams Resting on Winkler-Pasternak Foundation, International Journal of Engineering and Applied Sciences, 7: 1–15, doi: 10.1088/2053-1591/ab6ad1.
- [20] Akbaş, Ş. D. (2014). Wave propagation analysis of edge cracked circular beams under impact force. PloS one, 9(6), e100496. doi: 10.1371/journal.pone.0100496
- [21] Yayli, M.Ö. (2015). Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube, Acta Physica Polonica A, 127(3), 678-683, doi: 10.12693/APhysPolA.127.678
- [22] Yayli, M. Ö. (2017). A Compact Analytical Method for Vibration of Micro-Sized Beams with Different Boundary Conditions, Mechanics of Advanced Materials and Structures, 24(6), 496-508, doi: 10.1080/15376494.2016.1143989.
- [23] Yayli, M. Ö. (2018). On The Torsional Vibrations of Restrained Nanotubes Embedded in an Elastic Medium, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(9), 1-12, doi: 10.1007/s40430-018-1346-7.
- [24] Yayli, M. Ö. (2019). Effects Of Rotational Restraints on the Thermal Buckling of Carbon Nanotube, Micro & Nano Letters, 14(2), 158-162, doi: 10.1049/mnl.2018.5428.
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- [26] Akbaş, Ş.D. (2015). Free Vibration and Bending of Functionally Graded Beams Resting on Elastic Foundation, Research on Engineering Structures and Materials, 1: 1 25-37, doi: 10.17515/resm2015.03st0107.
- [27] Doğan, A. (2016). The Effect of Edge Ratio and Fiber Orientation on Free Vibration Analysis of Laminated Composite Plates on Elastic Foundation, Çukurova Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 31: 2, 217–225.
- [28] Yaylı, M. Ö. (2016). Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube Embedded in an Elastic Medium Using Nonlocal Elasticity, International Journal of Engineering and Applied Sciences, 8(2), 40-50, doi: 10.24107/ijeas.252144.
- [29] Yayli, M. Ö. (2017). Buckling Analysis of a Cantilever Single-Walled Carbon Nanotube Embedded in an Elastic Medium with an Attached Spring, Micro & Nano Letters, 12(4), 255-259, doi: 10.1049/mnl.2016.0662.
- [30] Avcar, M. (2016), Pasternak Zemine Oturan Eksenel Yüke Maruz Homojen Olmayan Kirişin Serbest Titreşimi, Politeknik Dergisi, 19: 507–512.
- [31] Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B.B. (2016). Free Vibration Analysis of FGM Nanoplate with Porosities Resting on Winkler Pasternak Elastic Foundations based on Two-Variable Refined Plate Theories, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38: 2193–2211, doi: 10.1007/s40430-015-0482-6.
- [32] Akbaş, Ş.D. (2016). Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium, Smart Structures and Systems, 18(6), 1125-1143, doi: 10.12989/sss.2016.18.6.1125.
- [33] Akbaş, Ş.D. (2017). Stability of a Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method, International Journal of Engineering and Applied Sciences, 9(2), 147-155, doi: 10.24107/ijeas.322375.
- [34] Akbaş, Ş. D. (2018). Geometrically Nonlinear Analysis of Functionally Graded Porous Beams, Wind and Structures, 27(1), 59-70, doi: 10.12989/was.2018.27.1.059.
- [35] Akbaş, Ş. D. (2019). Forced Vibration Analysis of Functionally Graded Sandwich Deep Beams, Coupled Systems Mechanics, 8(3), 259-271 doi: 10.12989/csm.2019.8.3.259.
- [36] Akbaş, Ş. D. (2019). Longitudinal Forced Vibration Analysis of Porous a Nanorod, Mühendislik Bilimleri ve Tasarım Dergisi, 7(4), 736-743, doi: 10.21923/jesd.553328.
- [37] Akbaş, Ş.D. (2020), Static Analysis of a Fiber Reinforced Composite Beam Resting on Winkler-Pasternak Foundation, International Journal of Engineering and Applied Sciences, 12: 88–98, doi: 10.24107/ijeas.790858.
- [38] Shi, D., Zhang, H., Wang, Q. and Zha, S. (2017). Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations, Shock and Vibration, 2017: 1–23, doi: 10.1155/2017/7820130.
- [39] Akgöz, B. and Civalek, Ö. (2017). A Size-Dependent Beam Model for Stability of Axially Loaded Carbon Nanotubes Surrounded by Pasternak Elastic Foundation, Composite Structures, 176, 1028-1038, doi: 10.1016/j.compstruct.2017.06.039.
- [40] Akgöz, B. and Civalek, Ö. (2018). Vibrational Characteristics of Embedded Microbeams Lying on a Two-Parameter Elastic Foundation in Thermal Environment, Composites Part B: Engineering, 150, 68-77, doi: 10.1016/j.compositesb.2018.05.049.
- [41] Kadıoğlu, H. and Yaylı, M. Ö. (2017). Buckling Analysis of Non-Local Timoshenko Beams by Using Fourier Series, International Journal of Engineering and Applied Sciences, 9(4), 89-99, doi: 10.24107/ijeas.362242.
- [42] Zenkour, A.M. and Radwan, A.F. (2018). Free Vibration Analysis of Multilayered Composite and Soft Core Sandwich Plates Resting on Winkler–Pasternak Foundations, Journal of Sandwich Structures and Materials, 20: 169–190, doi: 10.1177/1099636216644863.
- [43] Yüksel, Y.Z. and Akbaş, Ş.D. (2018). Free Vibration Analysis of a Cross-Ply Laminated Plate in Thermal Environment, International Journal of Engineering and Applied Sciences, 10(3), 176-189, doi: 10.24107/ijeas.456755.
- [44] Dastjerdi, S., and Akgöz, B. (2018). New Static and Dynamic Analyses Of Macro and Nano FGM Plates Using Exact Three-Dimensional Elasticity in Thermal Environment, Composite Structures, 192, 626-641, doi: 10.1016/j.compstruct.2018.03.058.
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- [46] Uzun, B., and Yaylı, M. Ö. (2020). Nonlocal Vibration Analysis of Ti-6Al-4V/Zro 2 Functionally Graded Nanobeam on Elastic Matrix, Arabian Journal of Geosciences, 13(4), 1-10, doi: 10.1007/s12517-020-5168-4.
- [47] Civalek, Ö., Dastjerdi, S. and Akgöz, B. (2020). Buckling And Free Vibrations Of CNT-Reinforced Cross-Ply Laminated Composite Plates, Mechanics Based Design of Structures and Machines, 1-18, doi: 10.1080/15397734.2020.1766494.
- [48] Ye, W., Liu, J., Fang, H. and Lin, G. (2020). Numerical Solutions for Magneto–Electro–Elastic Laminated Plates Resting on Winkler Foundation or Elastic Half-Space, Computers and Mathematics with Applications, 79: 2388–2410, doi: 10.1016/j.camwa.2019.11.007.
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Vibration Analysis of a Sandwich Plate with Laminated Face and Porous Core Layers Resting on Elastic Foundation
Year 2022,
, 32 - 45, 08.06.2022
Yusuf Ziya Yüksel
,
Şeref Doğuşcan Akbaş
Abstract
In this study, free vibration responses of a sandwich plate resting on Winkler-Pasternak foundation are investigated by using the first order shear deformation plate theory. The sandwich plate is considered as laminated face and porous core layers. Material properties of laminas are considered as orthotropic and core material is porous property. The Navier procedure is used for the solution of vibration analysis. In numerical examples, vibration frequencies of the composite plate are presented and discussed for various evaluation of mode numbers, sequences of layers, foundation parameters and porosity parameters.
References
- [1] Laura, P.A.A., Gutierrez, R.H., Carnicer and R., Sanzi, H.C. (1991). Free Vibrations of a Solid Circular Plate of Linearly Varying Thickness and Attached to a Winkler Foundation, Journal of Sound and Vibration, 144: 149–161, doi: 10.1016/0022-460X(91)90738-6.
- [2] Xiang, Y., Wang, C.M. and Kitipornchai, S. (1994). Exact Vibration Solution for Initially Stressed Mindlin Plates on Pasternak Foundations, International Journal of Mechanical Sciences, 36: 311–316, doi: 10.1016/0020-7403(94)90037-X.
- [3] Xiang, Y., Kitipornchai, S. and Liew, K.M. (1996). Buckling and Vibration of Thick Laminates on Pasternak Foundations, Journal of Engineering Mechanics, 122: 54–63, doi: 10.1061/(asce)0733-9399(1996)122:1(54).
- [4] Parida, S and Mohanty, S. C. (2018). Free vibration and buckling analysis of functionally graded plates resting on elastic foundation using higher order theory. International Journal of Structural Stability and Dynamics, 18(04), 1850049, doi: https://doi.org/10.1142/S0219455418500499
- [5] Manoj, T., Ayyappan, M., Krishnan, K.S. and Nageswara Rao, B. (2000). Nonlinear Vibration Analysis of Thin Laminated Rectangular Plates on Elastic Foundations, ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik, 80: 183–192, doi: 10.1002/(SICI)1521-4001(200003)80:3<183::AID-ZAMM183>3.0.CO;2-P.
- [6] Shen, H.S., Zheng, J.J. and Huang, X.L. (2003). Dynamic Response of Shear Deformable Laminated Plates Under Thermomechanical Loading and Resting on Elastic Foundatios, Composite Structures, 60: 57–66, doi: 10.1016/S0263-8223(02)00295-7.
- [7] Zhou, D., Cheung, Y.K., Lo, S.H. and Au, F.T.K. (2004). Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation, International Journal for Numerical Methods in Engineering, 59: 1313–1334, doi: 10.1002/nme.915.
- [8] Hosseini-Hashemi, S., Rokni Damavandi Taher, H., Akhavan, H. and Omidi, M. (2010). Free Vibration of Functionally Graded Rectangular Plates Using First-Order Shear Deformation Plate Theory, Applied Mathematical Modelling, 34: 1276–1291, doi: 10.1016/j.apm.2009.08.008.
- [9] Civalek, Ö. andYavas, A. (2006). Large deflection static analysis of rectangular plates on two parameter elastic foundations. International journal of science and technology, 1(1), 43-50.
- [10] Dehghan, M. and Baradaran, G.H. (2011). Buckling and Free Vibration Analysis of Thick Rectangular Plates Resting on Elastic Foundation Using Mixed Finite Element And Differential Quadrature Method, Applied Mathematics and Computation, 218: 2772–2784, doi: 10.1016/j.amc.2011.08.020.
- [11] Akgöz, B. and Civalek, O. (2011). Nonlinear Vibration Analysis of Laminated Plates Resting on Nonlinear Two-Parameters Elastic Foundations, Steel and Composite Structures, 11(5), 403-421.
- [12] Zhu, P., Lei, Z.X. and Liew, K.M. (2012). Static and Free Vibration Analyses of Carbon Nanotube-Reinforced Composite Plates Using Finite Element Method with First Order Shear Deformation Plate Theory, Composite Structures, 94: 1450–1460, doi: 10.1016/j.compstruct.2011.11.010.
- [13] Long, R., Barry, O., and Oguamanam, D.C.D. (2012). Finite Element Free Vibration Analysis of Soft-Core Sandwich Beams, AIAA journal, 50(1), 235-238, doi: 10.2514/1.J050697.
- [14] Sharaf, T. and Fam, A. (2012). Numerical Modelling of Sandwich Panels with Soft Core and Different Rib Configurations, Journal of Reinforced Plastics and Composites, 31(11), 771-784, doi: 10.1177/0731684412445494.
- [15] Sobhy, M. (2012). Buckling and Free Vibration of Exponentially Graded Sandwich Plates Resting on Elastic Foundations under Various Boundary Conditions, Composite Structures, 99: 76–87, doi: 10.1016/j.compstruct.2012.11.018.
- [16] Nedri, K., El Meiche, N. and Tounsi, A. (2014). Free Vibration Analysis of Laminated Composite Plates Resting on Elastic Foundations by Using a Refined Hyperbolic Shear Deformation Theory, Mechanics of Composite Materials, 49: 629–640, doi: 10.1007/s11029-013-9379-6.
- [17] Mercan, K., Demir, Ç. and Civalek, Ö. (2016). Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique. Curved and Layered Structures, 3(1), doi: https://doi.org/10.1515/cls-2016-0007
- [18] Akbaş, Ş.D. (2014). Wave propagation analysis of edge cracked beams resting on elastic foundation, International Journal of Engineering & Applied Sciences (IJEAS), 6: 40–52. doi: 10.1371/journal.pone.0100496.
- [19] Akbaş, Ş.D. (2015). Free Vibration Analysis of Edge Cracked Functionally Graded Beams Resting on Winkler-Pasternak Foundation, International Journal of Engineering and Applied Sciences, 7: 1–15, doi: 10.1088/2053-1591/ab6ad1.
- [20] Akbaş, Ş. D. (2014). Wave propagation analysis of edge cracked circular beams under impact force. PloS one, 9(6), e100496. doi: 10.1371/journal.pone.0100496
- [21] Yayli, M.Ö. (2015). Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube, Acta Physica Polonica A, 127(3), 678-683, doi: 10.12693/APhysPolA.127.678
- [22] Yayli, M. Ö. (2017). A Compact Analytical Method for Vibration of Micro-Sized Beams with Different Boundary Conditions, Mechanics of Advanced Materials and Structures, 24(6), 496-508, doi: 10.1080/15376494.2016.1143989.
- [23] Yayli, M. Ö. (2018). On The Torsional Vibrations of Restrained Nanotubes Embedded in an Elastic Medium, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(9), 1-12, doi: 10.1007/s40430-018-1346-7.
- [24] Yayli, M. Ö. (2019). Effects Of Rotational Restraints on the Thermal Buckling of Carbon Nanotube, Micro & Nano Letters, 14(2), 158-162, doi: 10.1049/mnl.2018.5428.
- [25] Zhang, L.W., Lei, Z.X. and Liew, K.M. (2015). Computation of Vibration Solution for Functionally Graded Carbon Nanotube-Reinforced Composite Thick Plates Resting on Elastic Foundations Using the Element-Free IMLS-Ritz Method, Applied Mathematics and Computation, 256: 488–504, doi: 10.1016/j.amc.2015.01.066.
- [26] Akbaş, Ş.D. (2015). Free Vibration and Bending of Functionally Graded Beams Resting on Elastic Foundation, Research on Engineering Structures and Materials, 1: 1 25-37, doi: 10.17515/resm2015.03st0107.
- [27] Doğan, A. (2016). The Effect of Edge Ratio and Fiber Orientation on Free Vibration Analysis of Laminated Composite Plates on Elastic Foundation, Çukurova Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 31: 2, 217–225.
- [28] Yaylı, M. Ö. (2016). Buckling Analysis of a Rotationally Restrained Single Walled Carbon Nanotube Embedded in an Elastic Medium Using Nonlocal Elasticity, International Journal of Engineering and Applied Sciences, 8(2), 40-50, doi: 10.24107/ijeas.252144.
- [29] Yayli, M. Ö. (2017). Buckling Analysis of a Cantilever Single-Walled Carbon Nanotube Embedded in an Elastic Medium with an Attached Spring, Micro & Nano Letters, 12(4), 255-259, doi: 10.1049/mnl.2016.0662.
- [30] Avcar, M. (2016), Pasternak Zemine Oturan Eksenel Yüke Maruz Homojen Olmayan Kirişin Serbest Titreşimi, Politeknik Dergisi, 19: 507–512.
- [31] Mechab, I., Mechab, B., Benaissa, S., Serier, B. and Bouiadjra, B.B. (2016). Free Vibration Analysis of FGM Nanoplate with Porosities Resting on Winkler Pasternak Elastic Foundations based on Two-Variable Refined Plate Theories, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38: 2193–2211, doi: 10.1007/s40430-015-0482-6.
- [32] Akbaş, Ş.D. (2016). Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium, Smart Structures and Systems, 18(6), 1125-1143, doi: 10.12989/sss.2016.18.6.1125.
- [33] Akbaş, Ş.D. (2017). Stability of a Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method, International Journal of Engineering and Applied Sciences, 9(2), 147-155, doi: 10.24107/ijeas.322375.
- [34] Akbaş, Ş. D. (2018). Geometrically Nonlinear Analysis of Functionally Graded Porous Beams, Wind and Structures, 27(1), 59-70, doi: 10.12989/was.2018.27.1.059.
- [35] Akbaş, Ş. D. (2019). Forced Vibration Analysis of Functionally Graded Sandwich Deep Beams, Coupled Systems Mechanics, 8(3), 259-271 doi: 10.12989/csm.2019.8.3.259.
- [36] Akbaş, Ş. D. (2019). Longitudinal Forced Vibration Analysis of Porous a Nanorod, Mühendislik Bilimleri ve Tasarım Dergisi, 7(4), 736-743, doi: 10.21923/jesd.553328.
- [37] Akbaş, Ş.D. (2020), Static Analysis of a Fiber Reinforced Composite Beam Resting on Winkler-Pasternak Foundation, International Journal of Engineering and Applied Sciences, 12: 88–98, doi: 10.24107/ijeas.790858.
- [38] Shi, D., Zhang, H., Wang, Q. and Zha, S. (2017). Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations, Shock and Vibration, 2017: 1–23, doi: 10.1155/2017/7820130.
- [39] Akgöz, B. and Civalek, Ö. (2017). A Size-Dependent Beam Model for Stability of Axially Loaded Carbon Nanotubes Surrounded by Pasternak Elastic Foundation, Composite Structures, 176, 1028-1038, doi: 10.1016/j.compstruct.2017.06.039.
- [40] Akgöz, B. and Civalek, Ö. (2018). Vibrational Characteristics of Embedded Microbeams Lying on a Two-Parameter Elastic Foundation in Thermal Environment, Composites Part B: Engineering, 150, 68-77, doi: 10.1016/j.compositesb.2018.05.049.
- [41] Kadıoğlu, H. and Yaylı, M. Ö. (2017). Buckling Analysis of Non-Local Timoshenko Beams by Using Fourier Series, International Journal of Engineering and Applied Sciences, 9(4), 89-99, doi: 10.24107/ijeas.362242.
- [42] Zenkour, A.M. and Radwan, A.F. (2018). Free Vibration Analysis of Multilayered Composite and Soft Core Sandwich Plates Resting on Winkler–Pasternak Foundations, Journal of Sandwich Structures and Materials, 20: 169–190, doi: 10.1177/1099636216644863.
- [43] Yüksel, Y.Z. and Akbaş, Ş.D. (2018). Free Vibration Analysis of a Cross-Ply Laminated Plate in Thermal Environment, International Journal of Engineering and Applied Sciences, 10(3), 176-189, doi: 10.24107/ijeas.456755.
- [44] Dastjerdi, S., and Akgöz, B. (2018). New Static and Dynamic Analyses Of Macro and Nano FGM Plates Using Exact Three-Dimensional Elasticity in Thermal Environment, Composite Structures, 192, 626-641, doi: 10.1016/j.compstruct.2018.03.058.
- [45] Uzun, B., Yaylı, M. Ö., and Deliktaş, B. (2020). Free Vibration of FG Nanobeam Using a Finite-Element Method, Micro & Nano Letters, 15(1), 35-40, doi: 10.1049/mnl.2019.0273.
- [46] Uzun, B., and Yaylı, M. Ö. (2020). Nonlocal Vibration Analysis of Ti-6Al-4V/Zro 2 Functionally Graded Nanobeam on Elastic Matrix, Arabian Journal of Geosciences, 13(4), 1-10, doi: 10.1007/s12517-020-5168-4.
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