DOI QR코드

DOI QR Code

Dynamic analysis of porous functionally graded layered deep beams with viscoelastic core

  • Assie, Amr (Mechanical Engineering Department, Faculty of Engineering, Jazan University) ;
  • Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University) ;
  • Kabeel, Abdallah M. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University) ;
  • Abdelrahman, Alaa A. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University) ;
  • Eltaher, Mohamed A. (Mechanical Design & Production Department, Faculty of Engineering, Zagazig University)
  • 투고 : 2020.08.29
  • 심사 : 2022.04.08
  • 발행 : 2022.04.10

초록

In this study, the dynamic behavior of functionally graded layered deep beams with viscoelastic core is investigated including the porosity effect. The material properties of functionally graded layers are assumed to vary continuously through thickness direction according to the power-law function. To investigate porosity effect in functionally graded layers, three different distribution models are considered. The viscoelastically cored deep beam is exposed to harmonic sinusoidal load. The composite beam is modeled based on plane stress assumption. The dynamic equations of motion of the composite beam are derived based on the Hamilton principle. Within the framework of the finite element method (FEM), 2D twelve -node plane element is exploited to discretize the space domain. The discretized finite element model is solved using the Newmark average acceleration technique. The validity of the developed procedure is demonstrated by comparing the obtained results and good agreement is detected. Parametric studies are conducted to demonstrate the applicability of the developed methodology to study and analyze the dynamic response of viscoelastically cored porous functionally graded deep beams. Effects of viscoelastic parameter, porosity parameter, graduation index on the dynamic behavior of porous functionally graded deep beams with viscoelastic core are investigated and discussed. Material damping and porosity have a significant effect on the forced vibration response under harmonic excitation force. Increasing the material viscosity parameters results in decreasing the vibrational amplitudes and increasing the vibration time period due to increasing damping effect. Obtained results are supportive for the design and manufacturing of such type of composite beam structures.

키워드

참고문헌

  1. Abdelrahman, A.A. and El-Shafei, A.G. (2020), "Modeling and analysis of the transient response of viscoelastic solids", Waves Random Complex Media, 31(6), 1990-2020. https://doi.org/10.1080/17455030.2020.1714790.
  2. Abdelrahman, A.A., Mohamed, N.A. and Eltaher, M.A. (2020a), "Static bending of perforated nanobeams including surface energy and microstructure effects", Eng. Comput., 1-21. https://doi.org/10.1007/s00366-020-01149-x.
  3. Abdelrahman, A.A., Nabawy, A.E., Abdelhaleem, A.M., Alieldin, S.S. and Eltaher, M.A. (2020a), "Nonlinear dynamics of viscoelastic flexible structural systems by finite element method", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-020-01141-5.
  4. Abdalrahmaan, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A.M., and Hendi, A.A. (2019), "Free and Forced Analysis of Perforated Beams", Steel Compos. Struct., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489.
  5. Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147.
  6. Akgoz, B. and Civalek, O. (2013a), "Free vibration analysis of axially functionally graded tapered Bernoulli-Euler microbeams based on the modified couple stress theory", Compos. Struct., 98, 314-322. https://doi.org/10.1016/j.compstruct.2012.11.020.
  7. Akgoz, B. and Civalek, O. (2013b), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mechanica, 224(9), 2185-2201. https://doi.org/10.1007/s00707-013-0883-5.
  8. Akbas, S.D. (2018a), "Forced vibration analysis of cracked nanobeams", J. Brazilian Soc. Mech. Sci. Eng., 40(8), 392. https://doi.org/10.1007/s40430-018-1315-1.
  9. Akbas, S.D. (2018b), "Forced vibration analysis of cracked functionally graded microbeams", Adv. Nano Res., 6(1), 39-55. https://doi.org/10.12989/anr.2018.6.1.039.
  10. Akbas, S.D. (2019a), "Hygro-Thermal Nonlinear Analysis of a Functionally Graded Beam", J. Appl. Comput. Mech., 5(2), 477-485.
  11. Akbas, S.D. (2019b), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., 8(3), 259-271. http://doi.org/ 10.22055/JACM.2018.26819.1360.
  12. Akbas, S.D., Fageehi, Y.A., Assie, E.A. and Eltaher, M.A. (2020), "Dynamic Analysis of Visco-Elastic Functionally Graded Porous Thick Beams under Pulse load", Eng. Comput., 1-18. https://doi.org/ 10.1007/s00366-020-01070-3.
  13. Akbas, S.D., Bashiri, A.H., Assie, A.E. and Eltaher, M.A. (2021a), "Dynamic analysis of thick beams with functionally graded porous layers and viscoelastic support", J. Vib. Control, 27(13-14), 1644-1655. https://doi.org/10.1177/1077546320947302.
  14. Alazwari, M.A., Esen, I., Abdelrahman, A.A., Abdraboh, A.M. and Eltaher, M.A. (2022), "Dynamic analysis of functionally graded (FG) nonlocal strain gradient nanobeams under thermomagnetic fields and moving load", Adv. Nano Res., 34(4), 231-251. https://doi.org/10.12989/anr.2022.12.3.231.
  15. Almitani, K.H., Abdalrahmaan, A.A. and Eltaher, M.A., (2019), "On Forced and Free Vibrations of Cutout Squared Beams", Steel Compos. Struct., 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643.
  16. Almitani, K.H., Abdalrahmaan, A.A. and Eltaher, M.A. (2020), "Stability of Perforated Nanobeams Incorporating Surface Energy Effects", Steel Compos. Struct., 35(4), 643-655. https://doi.org/10.12989/scs.2020.35.4.555.
  17. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A. (2021a), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. https://doi.org/10.12989/gae.2021.24.1.091.
  18. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A.E. (2021b), "Damped forced vibration analysis of layered functionally graded thick beams with porosity", Smart Struct. Syst., 27(4), 679-689. http://dx.doi.org/10.12989/sss.2021.27.4.669.
  19. Alshorbagy, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Free vibration characteristics of a functionally graded beam by finite element method", Appl. Math. Modelling, 35(1), 412-425. https://doi.org/10.1016/j.apm.2010.07.006.
  20. Arioui, O., Belakhdar, K., Kaci, A. and Tounsi, A. (2018), "Thermal buckling of FGM beams having parabolic thickness variation and temperature dependent materials", Steel Compos. Struct., 27(6), 777-788. https://doi.org/10.12989/scs.2018.27.6.777.
  21. Assie, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Behavior of a viscoelastic composite plates under transient load", J. Mech. Sci. Technol., 25(5), 1129. https://doi.org/10.1007/s12206-011-0302-6.
  22. Arshid, E., Khorasani, M., Soleimani-Javid, Z., Amir, S. and Tounsi, A. (2021), "Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-021-01382-y.
  23. Atmane, H.A., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369.
  24. Attia, M.A. and Mahmoud, F.F. (2017), "Analysis of viscoelastic Bernoulli-Euler nanobeams incorporating nonlocal and microstructure effects", J. Mech. Mater. Design, 13(3), 385-406. https://doi.org/10.1007/s10999-016-9343-4.
  25. Attia, M.A. and Emam, S.A. (2018), "Electrostatic nonlinear bending, buckling and free vibrations of viscoelastic microbeams based on the modified couple stress theory", Acta Mechanica, 229(8), 3235-3255. https://doi.org/10.1007/s00707-018-2162-y.
  26. Attia, M.A., Eltaher, M.A., Soliman, A., Abdelrahman, A.A. and Alshorbagy, A.E. (2018), "Thermoelastic Crack Analysis in Functionally Graded Pipelines Conveying Natural Gas by an FEM", J. Appl. Mech., 10(04), 1850036. https://doi.org/10.1142/S1758825118500369.
  27. Attia, M.A. and Rahman, A.A.A. (2018), "On vibrations of functionally graded viscoelastic nanobeams with surface effects", J. Eng. Sci., 127, 1-32. https://doi.org/10.1016/j.ijengsci.2018.02.005.
  28. Barati, M.R. (2017), "Investigating dynamic response of porous inhomogeneous nanobeams on hybrid Kerr foundation under hygro-thermal loading", Appl. Phys. A, 123(5), 332. https://doi.org/10.1007/s00339-017-0908-3.
  29. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091.
  30. Bashiri, A.H., Akbas, S.D., Abdelrahman, A.A., Assie, A., Eltaher, M.A. and Mohamed, E.F. (2021), "Vibration of multilayered functionally graded deep beams under thermal load", Geomech. Eng., 24(6), 545-557. https://doi.org/10.12989/gae.2021.24.6.545.
  31. Calim, F.F. (2016), "Free and forced vibration analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation", Compos. Part B Eng., 103, 98-112. https://doi.org/10.1016/j.compositesb.2016.08.008.
  32. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052.
  33. Dastjerdi, S., Tadi Beni, Y. and Malikan, M. (2020), "A comprehensive study on nonlinear hygro-thermo-mechanical analysis of thick functionally graded porous rotating disk based on two quasi-three-dimensional theories", Mech. Based Des. Struct. Machine, 1-30. https://doi.org/10.1080/15397734.2020.1814812.
  34. Dastjerdi, S., Malikan, M., Dimitri, R. and Tornabene, F. (2021), "Nonlocal elasticity analysis of moderately thick porous functionally graded plates in a hygro-thermal environment", Compos. Struct., 255, 112925. https://doi.org/10.1016/j.compstruct.2020.112925.
  35. de Galarreta, S.R., Jeffers, J.R. and Ghouse, S. (2020), "A validated finite element analysis procedure for porous structures", Mater. Des., 189, 108546. https://doi.org/10.1016/j.matdes.2020.108546.
  36. Deng, J., Liu, Y., Zhang, Z. and Liu, W. (2017), "Stability analysis of multi-span viscoelastic functionally graded material pipes conveying fluid using a hybrid method", European J. Mech. A/Solids, 65, 257-270. https://doi.org/10.1016/j.euromechsol.2017.04.003.
  37. Ebrahimi, F. and Barati, M.R. (2017), "Vibration analysis of viscoelastic inhomogeneous nanobeams resting on a viscoelastic foundation based on nonlocal strain gradient theory incorporating surface and thermal effects", Acta Mechanica, 228(3), 1197-1210. https://doi.org/10.1007/s00707-016-1755-6.
  38. Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201. https://doi.org/10.1016/j.compstruct.2012.11.039.
  39. Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014a), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072.
  40. Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014a), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028.
  41. Eltaher, M.A., Attia, M.A., Soliman, A.E. and Alshorbagy, A.E. (2018a), "Analysis of crack occurs under unsteady pressure and temperature in a natural gas facility by applying FGM", Struct. Eng. Mech., 66(1), 97-111. https://doi.org/10.12989/sem.2018.66.1.097.
  42. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018b), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazilian Soc. Mech. Sci. Eng., 40(3), 1-10. https://doi.org/10.1007/s40430-018-1065-0.
  43. Eltaher, M.A., Mohamed, S.A., (2020), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(4), 241-260. http://dx.doi.org/10.12989/scs.2020.34.2.241.
  44. Eltaher, M.A., Mohamed, S.A. and Melaibari, A. (2020a), "Static stability of a unified composite beams under varying axial loads", Thin-Wall. Struct., 147, 106488. https://doi.org/10.1016/j.tws.2019.106488.
  45. Emam, S., Eltaher, M., Khater, M. and Abdalla, W. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238.
  46. Esen, I., Abdelrhmaan, A.A. and Eltaher, M.A. (2021a), "Free vibration and buckling stability of FG nanobeams exposed to magnetic and thermal fields", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-021-01389-5.
  47. Esen, I., Ozarpa, C. and Eltaher, M.A. (2021b), "Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment", Compos. Struct., 261, 113552. https://doi.org/10.1016/j.compstruct.2021.113552.
  48. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021c), "On vibration of sigmoid/symmetric functionally graded nonlocal strain gradient nanobeams under moving load", J. Mech. Mater. Design, 17, 721-742. https://doi.org/10.1007/s10999-021-09555-9.
  49. Esen, I., Eltaher, M.A. and Abdelrahman, A.A. (2021d), "Vibration response of symmetric and sigmoid functionally graded beam rested on elastic foundation under moving point mass", Mech. Based Design Struct. Machine, 1-25. https://doi.org/10.1080/15397734.2021.1904255.
  50. Ghadiri, M., Shafiei, N. and Babaei, R. (2017), "Vibration of a rotary FG plate with consideration of thermal and Coriolis effects", Steel Compos. Struct., 25(2), 197-207. https://doi.org/10.12989/scs.2017.25.2.197
  51. Ghandourh, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compos. Struct., 36(3), 293-305. https://doi.org/10.12989/scs.2020.36.3.293
  52. Ghayesh, M.H. (2019a), "Resonant vibrations of FG viscoelastic imperfect Timoshenko beams", J. Vib. Control, 25(12), 1823-1832. https://doi.org/10.1177/1077546318825167.
  53. Ghayesh, M.H. (2019b), "Viscoelastic nonlinear dynamic behaviour of Timoshenko FG beams", Europ. Phys. J. Plus, 134(8), 401. https://doi.org/10.1140/epjp/i2019-12472-x
  54. Golmakani, M.E., Malikan, M., Pour, S.G. and Eremeyev, V.A. (2021), "Bending analysis of functionally graded nanoplates based on a higher-order shear deformation theory using dynamic relaxation method", Continuum Mech. Thermodynam., 1-20. https://doi.org/10.1007/s00161-021-00995-4
  55. Guellil, M., Saidi, H., Bourada, F., Bousahla, A.A., Tounsi, A., Al-Zahrani, M.M., and Mahmoud, S.R. (2021), "Influences of porosity distributions and boundary conditions on mechanical bending response of functionally graded plates resting on Pasternak foundation", Steel Compos. Struct., 38(1), 1-15. https://doi.org/10.12989/scs.2021.38.1.001.
  56. Hamed, M.A., Sadoun, A.M. and Eltaher, M.A. (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089./
  57. Hamed, M.A., Abo-bakr, R.M., Mohamed, S.A. and Eltaher, M. A. (2020a), "Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core", Eng. Comput., 1-18. https://doi.org/10.1007/s00366-020-01023-w
  58. Hamed M.A., Mohamed, S.A. and Eltaher, M.A. (2020b), "Buckling Analysis of Sandwich Beam Rested on Elastic Foundation and Subjected to Varying Axial In-Plane Loads", Steel Compos. Struct., 34(2), 75-89. https://doi.org/10.12989/scs.2020.34.1.075.
  59. Jena, S.K., Chakraverty, S., Malikan, M. and Sedighi, H. (2020), "Implementation of Hermite-Ritz method and Navier's technique for vibration of functionally graded porous nanobeam embedded in Winkler-Pasternak elastic foundation using bi-Helmholtz nonlocal elasticity", J. Mech. Mater. Struct., 15(3), 405-434. https://doi.org/10.2140/jomms.2020.15.405.
  60. Jena, S.K., Chakraverty, S. and Malikan, M. (2021), "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", Eng. Comput., 37(4), 3569-3589. https://doi.org/10.1007/s00366-020-01018-7.
  61. Joseph, S.V. and Mohanty, S.C. (2017), "Free vibration of a rotating sandwich plate with viscoelastic core and functionally graded material constraining layer", J. Struct. Stability Dyn., 17(10), 1750114. https://doi.org/10.1142/S0219455417501140
  62. Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. and Ebrahimi, A. (2018), "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct., 29(3), 349-362. https://doi.org/10.12989/scs.2018.29.3.349.
  63. Koutromanos, I. (2018), Fundamentals of Finite Element Analysis: Linear Finite Element Analysis, John Wiley and Sons, NJ, USA.
  64. Liang, X., Wang, Z., Wang, L. and Liu, G. (2014), "Semianalytical solution for three-dimensional transient response of functionally graded annular plate on a two parameter viscoelastic foundation", J. Sound Vib., 333(12), 2649-2663. https://doi.org/10.1016/j.jsv.2014.01.021.
  65. Loghman, E., Kamali, A., Bakhtiari-Nejad, F. and Abbaszadeh, M. (2021), "Nonlinear free and forced Vibrations of fractional modeled viscoelastic FGM micro-beam", Appl. Math. Modelling, 92, 297-314. https://doi.org/10.1016/j.apm.2020.11.011
  66. Malikan, M., Tornabene, F. and Dimitri, R. (2018), "Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals", Materials Res. Express, 5(9), 095006. https://doi.org/10.1088/2053-1591/aad4c3.
  67. Malikan, M. and Eremeyev, V.A. (2020), "A new hyperbolic-polynomial higher-order elasticity theory for mechanics of thick FGM beams with imperfection in the material composition", Compos. Struct., 249, 112486. https://doi.org/10.1016/j.compstruct.2020.112486.
  68. Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A.M.S. and Kazemi, M. (2017), "Thermal vibration of two-dimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.
  69. Mohamed, N., Eltaher, M.A., Mohamed, S. and Seddek, L.F., (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.
  70. Mohammadimehr, M., Monajemi, A.A. and Afshari, H. (2020), "Free and forced vibration analysis of viscoelastic damped FG-CNT reinforced micro composite beams", Microsyst. Technol., 26(10), 3085-3099. https://doi.org/10.1007/s00542-017-3682-4.
  71. Musuva, M. and Mares, C. (2015), "The wavelet finite element method in the dynamic analysis of a functionally graded beam resting on a viscoelastic foundation subjected to a moving load", Europ. J. Comput. Mech., 24(5), 171-209. https://doi.org/10.1080/17797179.2015.1096229
  72. Rouabhia, A., Abdelbaki C., Abdelmoumen A.B., Fouad Bourada, H.H., Abdeldjebbar T., Benrahou K.H., Abdelouahed T. and Mesfer Mohammad A.Z. (2020), "Physical stability response of a SLGS resting on viscoelastic medium using nonlocal integral first-order theory." Steel Compos. Struct., 37(6), 695-709. https://doi.org/10.12989/scs.2020.37.6.695.
  73. Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A. and 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.
  74. Sayyad, A. and Ghumare, S. (2019), "A new quasi-3D model for functionally graded plates", J. Appl. Comput. Mech., 5(2), 367-380. https://doi.org/10.22055/JACM.2018.26739.1353
  75. Sepehri-Amin, S., Faal, R.T. and Das, R. (2020), "Analytical and numerical solutions for vibration of a functionally graded beam with multiple fractionally damped absorbers", Thin-Walled Struct., 157, 106711. https://doi.org/10.1016/j.tws.2020.106711.
  76. Shafiei, N., Mirjavadi, S.S., MohaselAfshari, B., Rabby, S. and Kazemi, M. (2017), "Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Methods Appl. Mech. Eng., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007.
  77. She, G.L., Liu, H.B. and Karami, B. (2020), "On resonance behavior of porous FG curved nanobeams", Steel Compos. Struct, 36(2), 179-186. https://doi.org/10.12989/scs.2020.36.2.179.
  78. Soliman, A.E., Eltaher, M.A., Attia, M.A. and Alshorbagy, A.E. (2018), "Nonlinear transient analysis of FG pipe subjected to internal pressure and unsteady temperature in a natural gas facility", Struct. Eng. Mech., 66(1), 85-96. https://doi.org/10.12989/sem.2018.66.1.085.
  79. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.