Dynamics of functionally graded beams carrying a moving load with influence of porosities and partial foundation support
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https://doi.org/10.15625/2525-2518/17507Keywords:
FG beam, porosities, partial foundation support, refined shear deformation theory, moving load, dynamic analysisAbstract
The novelty of the present work is to study the simultaneous influence of porosities and partial Pasternak foundation support on dynamics of functionally graded (FG) beams carrying a moving load. The beams are made from an open-cell steel foam with symmetric and asymmetric porosity distributions in the thickness direction. Based on a refined third-order shear deformation theory, a two-node beam element with ten degrees of freedom is derived and employed to construct the discretized equation of motion for the beams. Dynamic characteristics, including the time histories for mid-span deflection, dynamic magnification factor (DMF) and the stress distribution, are computed with the aid of the Newmark method. The numerical result reveals that the foundation supporting length has an important role on the dynamics of the beams, and the dependence of the DMF upon the porosity coefficient is governed by the foundation supporting length. It is also found that the asymmetric porosity distribution has more impact on the dynamic response of the beams than the symmetric one does, and the difference between the DMFs obtained from the two porosity distributions is more significant for the beam with a higher porosity coefficient. The effects of the porosities, the foundation support and the moving load velocity on the dynamic behavior of the beams are examined in detail and highlighted
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References
Koizumi M. - FGM activities in Japan, Composites Part B: Engineering 28 (1-2) (1997) 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9. DOI: https://doi.org/10.1016/S1359-8368(96)00016-9
Şimşek M. and Kocaturk T. - Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Composite Structures 90 (4) (2009) 465-473. https://doi.org/10.1016/j.compstruct.2009.04.024. DOI: https://doi.org/10.1016/j.compstruct.2009.04.024
Şimşek M. - Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Composite structures 92 (4) (2010) 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030. DOI: https://doi.org/10.1016/j.compstruct.2009.09.030
Khalili S. M. R., Jafari A. A. and Eftekhari S. A. - A mixed ritz-dq method for forced vibration of functionally graded beams carrying moving loads, Composite Structures 92 (10) (2010) 2497-2511. https://doi.org/10.1016/j.compstruct.2010.02.012. DOI: https://doi.org/10.1016/j.compstruct.2010.02.012
Rajabi K., Kargarnovin M. H. and Gharini M. - Dynamic analysis of a functionally graded simply supported Euler-Bernoulli beam subjected to a moving oscillator, Acta Mechanica 224 (2) (2013) 425-446. https://doi.org/10.1007/s00707-012-0769-y. DOI: https://doi.org/10.1007/s00707-012-0769-y
Wang Y. and Wu D. - Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load, Acta Astronautica 127 (2016) 171-181. https://doi.org/10.1016/j.actaastro.2016.05.030. DOI: https://doi.org/10.1016/j.actaastro.2016.05.030
Songsuwan W., Pimsarn M. and Wattanasakulpong N. - Dynamic responses of functionally graded sandwich beams resting on elastic foundation under harmonic moving loads, International Journal of Structural Stability and Dynamics 18 (9) (2018) 1850112. https://doi.org/10.1142/S0219455418501122. DOI: https://doi.org/10.1142/S0219455418501122
Ga B. S., Trinh T. H., Le T. H. and Nguyen D. K. - Dynamic response of nonuniform timoshenko beams made of axially FGM subjected to multiple moving point loads, Structural Engineering and Mechanics 53 (5) (2015) 981-995. DOI: https://doi.org/10.12989/sem.2015.53.5.981
Esen I. - Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass, International Journal of Mechanical Sciences 153 (2019) 21-35. https://doi.org/10.1016/j.ijmecsci.2019.01.033. DOI: https://doi.org/10.1016/j.ijmecsci.2019.01.033
Esen I. - Dynamic response of functional graded Timoshenko beams in a thermal environment subjected to an accelerating load, European Journal of Mechanics-A/Solids 78 (2019), 103841. https://doi.org/10.1016/j.euromechsol.2019.103841. DOI: https://doi.org/10.1016/j.euromechsol.2019.103841
Esen I., Eltaher M. A. and Abdelrahman A. A. - Vibration response of symmetric and sigmoid functionally graded beam rested on elastic foundation under moving point mass, Mechanics Based Design of Structures and Machines (2021) 1-25. https://doi.org/ 10.1080/15397734.2021.1904255. DOI: https://doi.org/10.1080/15397734.2021.1904255
Nguyen D. K., Nguyen Q. H., Tran T. T. and Bui V. T. - Vibration of bidimensional functionally graded Timoshenko beams excited by a moving load, Acta Mechanica 228 (1) (2017) 141-155. https://doi.org/10.1007/s00707-016-1705-3. DOI: https://doi.org/10.1007/s00707-016-1705-3
Nguyen D. K., Vu A. N. T., Le N. A. T. and Pham V. N. - Dynamic behavior of a bidirectional functionally graded sandwich beam under nonuniform motion of a moving load, Shock and Vibration 2020 (2020). https://doi.org/10.1155/2020/8854076. DOI: https://doi.org/10.1155/2020/8854076
Nguyen D. K., Vu A. N. T., Pham V. N. and Truong T. T. - Vibration of a threephase bidirectional functionally graded sandwich beam carrying a moving mass using an enriched beam element, Engineering with Computers 38 (2021) 1-12. https://doi.org/ 10.1007/s00366-021-01496-3. DOI: https://doi.org/10.1007/s00366-021-01496-3
Nguyen D. K., Tran T. T., Pham V. N. and Le N. A. T. - Dynamic analysis of an inclined sandwich beam with bidirectional functionally graded face sheets under a moving mass, European Journal of Mechanics-A/Solids 88 (2021) 104276. https://doi.org/10.1016/ j.euromechsol.2021.104276. DOI: https://doi.org/10.1016/j.euromechsol.2021.104276
Wattanasakulpong N. and Ungbhakorn V. - Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities, Aerospace Science and Technology 32 (1) (2014) 111-120. https://doi.org/10.1016/j.ast.2013.12.002. DOI: https://doi.org/10.1016/j.ast.2013.12.002
Chen D., Yang J. and Kitipornchai S. - Free and forced vibrations of shear deformable functionally graded porous beams, International Journal of Mechanical Sciences 108 (2016) 14-22. https://doi.org/10.1016/j.ijmecsci.2016.01.025. DOI: https://doi.org/10.1016/j.ijmecsci.2016.01.025
Ebrahimi F. and Jafari A. - A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities, Journal of Engineering 2016 (2016). https://doi.org/10.1155/2016/9561504. DOI: https://doi.org/10.1155/2016/9561504
Ebrahimi F. and Jafari A. - Thermo-mechanical vibration analysis of temperature-dependent porous FG beams based on Timoshenko beam theory, Structural Engineering and Mechanics 59 (2) (2016) 343-371. https://dx.doi.org/10.12989/sem.2016.59.2.343. DOI: https://doi.org/10.12989/sem.2016.59.2.343
Ebrahimi F. and Jafari A. - A four-variable refined shear-deformation beam theory for thermomechanical vibration analysis of temperature-dependent FGM beams with porosities, Mechanics of Advanced Materials and Structures 25 (3) (2018) 212-224. https://doi.org/10.1080/15376494.2016.1255820. DOI: https://doi.org/10.1080/15376494.2016.1255820
Ebrahimi F., Ghasemi F. and Salari E. - Investigating thermal effects on vibration behavior of temperature-dependent compositionally graded Euler beams with porosities, Meccanica 51 (1) (2016) 223-249. https://doi.org/10.1007/s11012-015-0208-y. DOI: https://doi.org/10.1007/s11012-015-0208-y
Atmane H. A., Tounsi A. and Bernard F. - Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations, International Journal of Mechanics and Materials in Design 13 (1) (2017) 71-84. https://doi.org/10.1007/s10999-015-9318-x. DOI: https://doi.org/10.1007/s10999-015-9318-x
Akbaş Ş. D., Fageehi Y. A., Assie A. E. and Eltaher M. A. - Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load, Engineering with Computers (2020) 1-13. https://doi.org/10.1007/s00366-020-01070-3. DOI: https://doi.org/10.1007/s00366-020-01070-3
Jena S. K., Chakraverty S. and Malikan M. - Application of shifted Chebyshev polynomialbased RayleighRitz method and Naviers technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation, Engineering with Computers 37 (4) (2021) 3569-3589. https://doi.org/10.1007/s00366-020-01018-7. DOI: https://doi.org/10.1007/s00366-020-01018-7
Vu A. N. T., Le N. A. T. and Nguyen D. K. - Dynamic behaviour of bidirectional functionally graded sandwich beams under a moving mass with partial foundation supporting effect, Acta Mechanica 232 (7) (2021) 2853-2875. https://doi.org/ 10.1007/s00707-021-02948-z. DOI: https://doi.org/10.1007/s00707-021-02948-z
Fahsi B., Bouiadjra R. B., Mahmoudi A., Benyoucef S. and Tounsi S. - Assessing the effects of porosity on the bending, buckling, and vibrations of functionally graded beams resting on an elastic foundation by using a new refined quasi-3D theory, Mechanics of Composite Materials 55 (2) (2019) 219-230. https://doi.org/10.1007/s11029-019-09805-0. DOI: https://doi.org/10.1007/s11029-019-09805-0
Thai H, T. and Kim S. E. - A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates, Composite Structures 96 (2013) 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025 DOI: https://doi.org/10.1016/j.compstruct.2012.08.025
Geradin M. and Rixen D. - Mechanical Vibrations, Theory and Application to Structural Dynamics, John Wiley & Sons, Chichester, 1997.
Song Q., Shi J. and Liu Z. - Vibration analysis of functionally graded plate with a moving mass, Applied Mathematical Modelling 46 (2017) 141-160. https://doi.org/10.1016/ j.apm.2017.01.073. DOI: https://doi.org/10.1016/j.apm.2017.01.073
Olsson M. - On the fundamental moving load problem, Journal of Sound and Vibration 145 (2) (1991) 299-307. https://doi.org/10.1016/0022-460X(91)90593-9. DOI: https://doi.org/10.1016/0022-460X(91)90593-9
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