Membrane and Water Treatment

  • 제11권4호
  • /
  • Pages.295-302
  • /
  • 2020
  • /
  • 2005-8624(pISSN)
  • /
  • 2092-7037(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

A theoretical approach in 2d-space with applications of the periodic wave solutions in the elastic body

  • Ramady, Ahmed (GRC Department, Jeddah Community College, King Abdulaziz University) ;
  • Mahmoud, S.R. (GRC Department, Jeddah Community College, King Abdulaziz University) ;
  • Atia, H.A. (Mathematics Department, Arts - Rabigh& College of Sciences, King Abdulaziz University)
  • 투고 : 2020.03.17
  • 심사 : 2020.05.18
  • 발행 : 2020.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, theoretical approach with applications of the periodic wave solutions in an elastic material is applied by study the effect of initial stress, and rotation, on the radial displacement and the corresponding stresses in non-homogeneous orthotropic material. An Analytical solution for the elastodynamic equation has obtained concerning the component of displacement. The variations of stresses and displacements have shown graphically. Comparisons with previously published results in the absence of initial stress, rotation and non-homogeneity have made. Finally, numerical results have given and illustrated graphically for each case considered.

키워드

과제정보

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under grant No. G-397-130-36. The authors, therefore, acknowledge with thanks DSR for technical and financial support.

참고문헌

  1. Abd-Alla, A.M and Mahmoud, S.R, (2010), "Magneto-thermoelastic problem in rotating non-homogeneous orthotropic hollow cylindrical under the hyperbolic heat conduction model", Meccanica, 45(4), 451-462. https://doi.org/10.1007/s11012-009-9261-8.
  2. Abd-Alla, A.M and Mahmoud, S.R, (2013), "On the problem of radial vibrations in the non-homogeneity isotropic cylinder under the influence of initial stress and magnetic field", J. Vib. Control, 19(9), 1283-1293. https://doi.org/10.1177/1077546312441043.
  3. Abd-Alla, A.M, Yahya, G.A., Mahmoud, S.R, (2013), "Radial vibrations in a non-homogeneous orthotropic elastic hollow sphere subjected to rotation", J. Comput. Theoretical Nanosci., 10(2), 455-463. https://doi.org/10.1166/jctn.2013.2718.
  4. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A., Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498.https://doi.org/10.12989/cac.2019.24.6.489.
  5. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  6. Akbarov, S.D., Guliyev, H.H., Sevdimaliyev, Y.M., Yahnioglu, N. (2018), "The discrete-analytical solution method for investigation dynamics of the sphere with inhomogeneous initial stresses", Comput. Mater. Continua, 55(2), 359-380. doi:10.3970/cmc.2018.00173.
  7. Alimirzaei, S., Mohammadimehr, M., Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485
  8. Al-Maliki, A.F., Faleh, N.M., Alasadi, A.A. (2019) "Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities", Str Monit Maint., 6(2), 147-159. https://doi.org/10.12989/smm.2019.6.2.147
  9. Al-Maliki, A.F.H., Ahmed, R.A., Moustafa, N.M. and Faleh, N.M. (2020), "Finite element based modeling and thermal dynamic analysis of functionally graded graphene reinforced beams", Adv. Comput. Design., 5(2), 177-193. https://doi.org/10.12989/acd.2020.5.2.177.
  10. Argatov, I.I. (2005), "Approximate solution of the axisymmetric contact problem for an elastic sphere", J. Appl. Math. Mech., 69, 275-286. https://doi.org/10.1016/j.jappmathmech.2005.03.014.
  11. Asghar, S., Naeem, M.N., Hussain, M., Taj, M., Tounsi, A. (2020), "Prediction and assessment of nonlocal natural frequencies of DWCNTs: Vibration analysis", Comput. Concrete, 25(2), 133-144. https://doi.org/10.12989/cac.2020.25.2.133
  12. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  13. Bahrami, A., Ilkhani, M.R., Bahrami, M.N. (2013), "Wave propagation technique for free vibration analysis of annular circular and sectorial membranes", J. Vib. Control, 21(9), 1866-1872. https://doi.org/10.1177/1077546313505123.
  14. Bakhshi, N., Taheri-Behrooz, F. (2019), "Length effect on the stress concentration factor of a perforated orthotropic composite plate under in-plane loading", Compos. Mater. Eng.., 1(1),71-90. https://doi.org/10.12989/cme.2019.1.1.071.
  15. Barati, M.R. (2019), "Vibration analysis of FG nanoplates with nanovoids on viscoelastic substrate under hygro-thermo-mechanical loading using nonlocal strain gradient theory", Struct. Eng. Mech., 64(6), 683-693. https://doi.org/10.12989/sem.2017.64.6.683.
  16. Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A., Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699
  17. Bedia, W.A., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T., Alhodaly, M.Sh. (2019), "A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams", J. Nano Res., 57, 175-191. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175
  18. Behera, S., Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Design, 3(3), 213-232. https://doi.org/10.12989/acd.2017.2.3.165.
  19. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A., Mohammadimehr, M. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 81-92. https://doi.org/10.12989/scs.2019.33.1.081
  20. Berghouti, H., Adda Bedia, E.A., Benkhedda, A., Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351
  21. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503
  22. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A., Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  23. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A., Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of - different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197
  24. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A., Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185
  25. Draoui, A., Zidour, M., Tounsi, A., Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117
  26. Farhan, A.M. (2017), "Effect of rotation on the propagation of waves in hollow poroelastic circular cylinder with magnetic field", Comput. Mater. Continua, 53(2), 129-156. https://doi.org/10.3970/cmc.2017.053.133.
  27. Fenjan, R.M., Ahmed, R.A., Alasadi, A.A., Faleh, N.M. (2019). "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and non-uniform porosities", Coupled Syst Mech., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247.
  28. Fladr,J., Bily,P. and Broukalova, I. (2019)," Evaluation of steel fiber distribution in concrete by computer aided image analysis", Compos. Mater. Eng..,1(1),49-70. https://doi.org/10.12989/cme.2019.1.1.049.
  29. Ghadimi, M.G. (2020), "Buckling of non-sway Euler composite frame with semi-rigid connection", Compos. Mater. Eng.., 2(1), 13-24. https://doi.org/10.12989/cme.2020.2.1.013.
  30. Ghannadpour, S.A.M. and Mehrparvar, M. (2020), "Modeling and evaluation of rectangular hole effect on nonlinear behavior of imperfect composite plates by an effective simulation technique", Compos. Mater. Eng.., 2(1),25-41. https://doi.org/10.12989/cme.2020.2.1.025.
  31. Gupta, V. and Anandkumar, J. (2019), "Phenol removal by tailor-made polyamide-fly ash composite membrane: Modeling and optimization", Membr. Water Treat., 10(6), 431-440. https://doi.org/10.12989/mwt.2019.10.6.431.
  32. Huang, C.S. and Ho, K.H. (2004), "An analytical solution for vibrations of a polarly orthotropic Mindlin sectorial plate with simply supported radial edges", J. Sound Vib., 273, 277-29. https://doi.org/10.1016/S0022-460X(03)00501-7.
  33. Hussain, M., Naeem, M.N., Taj, M., Tounsi, A. (2020a), "Simulating vibrations of vibration of single-walled carbon nanotube using Rayleigh-Ritz's method", Adv. Nano Res., 8(3), 215-228. https://doi.org/10.12989/anr.2020.8.3.215
  34. Hussain, M., Naeem, M.N., Tounsi, A. (2020b), "On mixing the Rayleigh-Ritz formulation with Hankel's function for vibration of fluid-filled FG cylindrical shell", Adv. Comput. Design, (Accepted).
  35. Hussain, M., Naeem, M.N., Tounsi, A., Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431
  36. Kaddari, M., Kaci, A., Bousahla, A.A.,Tounsi, A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and Free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037
  37. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9
  38. Karami, B., Janghorban, M., Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 70(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055
  39. Karami, B., Janghorban, M., Tounsi, A. (2019d), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487
  40. Karami, B., Shahsavari, D., Janghorban, M., Tounsi, A. (2019c), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036
  41. Karami, B.,Janghorban, M., Tounsi, A.(2019e), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazilian Soc. Mech. Sci. Eng., 41, 495. https://doi.org/10.1007/s40430-019-1996-0
  42. Khorasani, M., Eyvazian, A., Karbon, M., Tounsi, A., Lampani, L., Sebaey, T.A. (2020), "Magneto-Electro-Elastic Vibration Analysis of Modified Couple Stress-Based Three-Layered Micro Rectangular Plates Exposed to Multi-Physical Fields Considering the Flexoelectricity Effects", Smart Struct. Syst., (Accepted).
  43. Kim, I., Zhu, T., Jeon, C.H., Lawler, D.F. (2020), "Detachment of nanoparticles in granular media filtration", Membr. Water Treat., 11(1), 1-10. https://doi.org/10.12989/mwt.2020.11.1.001.
  44. Kossakowski, P.G. and Uzarska, I. (2019), "Numerical modeling of an orthotropic RC slab band system using the Barcelona model", Adv. Comput. Design., 4(3), 211-221. https://doi.org/10.12989/acd.2019.4.3.211.
  45. Lal, A.,Jagtap, K.R., Singh, B.N. (2017), "Thermo-mechanically induced finite element based nonlinear static response of elastically supported functionally graded plate with random system properties", Adv. Comput. Design, 2(3), 165-194. https://doi.org/10.12989/acd.2017.2.3.165.
  46. Lata, P. (2019), "Time harmonic interactions in fractional thermoelastic diffusive thick circular plate", Coupl. Syst. Mech., 8(1), 39-53. https://doi.org/10.12989/csm.2019.8.1.039.
  47. Lekhnitskii, S.G. (1981), Theory of Elasticity of an Anisotropic Body, Mir Publishers, Moscow, Russia.
  48. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595
  49. Mofakhamia, M.R., Toudeshkya, H.H., Hashmi, Sh.H. (2006), "Finite cylinder vibrations with different and boundary conditions", J. Sound Vib., 297, 293-314. https://doi.org/10.1016/j.jsv.2006.03.041.
  50. Narwariya, M.,Choudhury, A., Sharma, A.K. (2018), "Harmonic analysis of moderately thick symmetric cross-ply laminated composite plate using FEM", Adv. Comput. Design, 3(2), 113-132. https://doi.org/10.12989/acd.2018.3.2.113.
  51. Nikkhoo, A., Asili, S., Sadigh, S., Hajirasouliha, I. and Karegar, H. (2019), "A low computational cost method for vibration analysis of rectangular plates subjected to moving sprung masses", Adv. Comput. Design., 4(3), 307-326. https://doi.org/10.12989/acd.2019.4.3.307.
  52. Othman, M. and Fekry, M. (2018), "Effect of rotation and gravity on generalized thermo-viscoelastic medium with voids", Multidiscipline Model. Mater. Struct., 14(2), 322-338. https://doi.org/10.1108/MMMS-08-2017-0082.
  53. Ozisik, M. Mehdiyev, M.A., Akbarov, S.D. (2018), "The influence of the imperfectness of contact conditions on the critical velocity of the moving load acting in the interior of the cylinder surrounded with elastic medium", Comput. Mater. Continua, 54(2), 103-136. https://doi.org/10.3970/cmc.2018.054.103.
  54. Panjehpour, M., Eric Woo Kee, Loh and Deepak, T.J. (2018), "Structural Insulated Panels: State-of-the-Art", Trends Civil Eng. Architecture, 3(1) 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151
  55. Polyanin, A.D. and Zaitsev, V.F. (2003), Handbook of Exact Solutions for Ordinary Differential Equations, CRC Press, New York, USA.
  56. Pradyumna, S. and Bandyopadhyay, J.N. (2008), "Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation", J. Sound Vib., 318, 176-192. https://doi.org/10.1016/j.jsv.2008.03.056.
  57. Sahla, F., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663
  58. Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A., Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., 33(6), 805-822. https://doi.org/10.12989/scs.2019.33.6.805
  59. Selmi, A. (2019), "Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy", Adv. Nano Res., 7(5), 365-377. https://doi.org/10.12989/anr.2019.7.5.365.
  60. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non-local FSDT", Adv. Nano Res., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
  61. Shariati, A., Ghabussi, A., Habibi, M., Safarpour, H., Safarpour, M., Tounsi, A., Safa, M. (2020b), ""Extremely large oscillation and nonlinear frequency of a multi-scale hybrid disk resting on nonlinear elastic foundations", Thin-Walled Structures, 154, 106840. https://doi.org/10.1016/j.tws.2020.106840.
  62. Shariati, A., Habibi, M., Tounsi, A., Safarpour, H. and Safa, M. (2020a), "Application of exact continuum size-dependent theory for stability and frequency analysis of a curved cantilevered microtubule by considering viscoelastic properties", Eng. Comput., (In press). https://doi.org/10.1007/s00366-020-01024-9
  63. Shokrieh, M.M. and Kondori, M.S, (2020), "Effects of adding graphene nanoparticles in decreasing of residual stresses of carbon/epoxy laminated composites", Compos. Mater. Eng.., 2(1),53-64. https://doi.org/10.12989/cme.2020.2.1.053.
  64. Singh, A and Kumari, P. (2020), "Analytical free vibration solution for angle-ply piezolaminated plate under cylindrical bending: A piezo-elasticity approach", Adv. Comput. Design., 5(1), 55-89. https://doi.org/10.12989/acd.2020.5.1.055.
  65. Sofiyev, A.H. and Karaca, Z. (2009), "The vibration and buckling of laminated non-homogeneous orthotropic conical shells subjected to external pressure", Eur. J. Mech. A/Solids, 28, 317- 328. https://doi.org/10.1016/j.euromechsol.2008.06.002.
  66. Stavsky, Y. and Greenberg, B.J., (2003), "Radial vibrations of orthotropic laminated hollow spheres," J. Acoust. Soc. Am., 113(2), 847-851. https://doi.org/10.1121/1.1536625.
  67. Steven Chapra, C. (2004), Applied Numerical Methods with MATLAB for Engineering and Science, McGraw-Hill, New York, USA.
  68. Taj, M., Majeed, A., Hussain, M., Naeem, M.N., Safeer, M., Ahmad, M., Khan, H.U. and Tounsi, A. (2020), "Non-local orthotropic elastic shell model for vibration analysis of protein microtubules", Comput. Concrete, 25(3), 245-253. https://doi.org/10.12989/cac.2020.25.3.245
  69. Theotokoglou E.E. and Stampouloglou, I.H., (2008), "The radially non-homogeneous axisymmetric problem", J. Solids Struct., 45, 6535-6552, https://doi.org/10.1016/j.ijsolstr.2008.08.011.
  70. Timesli, A. (2020), "An efficient approach for prediction of the nonlocal critical buckling load of double-walled carbon nanotubes using the nonlocal Donnell shell theory", SN Appl. Sci., 2, 407. https://doi.org/10.1007/s42452-020-2182-9.
  71. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  72. Towfighi, S. and Kundu, T. (2003), "Elastic wave propagation in anisotropic spherical curved plates", Int. J. Solids Struct., 40, 5495-5510. https://doi.org/10.1016/S0020-7683(03)00278-6.
  73. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.

피인용 문헌

  1. A mechanical model to investigate Aedesaegypti mosquito bite using new techniques and its applications vol.11, pp.6, 2020, https://doi.org/10.12989/mwt.2020.11.6.399
  2. 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
  3. Mathematical approach for the effect of the rotation, the magnetic field and the initial stress in the non-homogeneous an elastic hollow cylinder vol.79, pp.5, 2020, https://doi.org/10.12989/sem.2021.79.5.593