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Free vibrations of uniform Timoshenko beams on Pasternak foundation using Coupled Displacement Field method

Korabathina Rajesh Koppanati Meera Saheb
Archive of Mechanical Engineering | 2017 | vol. 64 | No 3 | 359-373 | DOI: 10.1515/meceng-2017-0022
Keywords free vibration Coupled Displacement Field method uniform Timoshenko beam Pasternak foundation
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Abstract

Complex structures used in various engineering applications are made up of simple structural members like beams, plates and shells. The fundamental frequency is absolutely essential in determining the response of these structural elements subjected to the dynamic loads. However, for short beams, one has to consider the effect of shear deformation and rotary inertia in order to evaluate their fundamental linear frequencies. In this paper, the authors developed a Coupled Displacement Field method where the number of undetermined coefficients 2n existing in the classical Rayleigh-Ritz method are reduced to n, which significantly simplifies the procedure to obtain the analytical solution. This is accomplished by using a coupling equation derived from the static equilibrium of the shear flexible structural element. In this paper, the free vibration behaviour in terms of slenderness ratio and foundation parameters have been derived for the most practically used shear flexible uniform Timoshenko Hinged-Hinged, Clamped-Clamped beams resting on Pasternak foundation. The findings obtained by the present Coupled Displacement Field Method are compared with the existing literature wherever possible and the agreement is good.

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Bibliography

[1] C.F. Lü, C.W. Lim, and W.A. Yao. A new analytic symplectic elasticity approach for beams resting on Pasternak elastic foundations. Journal of Mechanics of Materials and Structures, 4(10):1741–1754, 2010. doi: 10.2140/jomms.2009.4.1741.
[2] C. Franciosi and A. Masi. Free vibrations of foundation beams on two-parameter elastic soil. Computers & Structures, 47(3):419–426, 1993. doi: 10.1016/0045-7949(93)90237-8.
[3] I. Caliò and A. Greco. Free vibrations of Timoshenko beam-columns on Pasternak foundations. Journal of Vibration and Control, 19(5):686–696, 2013. doi: 10.1177/1077546311433609.
[4] S. Lee, J.K. Kyu Jeong and J. Lee. Natural frequencies for flexural and torsional vibrations of beams on Pasternak foundation. Soils and Foundations, 54(6):1202–1211, 2014. doi: 10.1016/j.sandf.2014.11.013.
[5] M.A. De Rosa. Free vibrations of Timoshenko beams on two-parameter elastic foundation. Computers & Structures, 57(1):151–156, 1995. doi: 10.1016/0045-7949(94)00594-S.
[6] M.A. De Rosa and M.J. Maurizi. The influence of concentrated masses and Pasternak soil on the free vibrations of Euler beams—exact solution. Journal of Sound and Vibration, 212(4):573–581, 1998. doi: 10.1006/jsvi.1997.1424.
[7] M. Karkon and H. Karkon. New element formulation for free vibration analysis of Timoshenko beam on Pasternak elastic foundation. Asian Journal of Civil Engineering (BHRC), 17(4):427–442, 2016.
[8] K. Meera Saheb et al. Free vibration analysis of Timoshenko beams using Coupled Displacement Field Method. Journal of Structural Engineering, 34:233–236, 2007.
[9] M.T. Hassan and M. Nassar. Analysis of stressed Timoshenko beams on two parameter foundations. KSCE Journal of Civil Engineering, 19(1):173–179, 2015. doi: 10.1007/s12205-014-0278-8.
[10] N.D. Kien. Free vibration of prestress Timoshenko beams resting on elastic foundation. Vietnam Journal of Mechanics, 29(1):1–12, 2007. doi: 10.15625/0866-7136/29/1/5586.
[11] P. Obara. Vibrations and stability of Bernoulli-Euler and Timoshenko beams on two-parameter elastic foundation. Archives of Civil Engineering, 60(4):421–440, 2014. doi: 10.2478/ace-2014-0029.
[12] S.Y. Lee, Y.H. Kuo, and F.Y. Lin. Stability of a Timoshenko beam resting on a Winkler elastic foundation. Journal of Sound and Vibration, 153(2):193–202, 1992. doi: 10.1016/S0022-460X(05)80001-X.
[13] T.M. Wang and J.E. Stephens. Natural frequencies of Timoshenko beams on Pasternak foundations. Journal of Sound and Vibration, 51(2):149–155, 1977. doi: 10.1016/S0022-460X(77)80029-1.
[14] T.M. Wang and L.W. Gagnon. Vibrations of continuous Timoshenko beams on Winkler-Pasternak foundations. Journal of Sound and Vibration, 59(2):211–220, 1978. doi: 10.1016/0022-460X(78)90501-1.
[15] T. Yokoyama. Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations. Computers & Structures, 61(6):995–1007, 1996. doi: 10.1016/0045-7949(96)00107-1.
[16] T. Yokoyama. Parametric instability of Timoshenko beams resting on an elastic foundation. Computers & Structures, 28(2):207–216, 1988. doi: 10.1016/0045-7949(88)90041-7.
[17] W.Q. Chen, C.F. Lü, and Z.G. Bian. A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation. Applied Mathematical Modelling, 28(10):877–890, 2004. doi: 10.1016/j.apm.2004.04.001.
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Authors and Affiliations

Korabathina Rajesh
1
Koppanati Meera Saheb
1
  1. Jawaharlal Nehru Technological University Kakinada, Andhra Pradesh, India

Free vibration analysis of Mindlin plates resting on Pasternak foundation using coupled displacement method

Korabathina Rajesh Koppanati Meera Saheb
Archive of Mechanical Engineering | 2018 | vol. 65 | No 1 | 107-128
Keywords fundamental frequency parameter Mindlin plates linear free vibrations CDF Method Pasternak foundation
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Abstract

The authors developed a simple and efficient method, called the Coupled Displacement method, to study the linear free vibration behavior of the moderately thick rectangular plates in which a single-term trigonometric/algebraic admissible displacement, such as total rotations, are assumed for one of the variables (in both X,Y directions), and the other displacement field, such as transverse displacement, is derived by making use of the coupling equations. The coupled displacement method makes the energy formulation to contain half the number of unknown independent coefficients in the case of a moderately thick plate, contrary to the conventional Rayleigh-Ritz method. The smaller number of undetermined coefficients significantly simplifies the vibration problem. The closed form expression in the form of fundamental frequency parameter is derived for all edges of simply supported moderately thick rectangular plate resting on Pasternak foundation. The results obtained by the present coupled displacement method are compared with existing open literature values wherever possible for various plate boundary conditions such as all edges simply supported, clamped and two opposite edges simply supported and clamped and the agreement found is good.

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Authors and Affiliations

Korabathina Rajesh
Koppanati Meera Saheb

Static behaviour of functionally graded plates resting on elastic foundations using neutral surface concept

Van Loi Nguyen Minh Tu Tran Van Long Nguyen Quang Huy Le
Archive of Mechanical Engineering | 2021 | vol. 68 | No 1 | 5-22 | DOI: 10.24425/ame.2020.131706
Keywords static analysis functionally graded plated Winkler-Pasternak foundation physical neutral surface four-variable refined theory
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Abstract

In this study, static behaviors of functionally graded plates resting on Winkler-Pasternak elastic foundation using the four-variable refined theory and the physical neutral surface concept is reported. The four-variable refined theory assumes that the transverse shear strain has a parabolic distribution across the plate’s thickness, thus, there is no need to use the shear correction factor. The material properties of the plate vary continuously and smoothly according to the thickness direction by a power-law distribution. The geometrical middle surface of the functionally graded plate selected in computations is very popular in the existing literature. By contrast, in this study, the physical neutral surface of the plate is used. Based on the four-variable refined plate theory and the principle of virtual work, the governing equations of the plate are derived. Next, an analytical solution for the functionally graded plate resting on the Winkler-Pasternak elastic foundation is solved using the Navier’s procedure. In numerical investigations, a comparison of the static behaviors of the functionally graded plate between several models of displacement field using the physical neutral surface is given, and parametric studies are also presented.
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Bibliography

[1] J.N. Reddy and C.D. Chin. Thermomechanical analysis of functionally graded cylinders and plates. Journal of Thermal Stresses, 21(6):593–626, 1998. doi: 10.1080/01495739808956165.
[2] S-H. Chi and Y-L.Chung. Mechanical behavior of functionally graded material plates under transverse load – Part I: Analysis. International Journal of Solids and Structures, 43(13):3657–3674, 2006. doi: 10.1016/j.ijsolstr.2005.04.011.
[3] V-L. Nguyen and T-P. Hoang. Analytical solution for free vibration of stiffened functionally graded cylindrical shell structure resting on elastic foundation. SN Applied Sciences, 1(10):1150, 2019. doi: 10.1007/s42452-019-1168-y.
[4] A.M. Zenkour and N.A. Alghamdi. Thermoelastic bending analysis of functionally graded sandwich plates. Journal of Materials Science, 43(8):2574–2589, 2008. doi: 10.1007/s10853-008-2476-6.
[5] S.A. Sina, H.M. Navazi, and H. Haddadpour. An analytical method for free vibration analysis of functionally graded beams. Materials & Design, 30(3):741–747, 2009. doi: 10.1016/j.matdes.2008.05.015.
[6] I. Mechab, H.A. Atmane, A. Tounsi, H.A. Belhadj, E.A. Adda Bedia. A two variable refined plate theory for the bending analysis of functionally graded plates. Acta Mechanica Sinica, 26(6):941–949, 2010. doi: 10.1007/s10409-010-0372-1.
[7] M.T. Tran, V.L. Nguyen, and A.T. Trinh. Static and vibration analysis of cross-ply laminated composite doubly curved shallow shell panels with stiffeners resting on Winkler–Pasternak elastic foundations. International Journal of Advanced Structural Engineering, 9(2):153–164, 2017. doi: 10.1007/s40091-017-0155-z.
[8] A. Gholipour, H. Farokhi, and M.H. Ghayesh. In-plane and out-of-plane nonlinear size-dependent dynamics of microplates. Nonlinear Dynamics, 79(3):1771–1785, 2015. doi: 10.1007/s11071-014-1773-7.
[9] M.T. Tran, V.L. Nguyen, S.D. Pham, and J. Rungamornrat. Vibration analysis of rotating functionally graded cylindrical shells with orthogonal stiffeners. Acta Mechanica, 231:2545–2564, 2020. doi: 10.1007/s00707-020-02658-y.
[10] S-H. Chi and Y-L. Chung. Mechanical behavior of functionally graded material plates under transverse load – Part II: Numerical results. International Journal of Solids and Structures, 43(13):3675–3691, 2006. doi: 10.1016/j.ijsolstr.2005.04.010.
[11] S. Hosseini-Hashemi, H.R.D Taher, H. Akhavan, and M. Omidi. Free vibration of functionally graded rectangular plates using first-order shear deformation plate theory. Applied Mathematical Modelling, 34(5):1276–1291, 2010. doi: 10.1016/j.apm.2009.08.008.
[12] M.S.A. Houari, S. Benyoucef, I. Mechab, A. Tounsi, and E.A. Adda Bedia. Two-variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates. Journal of Thermal Stresses, 34(4):315–334, 2011. doi: 10.1080/01495739.2010.550806.
[13] M.Talha and B.N. Singh. Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Applied Mathematical Modelling, 34(12):3991–4011, 2010. doi: 10.1016/j.apm.2010.03.034.
[14] H-T. Thai and S-E. Kim. A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates. Composite Structures, 96:165–173, 2013. doi: 10.1016/j.compstruct.2012.08.025.
[15] A. Chikh, A. Tounsi, H. Hebali, and S.R. Mahmoud. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT. Smart Structures and Systems, 19(3):289–297, 2017. doi: 10.12989/sss.2017.19.3.289.
[16] H.H. Abdelaziz, M.A.A. Meziane, A.A. Bousahla, A. Tounsi, S.R. Mahmoud, and A.S. Alwabli. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions. Steel and Composite Structures, 25(6):693–704, 2017. doi: 10.12989/scs.2017.25.6.693.
[17] D-G. Zhang, Y-H. Zhou. A theoretical analysis of FGM thin plates based on physical neutral surface. Computational Materials Science, 44(2):716–720, 2008. doi: 10.1016/j.commatsci.2008.05.016.
[18] A.A. Bousahla, M.S.A. Houari, A. Tounsi A, E.A. Adda Bedia. A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates. International Journal of Computational Methods, 11(06):1350082, 2014. doi: 10.1142/S0219876213500825.
[19] Y. Liu, S. Su, H. Huang, and Y. Liang. Thermal-mechanical coupling buckling analysis of porous functionally graded sandwich beams based on physical neutral plane. Composites Part B: Engineering, 168:236–242, 2019. doi: 10.1016/j.compositesb.2018.12.063.
[20] D-G. Zhang. Thermal post-buckling and nonlinear vibration analysis of FGM beams based on physical neutral surface and high order shear deformation theory. Meccanica, 49(2):283–293, 2014. doi: 10.1007/s11012-013-9793-9.
[21] D-G. Zhang. Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory. Composite Structures, 100:121–126, 2013. doi: 10.1016/j.compstruct.2012.12.024.
[22] H-T. Thai and B. Uy. Levy solution for buckling analysis of functionally graded plates based on a refined plate theory. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 227(12):2649–2664, 2013. doi: 10.1177/0954406213478526.
[23] Y. Khalfi, M.S.A. Houari, and A. Tounsi. A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation. International Journal of Computational Methods, 11(05):1350077, 2014. doi: 10.1142/S0219876213500771.
[24] H. Bellifa, K.H. Benrahou, L. Hadji, M.S.A. Houari, and A. Tounsi. Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 38(1):265–275, 2016. doi: 10.1007/s40430-015-0354-0.
[25] H. Shahverdi and M.R. Barati. Vibration analysis of porous functionally graded nanoplates. International Journal of Engineering Science, 120:82–99, 2017. doi: 10.1016/j.ijengsci.2017.06.008.
[26] R.P. Shimpi and H.G. Patel. A two variable refined plate theory for orthotropic plate analysis. International Journal of Solids and Structures, 43(22-23):6783–6799, 2006. doi: 10.1016/j.ijsolstr.2006.02.007.
[27] H-T. Thai and D-H. Choi. A refined plate theory for functionally graded plates resting on elastic foundation. Composites Science and Technology, 71(16):1850–1858, 2011. doi: 10.1016/j.compscitech.2011.08.016.
[28] M.H. Ghayesh. Viscoelastic nonlinear dynamic behaviour of Timoshenko FG beams. The European Physical Journal Plus, 134(8):401, 2019. doi: 10.1140/epjp/i2019-12472-x .
[29] M.H. Ghayesh. Nonlinear oscillations of FG cantilevers. Applied Acoustics, 145:393–398, 2019. doi: 10.1016/j.apacoust.2018.08.014.
[30] M.H. Ghayesh. Dynamical analysis of multilayered cantilevers. Communications in Nonlinear Science and Numerical Simulation, 71:244–253, 2019. doi: 10.1016/j.cnsns.2018.08.012.
[31] M.H. Ghayesh. Mechanics of viscoelastic functionally graded microcantilevers. European Journal of Mechanics – A/Solids, 73:492–499, 2019. doi: 10.1016/j.euromechsol.2018.09.001.
[32] M.H. Ghayesh. Dynamics of functionally graded viscoelastic microbeams. International Journal of Engineering Science, 124:115–131, 2018. doi: 10.1016/j.ijengsci.2017.11.004.
[33] A.T. Trinh, M.T. Tran, H.Q. Tran, and V.L. Nguyen. Vibration analysis of cross-ply laminated composite doubly curved shallow shell panels with stiffeners. Vietnam Journal of Science and Technology, 55(3):382–392, 2017. doi: 10.15625/2525-2518/55/3/8823.
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Authors and Affiliations

Van Loi Nguyen
1
ORCID: ORCID
Minh Tu Tran
1
ORCID: ORCID
Van Long Nguyen
1
Quang Huy Le
2
  1. Department of Strength of Materials, National University of Civil Engineering, Hanoi, Vietnam
  2. Department of Highway Engineering, Faculty of Civil Engineering, University of Transport Technology, Hanoi, Vietnam

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