Structural Engineering and Mechanics

  • 제71권5호
  • /
  • Pages.485-502
  • /
  • 2019
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions

  • Alimirzaei, S. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, M. (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Tounsi, Abdelouahed (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • 투고 : 2019.01.22
  • 심사 : 2019.03.16
  • 발행 : 2019.09.10
⟨ 이전 논문 다음 논문 ⟩

초록

In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton's principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

키워드

과제정보

연구 과제 주관 기관 : University of Kashan

참고문헌

  1. Adnan Elshafei, M. (2013), "FE modeling and analysis of isotropic and orthotropic beams using first order shear deformation theory", Mater. Sci. Appl., 4(1), 77-102. http://dx.doi.org/10.4236/msa.2013.41010.
  2. Bakhadda, B., BachirBouiadjra, M., Bourada, F., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation", Wind. Struct., 27(5), 311-324. https://doi.org/10.12989/was.2018.27.5.311.
  3. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.
  4. Chakraborty, A., Mahaptra, D.R. and Gopalakrishnan, S. (2002), "Finite element analysis of free vibration and wave propagation in asymmetric composite beam with structural discontinuities", Compos. Struct., 55(1), 23-36. https://doi.org/10.1016/S0263-8223(01)00130-1.
  5. Ghorbanpour Arani A., Hashemian M., Loghman A., and Mohammadimehr M. (2011b), "Study of dynamic stability of the double-walled carbon nanotubes under axial loading embedded in an elastic medium by the energy method", J. Appl. Mech. Technical Physics, 52(5), 815-824. https://doi.org/10.1134/S0021894411050178.
  6. Ghorbanpour Arani A., Mohammadimehr M., Saidi A.R., Shogaei S. and Arefmanesh A. (2011a), "Thermal buckling analysis of double-walled carbon nanotubes considering the small-scale length effect", Proc. IMechE, Part C, J. Mech. Eng. Sci., 225(1), 248-256. https://doi.org/10.1177/09544062JMES1975.
  7. Ghorbanpour Arani, A. and Amir, S. (2013), "Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory", Physica B, 419, 1-6. https://doi.org/10.1016/j.physb.2013.03.010.
  8. Ghorbanpour Arani, A., Amir, S., Dashti, P. and Yousefi, M. (2014), "Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect", Comput. Mater. Sci., 86, 144-154. https://doi.org/10.1016/j.commatsci.2014.01.047.
  9. Ghorbanpour Arani, A., Amir, S., Shajari, A.R. and Mozdianfard, M.R. (2012), "Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory", Compos. Part B: Engineering, 43(2), 195-203. https://doi.org/10.1016/j.compositesb.2011.10.012.
  10. Ghorbanpour Arani, A., Mobarakeh, M.R., Shams, S. and Mohammadimehr, M. (2012). "The effect of CNT volume fraction on the magneto-thermo-electro-mechanical behavior of smart nanocomposite cylinder", J. Mech. Sci. Technol., 26(8), 2565-2572. https://doi.org/10.1007/s12206-012-0639-5.
  11. Ghorbanpour Arani, A., Rousta Navia B. and Mohammadimehr, M. (2015), "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nano-composite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189.
  12. Gu, X.J., Hao, Y.X., Zhang, W., Liu, L.T. and Chen, J. (2019), "Free vibration of rotating cantilever pre-twisted panel with initial exponential function type geometric imperfection", Appl. Math. Model. 68, 327-352. https://doi.org/10.1016/j.apm.2018.11.037.
  13. Heshmati, M. and Yas, M.H. (2013), "Dynamic analysis of functionally graded multi-walled carbon nanotube-polystyrene nanocomposite beams subjected to multi-moving loads", Mater. Design., 49, 894-904. https://doi.org/10.1016/j.matdes.2013.01.073.
  14. Karami, B., Janghorban, M. and Tounsi, A. (2018a), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos Struct., 27(2), 201-216. https://doi.org/10.12989/scs.2018.27.2.201.
  15. Karami, B., Janghorban, M. and Tounsi, A. (2018b), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Walled Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025.
  16. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids., 51(8), 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
  17. Lei, Z.X., Zhang, L.W. and Liew, K.M. (2016), "Analysis of laminated CNT reinforced functionally graded plates using the element-free kp-Ritz method", Compos. Struct., 84, 211-221. https://doi.org/10.1016/j.compositesb.2015.08.081.
  18. Liew, K.M., Lei, Z.X. and Zhang, L.W. (2015), "Mechanical analysis of functionally graded carbon nanotube reinforced Composites: A review", Compos. Struct., 120, 90-97. https://doi.org/10.1016/j.compstruct.2014.09.041.
  19. Liew, K.M., Lei, Z.X., Yu, J.L. and Zhang, L.W. (2014), "Post buckling of carbon nanotube-reinforced functionally graded cylindrical panels under axial compression using a meshless approach", Comput. Appl. Mech. Eng., 268, 1-17. https://doi.org/10.1016/j.cma.2013.09.001.
  20. Mehar, K. and Panda, S.K. (2017), "Thermoelastic analysis of FGCNT reinforced shear deformable composite plate under various loading", Int. J. Comput. Meth., 14(2). https://doi.org/10.1142/S0219876217500190.
  21. Mohammadimehr, M. and Rahmati, A.H. (2013), "Small scale effect on electro-thermo-mechanical vibration analysis of singlewalled boron nitride nanorods under electric excitation", Turkish J. Eng. Environ. Sci., 37(1), 1-15.
  22. Mohammadimehr, M., Rostami, R. and Arefi, M. (2016f), "Electro-elastic analysis of a sandwich thick plate considering FG core and composite piezoelectric layers on Pasternak foundation using TSDT", Steel Compos. Struct., 20(3), 513-544. https://doi.org/10.12989/scs.2016.20.3.513
  23. Mohammadimehr, M. and Shahedi, S. (2017b) "High-order buckling and free vibration analysis of two types sandwich beam including AL or PVC-foam flexible core and CNTs reinforced nanocomposite face sheets using GDQM", Compos. Part B Eng., 108, 91-107. https://doi.org/10.1016/j.compositesb.2016.09.040.
  24. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., 59(3), 431-454. http://dx.doi.org/10.12989/sem.2016.59.3.431.
  25. Mohammadimehr, M. and Alimirzaei, S. (2017), "Buckling and free vibration analysis of tapered FG- CNTRC micro Reddy beam under longitudinal magnetic field using FEM", Smart Struct. Sys., 19(3), 309-322. https://doi.org/10.12989/sss.2017.19.3.309.
  26. Mohammadimehr, M. and Mehrabi, M. (2017c), "Stability and free vibration analyses of double-bonded micro composite sandwich cylindrical shells conveying fluid flow", Appl. Math. Model., 47, 685-709. https://doi.org/10.1016/j.apm.2017.03.054.
  27. Mohammadimehr, M., Farahi, M.J. and Alimirzaei, S. (2016b), "Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory", Appl. Math. Mech., 37(10), 1375-1392. https://doi.org/10.1007/s10483-016-2138-9.
  28. Mohammadimehr, M., Mohammadimehr, M.A. and Dashti, P. (2016c), "Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic microplate based on surface stress and modified couple stress theories using differential quadrature method (DQM)", Appl. Math. Mech., 37(4), 529-554. https://doi.org/10.1007/s10483-016-2045-9.
  29. Mohammadimehr, M., Mohandes, M. and Moradi, M., (2016a), "Size dependent effect on the buckling and vibration analysis of double-bonded nanocomposite piezoelectric plate reinforced by boron nitride nanotube based on modified couple stress theory", J. Vib. Control., 22(7), 1790-1807. https://doi.org/10.1177/1077546314544513.
  30. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2015), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671. https://doi.org/10.1016/j.compstruct.2015.05.077.
  31. Mohammadimehr, M., Rousta Navi, B. and Ghorbanpour Arani, A. (2016d), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of doublecoupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part. B., 87, 132-148. https://doi.org/10.1016/j.compositesb.2015.10.007.
  32. Mohammadimehr, M., Saidi, A.R., Ghorbanpour Arani, A., Arefmanesh, A. and Han, Q. (2010), "Torsional buckling of a DWCNT embedded on Winkler and Pasternak Foundations using nonlocal theory", J. Mech. Sci. Tech., 24(6), 1289-1299. https://doi.org/10.1007/s12206-010-0331-6.
  33. Mohammadimehr, M., Salemi, M. and Rousta Navi, B. (2016e), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermomechanical loadings using DQM", Compos. Struct., 138, 361-380. https://doi.org/10.1016/j.compstruct.2015.11.055.
  34. Mohammadimehr, M., Zarei, H. B., Parakandeh, A. and Arani, A.G. (2017b), "Vibration analysis of double-bonded sandwich microplates with nanocomposite facesheets reinforced by symmetric and un-symmetric distributions of nanotubes under multi physical fields", Struct. Eng. Mech., 64(3), 361-379. https://doi.org/10.12989/sem.2017.64.3.361.
  35. Moradi, R., Foroutan M. and Pourasghar, A. (2013), "Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method", Mater. Design, 44, 256-266. https://doi.org/10.1016/j.matdes.2012.07.069.
  36. Mosallaie Barzok, A.A., Ghorbanpour Arani, A., Kolahchi, R. and Mozdianfard, M.R. (2012), "Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core", Appl. Math Model., 36, 2983-2995. https://doi.org/10.1016/j.apm.2011.09.093.
  37. Murmu, T. and Pradhan, S.C. (2009), "Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM", Physica. E., 41(7), 1232-1239. https://doi.org/10.1016/j.physe.2009.02.004.
  38. Narendar, S., Gupta, S.S. and Gopalakrishnan, S. (2012), "Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory", Appl. Math. Model., 36(9), 4529-4538. https://doi.org/10.1016/j.apm.2011.11.073.
  39. Nirmala, V. and Kolandaivel, P. (2007), "Structure and electronic properties of armchair boron nitride nanotubes", J. Molecular Struct., 817(1-3), 137-145. https://doi.org/10.1016/j.theochem.2007.04.033.
  40. Oh, E. (2011), "Elastic properties of various boron-nitride structures", Met. Mater. Int., 17(1), 21-27. https://doi.org/10.1007/s12540-011-0204-2.
  41. Reddy, J.N. (2004), An Introduction to nonlinear finite element analysis, New York, Oxford University Press, USA.
  42. Salehi-Khojin, M. and Jalili, N. (2008), "Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings", Compos. Sci. Tech., 68(6), 1489-1501. https://doi.org/10.1016/j.compscitech.2007.10.024.
  43. Vaccarini, L., Goze, C, Henrard, L., Hernandez, E., Bernier, P. and Rubio, A. (2000), "Mechanical and Electronic Properties of Carbon and Boron-Nitride Nanotubes", Carbon, 38, 1681. https://doi.org/10.1016/S0008-6223(99)00293-6.
  44. Wang, B., Deng, Z.C. and Zhang, K. (2013), "Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory", Appl. Math. Mech., 34(3), 269-280. https://doi.org/10.1007/s10483-013-1669-8.
  45. Wang, B., Zichen, D., Huajiang, O. and Jiaxi, Z. (2015), "Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory", Physica. E., 66, 283-292. https://doi.org/10.1016/j.physe.2014.09.015.
  46. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Pres. Ves. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012.
  47. Yas, M.H. and Heshmati, M. (2012), "Dynamic analysis of functionally graded nano composite beams reinforced by randomly oriented carbon nanotube under the action of moving load", Appl. Math. Model., 36(4), 1371-1394. https://doi.org/10.1016/j.apm.2011.08.037.
  48. Zhang, B., He, Y., Liu, D., Gan, Z. and Shen, L. (2014), "Nonclassical Timoshenko beam element based on the strain gradient elasticity theory", Finite Elem. Anal. Des., 79, 22-39. https://doi.org/10.1016/j.finel.2013.10.004.
  49. Zhang, L.W. and Selim, B.A. (2017), "Vibration analysis of CNTreinforced thick laminated composite plates based on Reddy's higher-order shear deformation theory", Compos. Struct., 160, 689-705. https://doi.org/10.1016/j.compstruct.2016.10.102.
  50. Zhang, L.W. and Xiao, L.N. (2016), "Mechanical behavior of laminated CNT-reinforced composite skew plates subjected to dynamic loading", Compos. Struct., 122, 219-230. https://doi.org/10.1016/j.compositesb.2017.03.041.
  51. Zhang, L.W., Liew, K.M. and Reddy, J.N. (2016), "Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression", Compos. Struct., 298, 1-28. https://doi.org/10.1016/j.cma.2015.09.016.
  52. Zhang, L.W., Song, G. and Liew, K.M. (2015), "Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLSRitz method", Compos. Struct., 128, 165-175. https://doi.org/10.1016/j.compstruct.2015.03.011.
  53. Zhang, L.W., Song, Z.G. and Liew, K.M. (2016), "Optimal shape control of CNT reinforced functionally graded composite plates using piezoelectric patches", Compos. part B, 85, 140-149. https://doi.org/10.1016/j.compositesb.2015.09.044.
  54. Zhang, L.W., Liu, W.H. and Liew, K.M. (2016), "Geometrically nonlinear large deformation analysis of triangular CNTreinforced composite plates", Int. J. Non-Linear Mech, 6, 122-132. https://doi.org/10.1016/j.ijnonlinmec.2016.08.004.
  55. Zhang, L.W., Zhu, P. and Liew, K.M. (2013), "Thermal buckling of functionally graded plates using a local Kriging meshless method", Compos. Struct., 108, 472-492. https://doi.org/10.1016/j.compstruct.2013.09.043.
  56. Zhu, P., Zhang, L.W. and Liew, K.M. (2014), "Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local PetrovCGalerkin approach with moving Kriging interpolation", Compos. Struct., 107(4), 298-314. https://doi.org/10.1016/j.compstruct.2013.08.001.

피인용 문헌

  1. Axisymmetric deformation in transversely isotropic thermoelastic medium using new modified couple stress theory vol.8, pp.6, 2019, https://doi.org/10.12989/csm.2019.8.6.501
  2. Design Optimization of Concrete Aqueduct Structure considering Temperature Effects vol.2020, 2019, https://doi.org/10.1155/2020/6679047
  3. Stability of Two Weakly Coupled Elastic Beams with Partially Local Damping vol.2020, 2019, https://doi.org/10.1155/2020/7169526
  4. Bending, Buckling and Free Vibration Analysis of Size-Dependent Nanoscale FG Beams Using Refined Models and Eringen’s Nonlocal Theory vol.12, pp.1, 2020, https://doi.org/10.1142/s1758825120500076
  5. Effect of thermal conductivity on isotropic modified couple stress thermoelastic medium with two temperatures vol.34, pp.2, 2019, https://doi.org/10.12989/scs.2020.34.2.309
  6. Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors vol.25, pp.3, 2019, https://doi.org/10.12989/cac.2020.25.3.215
  7. Effect of the rotation on the thermal stress wave propagation in non-homogeneous viscoelastic body vol.21, pp.1, 2019, https://doi.org/10.12989/gae.2020.21.1.001
  8. Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory vol.35, pp.1, 2020, https://doi.org/10.12989/scs.2020.35.1.147
  9. Analysis of post-buckling of higher-order graphene oxide reinforced concrete plates with geometrical imperfection vol.9, pp.4, 2019, https://doi.org/10.12989/acc.2020.9.4.397
  10. Finite element based post-buckling analysis of refined graphene oxide reinforced concrete beams with geometrical imperfection vol.25, pp.4, 2020, https://doi.org/10.12989/cac.2020.25.4.283
  11. A simple analytical model for free vibration and buckling analysis of orthotropic rectangular plates vol.75, pp.2, 2019, https://doi.org/10.12989/sem.2020.75.2.157
  12. Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core vol.36, pp.4, 2019, https://doi.org/10.1007/s00366-020-01023-w
  13. Multiphysical theoretical prediction and experimental verification of vibroacoustic responses of fruit fiber‐reinforced polymeric composite vol.41, pp.11, 2020, https://doi.org/10.1002/pc.25724
  14. Nonlocal nonlinear stability of higher-order porous beams via Chebyshev-Ritz method vol.76, pp.3, 2019, https://doi.org/10.12989/sem.2020.76.3.413
  15. A mechanical model to investigate Aedesaegypti mosquito bite using new techniques and its applications vol.11, pp.6, 2019, https://doi.org/10.12989/mwt.2020.11.6.399
  16. Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis vol.9, pp.4, 2019, https://doi.org/10.12989/amr.2020.9.4.265
  17. Time Harmonic interactions in the axisymmetric behaviour of transversely isotropic thermoelastic solid using New M-CST vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.521
  18. Dynamic analysis of a laminated composite beam under harmonic load vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.563
  19. Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.575
  20. Thermal frequency analysis of FG sandwich structure under variable temperature loading vol.77, pp.1, 2019, https://doi.org/10.12989/sem.2021.77.1.057
  21. Interactions in a homogeneous isotropic modified couple stress thermoelastic solid with multi-dual-phase-lag heat transfer and two temperature vol.38, pp.2, 2019, https://doi.org/10.12989/scs.2021.38.2.213
  22. Numerical and experimental investigation for monitoring and prediction of performance in the soft actuator vol.77, pp.2, 2021, https://doi.org/10.12989/sem.2021.77.2.167
  23. Lifetime seismic performance assessment of high-rise steel-concrete composite frame with buckling-restrained braces under wind-induced fatigue vol.77, pp.2, 2019, https://doi.org/10.12989/sem.2021.77.2.197
  24. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2019, https://doi.org/10.12989/sem.2021.77.2.217
  25. Frequency characteristics and sensitivity analysis of a size-dependent laminated nanoshell vol.10, pp.2, 2019, https://doi.org/10.12989/anr.2021.10.2.175
  26. Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity vol.10, pp.1, 2019, https://doi.org/10.12989/csm.2021.10.1.061
  27. Electromagnetic field and initial stress on a porothermoelastic medium vol.78, pp.1, 2021, https://doi.org/10.12989/sem.2021.78.1.001
  28. Post-buckling analysis of imperfect nonlocal piezoelectric beams under magnetic field and thermal loading vol.78, pp.1, 2019, https://doi.org/10.12989/sem.2021.78.1.015
  29. An analytical solution for equations and the dynamical behavior of the orthotropic elastic material vol.11, pp.4, 2021, https://doi.org/10.12989/acc.2021.11.4.315
  30. Computer simulation for stability analysis of the viscoelastic annular plate with reinforced concrete face sheets vol.27, pp.4, 2019, https://doi.org/10.12989/cac.2021.27.4.369
  31. Three-phase-lag model on a micropolar magneto-thermoelastic medium with voids vol.78, pp.2, 2019, https://doi.org/10.12989/sem.2021.78.2.187
  32. Stress analysis of a pre-stretched orthotropic plate with finite dimensions vol.45, pp.2, 2021, https://doi.org/10.1139/tcsme-2019-0241
  33. Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches vol.40, pp.2, 2021, https://doi.org/10.12989/scs.2021.40.2.157
  34. Surface wave scattering analysis in an initially stressed stratified media vol.38, pp.8, 2019, https://doi.org/10.1108/ec-03-2020-0133
  35. Free vibration of multi-cracked beams vol.79, pp.4, 2019, https://doi.org/10.12989/sem.2021.79.4.441
  36. New solution for damaged porous RC cantilever beams strengthening by composite plate vol.10, pp.3, 2019, https://doi.org/10.12989/amr.2021.10.3.169