Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation - Publication - Bridge of Knowledge

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Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation

Abstract

Present study is dealt with the applicability of shifted Chebyshev polynomial based Rayleigh-Ritz method and Navier’s technique on free vibration of Functionally Graded (FG) beam with uniformly distributed porosity along the thickness of the beam. The material properties such as Young’s modulus, mass density, and Poisson’s ratio are also considered to vary along the thickness of the FG beam as per the power-law exponent model. The porous FG beam is embedded in an elastic substrate; namely, the Kerr elastic foundation and the displacement field of the beam is governed by a Refined Higher Order Shear Deformation Theory (RHSDT). The effectiveness of the Rayleigh-Ritz method is due to the use of the shifted Chebyshev polynomials as a shape function. The orthogonality of shifted Chebyshev polynomial makes the technique more computationally efficient and avoid ill-conditioning for the higher number of terms of the polynomial. Hinged-Hinged (HH), Clamped-Hinged (CH), Clamped-Clamped (CC), and Clamped-Free (CF) boundary conditions have been taken into account for the parametric study. Validation of the present model is examined by comparing it with existing literature in special cases showing remarkable agreement. A pointwise convergence study is also carried out for shifted Chebyshev polynomial based Rayleigh-Ritz method and the effect of power-law exponent, porosity volume fraction index, and elastic foundation on natural frequencies are studied comprehensively.

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Category:
Articles
Type:
artykuły w czasopismach
Published in:
ENGINEERING WITH COMPUTERS no. 37, pages 3569 - 3589,
ISSN: 0177-0667
Language:
English
Publication year:
2021
Bibliographic description:
Jena S. K., Chakraverty S., Malikan M.: Application of shifted Chebyshev polynomial-based Rayleigh–Ritz method and Navier’s technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation// ENGINEERING WITH COMPUTERS -Vol. 37, (2021), s.3569-3589
DOI:
Digital Object Identifier (open in new tab) 10.1007/s00366-020-01018-7
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  1. Sina SA, Navazi HM, Haddadpour H (2009) An analytical method for free vibration analysis of functionally graded beams. Materials and Design 30:741-747 open in new tab
  2. Ke LL, Yang J, Kitipornchai S (2010) An analytical study on the nonlinear vibration of functionally graded beams. Meccanica 45:743-752 open in new tab
  3. Hein H, Feklistova L (2011) Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets. Engineering Structures 33:3696-3701 open in new tab
  4. Shooshtari A, Rafiee M (2011) Nonlinear forced vibration analysis of clamped functionally graded beams. Acta Mechanica 221:23-38 open in new tab
  5. Wattanasakulpong N, Prusty BG, Kelly DW (2011) Thermal buckling and elastic vibration of third-order shear deformable functionally graded beams. International Journal of Mechanical Sciences 53:734-743 35 open in new tab
  6. Wattanasakulpong N, Prusty BG, Kelly DW, Hoffman M (2012) Free vibration analysis of layered functionally graded beams with experimental validation. Materials and Design 36:182- 190 open in new tab
  7. Thai HT, Vo TP (2012) Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences 62: 57-66 open in new tab
  8. Fallah A, Aghdam MM (2012) Thermo-mechanical buckling and nonlinear free vibration analysis of functionally graded beams on nonlinear elastic foundation. Composites: Part B 43: 1523-1530 open in new tab
  9. Pradhan KK, Chakraverty S (2013) Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method. Composites: Part B 51:175-184 open in new tab
  10. Rahimi G H, Gazor M S, Hemmatnezhad M, Toorani H (2013) On the post buckling and free vibrations of FG Timoshenko beams. Composite Structures 95:247-253 open in new tab
  11. Vo TP, Thai HT, Nguyen TK, Maheri A, Lee J (2014) Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory. Engineering Structures 64:12-22 open in new tab
  12. Kanani AS, Niknam H, Ohadi AR, Aghdam MM (2014) Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam. Composite Structures 115:60-68 open in new tab
  13. Nguyen TK, Nguyen TTP, Vo TP, Thai HT (2015) Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory. Composites Part B: Engineering 76:273-285 open in new tab
  14. Su H, Banerjee JR (2015) Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams. Computers and Structures 147:107-116 open in new tab
  15. Tossapanon P, Wattanasakulpong N (2016) Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation. Composite Structures 142:215-225 36 open in new tab
  16. Huang Y, Zhang M, Rong H (2016) Buckling Analysis of Axially Functionally Graded and Non-Uniform Beams Based on Timoshenko Theory. Acta Mechanica Solida Sinica 29:200-207 open in new tab
  17. Chen D, Yang J, Kitipornchai S (2016) Free and forced vibrations of shear deformable functionally graded porous beams. International Journal of Mechanical Sciences 108-109:14-22. open in new tab
  18. Jing LL, Ming PJ, Zhang WP, Fu LR, Cao YP (2016) Static and free vibration analysis of functionally graded beams by combination Timoshenko theory and finite volume method. Composite Structures 138:192-213 open in new tab
  19. Sedighi HM, Shirazi KH, Attarzadeh MA (2013) A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches. Acta Astronautica 91:245-50 open in new tab
  20. Sedighi HM, Shirazi KH, Noghrehabadi A (2012) Application of recent powerful analytical approaches on the non-linear vibration of cantilever beams. International Journal of Nonlinear Sciences and Numerical Simulation 13(7-8):487-94 open in new tab
  21. Sedighi HM, Daneshmand F (2014) Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term. Journal of Applied and Computational Mechanics 1(1):1-9
  22. Esmaeili M, Tadi Beni Y (2019) Vibration and Buckling Analysis of Functionally Graded Flexoelectric Smart Beam. Journal of Applied and Computational Mechanics 5(5):900-17
  23. Karami B, Janghorban M, Rabczuk T (2020) Dynamics of two-dimensional functionally graded tapered Timoshenko nanobeam in thermal environment using nonlocal strain gradient theory. Composites Part B: Engineering 182:107622 open in new tab
  24. Karami B, Janghorban M, Li L (2018) On guided wave propagation in fully clamped porous functionally graded nanoplates. Acta Astronautica 143:380-90 open in new tab
  25. She GL, Yuan FG, Karami B, Ren YR, Xiao WS (2019) On nonlinear bending behavior of FG porous curved nanotubes. International Journal of Engineering Science 135:58-74 open in new tab
  26. She GL, Jiang XY, Karami B (2019) On thermal snap-buckling of FG curved nanobeams. Materials Research Express 6(11):115008 37 open in new tab
  27. Karami B, Shahsavari D, Janghorban M, Li L (2020) Free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment. Structural Engineering and Mechanics 73(2):191
  28. Karami B, Shahsavari D, Janghorban M, Li L (2019) On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory. International Journal of Engineering Science 144:103143 open in new tab
  29. Karami B, Shahsavari D, Li L (2018) Temperature-dependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field. Journal of Thermal Stresses 41(4):483-99 open in new tab
  30. Karami B, Janghorban M (2019) On the dynamics of porous nanotubes with variable material properties and variable thickness. International Journal of Engineering Science 136:53- 66. open in new tab
  31. 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. Structural Engineering and Mechanics 71(5):485-502
  32. Karami B, Janghorban M, Tounsi A (2019) Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions. Engineering with Computers 35(4):1297-316 open in new tab
  33. Tounsi A, Al-Dulaijan SU, Al-Osta MA, Chikh A, Al-Zahrani MM, Sharif A, 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 and Composite Structures 34(4):511-524
  34. Addou FY, Meradjah M, Bousahla AA, Benachour A, Bourada F, Tounsi A, Mahmoud SR (2019) Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/ Kerr foundation using quasi 3D HSDT. Computers and Concrete 24(4):347-67
  35. Chaabane LA, Bourada F, Sekkal M, Zerouati S, Zaoui FZ, Tounsi A, Derras A, Bousahla
  36. AA, Tounsi A. (2019) Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation. Structural Engineering and Mechanics 71(2):185-96 38
  37. Boukhlif Z, Bouremana M, Bourada F, Bousahla AA, Bourada M, Tounsi A, Al-Osta MA (2019) A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation. Steel and Composite Structures 31(5):503-16
  38. Boulefrakh L, Hebali H, Chikh A, Bousahla AA, Tounsi A, Mahmoud SR (2019) The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate. Geomechanics and Engineering 18(2):161-78
  39. Kaddari M, Kaci A, Bousahla AA, Tounsi A, Bourada F, Bedia EA, Al-Osta MA (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. Computers and Concrete 25(1):37
  40. Bourada F, Bousahla AA, Bourada M, Azzaz A, Zinata A, Tounsi A (2019) Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory. Wind and Structures 28(1):19-30
  41. Khiloun M, Bousahla AA, Kaci A, Bessaim A, Tounsi A, Mahmoud SR. (2019) Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT. Engineering with Computers 1-5 open in new tab
  42. Bousahla AA, Bourada F, Mahmoud SR, Tounsi A, Algarni A, Bedia EA, Tounsi A (2020)
  43. Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory. Computers and Concrete 25(2):155 open in new tab
  44. Boussoula A, Boucham B, Bourada M, Bourada F, Tounsi A, Bousahla AA, Tounsi A (2020) A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates. Smart Structures and Systems 25(2):197
  45. Paul A, Das D (2016) Free vibration analysis of pre-stressed FGM Timoshenko beams under large transverse deflection by a variational method. Engineering Science and Technology, an International Journal 19:1003-1017 open in new tab
  46. Wang X, Li Shirong (2016) Free vibration analysis of functionally graded material beams based on Levinson beam theory. Applied Mathematics and Mechanics 37: 861-878 open in new tab
  47. Kahya V, Turan M (2017) Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory. Composites Part B 109: 108-115 39 open in new tab
  48. Nguyen DK, Nguyen QH, Tran TT, Bui VT (2017) Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load. Acta Mechanica 228:141-155 open in new tab
  49. Deng H, Chen KD, Cheng W, Zhao SG (2017) Vibration and buckling analysis of double- functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation. Composite Structures 160:152-168 open in new tab
  50. Celebi K, Yarimpabuc D, Tutuncu N (2018) Free vibration analysis of functionally graded beams using complementary functions method. Archive of Applied Mechanics 88:729-739 open in new tab
  51. Sinir S, Çevik M, Sinir BG (2018) Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section. Composites Part B: Engineering 148:123-131
  52. Banerjee JR, Ananthapuvirajah A (2018) Free vibration of functionally graded beams and frameworks using the dynamic stiffness method. Journal of Sound and Vibration 422:34-47 open in new tab
  53. Karamanli A (2018) Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory. Composite Structures 189:127-136 open in new tab
  54. Fazzolari FA (2018) Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations. Composites Part B: Engineering 136:254-271 open in new tab
  55. Cao D, Gao Y (2019) Free vibration of non-uniform axially functionally graded beams using the asymptotic development method. Applied Mathematics and Mechanics 40:85-96 open in new tab
  56. Wattanasakulpong N, Ungbhakorn V (2014) Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities. Aerospace Science and Technology 32(1): 111-120 open in new tab
  57. Shahsavari D, Shahsavari M, Li L, Karami B (2018) A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerospace Science and Technology 72:134-149 open in new tab
  58. Malikan M, Tornabene F, Dimitri R (2018) Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals. Materials Research Express 5(9):095006 40 open in new tab
  59. Senthilnathan NR, Lim SP, Lee KH, Chow ST (1987) Buckling of shear-deformable plates. AIAA journal 25(9):1268-71 open in new tab
  60. Bekhadda A, Bensaid I, Cheikh A, Kerboua B (2019) Static buckling and vibration analysis of continuously graded ceramic-metal beams using a refined higher order shear deformation theory. Multidiscipline Modeling in Materials and Structures open in new tab
  61. Daikh AA (2019) Temperature dependent vibration analysis of functionally graded sandwich plates resting on Winkler/Pasternak/Kerr foundation. Materials Research Express 6(6):065702 open in new tab
  62. Jena SK, Chakraverty S, Malikan M (2020) Implementation of Non-Probabilistic Methods for Stability Analysis of Nonlocal Beam with Structural Uncertainties. Engineering with Computers doi.org/10.1007/s00366-020-00987-z open in new tab
  63. Jena SK, Chakraverty S, Malikan M, Tornabene F (2019) Stability Analysis of Single- Walled Carbon Nanotubes Embedded in Winkler Foundation Placed in a Thermal Environment Considering the Surface Effect Using a New Refined Beam Theory. Mechanics Based Design of Structures and Machines, An International Journal doi.org/10.1080/15397734.2019.1698437 open in new tab
  64. Jena SK, Chakraverty S, Malikan M (2019) Vibration and Buckling Characteristics of open in new tab
  65. Nonlocal Beam Placed in a Magnetic Field Embedded in Winkler-Pasternak Elastic Foundation Using a New Refined Beam Theory: An Analytical approach. The European Physical Journal Plus 135: 1-18 open in new tab
  66. Jena SK, Chakraverty S, Tornabene F (2019) Buckling Behavior of Nanobeam Placed in an Electro-Magnetic Field Using Shifted Chebyshev polynomials Based Rayleigh-Ritz Method. Nanomaterials 9(9): 1326 open in new tab
  67. Malikan M, Eremeyev VA (2020) Post-critical buckling of truncated conical carbon nanotubes considering surface effects embedding in a nonlinear Winkler substrate using the Rayleigh-Ritz method. Materials Research Express 7:025005 open in new tab
  68. Jena SK, Chakraverty S, Jena RM (2019) Propagation of Uncertainty in Free Vibration of open in new tab
  69. Euler-Bernoulli Nanobeam. Journal of the Brazilian Society of Mechanical Sciences and Engineering 41(10): 436
  70. Yang J, Shen HS (2002) Vibration characteristics and transient response of shear- deformable functionally graded plates in thermal environments. Journal of Sound and vibration 255(3):579-602 open in new tab
  71. Reddy JN, Chin CD (1998) Thermomechanical analysis of functionally graded cylinders and plates. Journal of thermal Stresses 21(6):593-626 open in new tab
  72. ŞimŞek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nuclear Engineering and Design 240(4): 697-705 open in new tab
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