A Unified Approach for Out-of-Plane Forced Vibration of Axially Functionally Graded Circular Rods
Year 2018,
Volume: 2 Issue: 2, 37 - 45, 20.06.2018
Timuçin Alp Aslan
,
Ahmad Reshad Noori
,
Beytullah Temel
Abstract
Out-of-plane forced vibration of axially inhomogeneous curved rods is examined by the Complementary Functions Method (CFM) in the Laplace domain. The material properties, Young’s modulus and density, of the circular rods are graded in the axial direction according to a power law distribution while the Poisson’s ratio is supposed to be constant. The effectiveness and accuracy of the proposed method are confirmed by comparing its numerical results with those obtained by ANSYS. Application of this unified approach provides accurate results of transient response for axially functionally graded (AFG) circular rods with different variations of material properties along the rod axis.
References
- [1] Elıshakoff, I. and Guede, Z., (2004)."Analytical Polynomial Solutions For Vibrating Axially Graded Beams", Mechanics of Advanced Materials and Structures, vol.11, pp.517–533
- [2] Aydogdu, M. and Taskin V., (2007)."Free Vibration Analysis of Functionally Graded Beams with Simply Supported Edges", Materials and Design vol.28, pp.1651–1656
- [3] Aydogdu, M., "Semi-inverse Method for Vibration and Buckling of Axially Functionally Graded Beams", Journal of Reinforced Plastics and Composites, DOI: 10.1177/0731684407081369 http://www.sagepublications.com
- [4] Li X. F., (2008). "A Unified Approach for Analyzing Static and Dynamic Behaviors Of functionally Graded Timoshenko and Euler–Bernoulli Beams.", J Sound Vib.;vol.318, pp.1210–29.
- [5] Sina, S. A., Navazi H. M.,and Haddadpour H., (2009)."An Analytical Method For Free Vibration Analysis of Functionally Graded Beams", Materials and Design, vol.30(3) pp.741–747.
- [6] Simsek M, and Kocaturk T., (2009)."Free and Forced Vibration Of A Functionally Graded Beam Subjected To A Concentrated Moving Harmonic Load " Composite Structures , vol.90(4),pp.465–73.
- [7] Huang, Y.,and X.F.Li., (2010)."A New Approach for Free Vibration of Axially Functionally Graded Beams with Non-Uniform Cross-Section", Journal of Sound and Vibration, vol.329, pp.2291–2303.
- [8] Filipich, C. P.,and Piovana, M. T., (2010)."The Dynamics of Thick Curved Beams Constructed with Functionally Graded Materials", Mechanics Research Communications, vol.37, pp.565–570.
- [9] Malekzadeh, P., (2009)."Two-Dimensional In-Plane Free Vibrations of Functionally Graded Circular Arches with Temperature-Dependent Properties", Composite Structures vol. 91, pp. 38–47.
- [10] Yousefi, A., and Rastgoo, A., (2011)."Free Vibration of Functionally Graded Spatial Curved Beams", Composite Structures, vol.93, pp.3048–3056.
- [11]Atmane, H. A., Tounsi, A., Meftah, S. A., and Belhadj, H. A., (2011)."Free Vibration Behavior of Exponential Functionally Graded Beams with Varying Cross-section", Journal of Vibration and Control, vol.17(2), pp.311–318.
- [12] H., Hein, Feklistova, L., (2011)."Free Vibrations of Non-Uniform And Axially Functionally Graded Beams Using Haar Wavelets", Engineering Structures, vol. 33, pp. 3696–3701.
- [13]Piovan, M.T., Domini, S., Ramirez, J.M., (2012)."In-Plane and Out-Of-Plane Dynamics And Buckling Of Functionally Graded Circular Curved Beams", Composite Structures, vol.94, pp.3194–3206.
- [14]Shahba, A. and Rajasekaran, S., (2012)."Free Vibration And Stability of Tapered Euler–Bernoulli Beams Made of Axially Functionally Graded Materials", Applied Mathematical Modelling, vol. 36, pp.3094–3111.
- [15]Bambill, D., V., Rossit, C. A.,and Felix, D. H., (2014). "Free Vibrations of Stepped Axially Functionally Graded Timoshenko Beams", Meccanica, DOI 10.1007/s11012-014-0053-4.
- [16]Li, X.-F., Kang, Y.-A., and Wu, J.-X., (2013)."Exact Frequency Equations of Free Vibration of Exponentially Functionally Graded Beams", Applied Acoustics, vol 74, pp.413–420.
- [17]Huang, Y., Yang L. E., and Luo, Q. Z., (2013)."Free Vibration of Axially Functionally Graded Timoshenko Beamswith Non-Uniform Cross-Section", Composites: Part B, vol.45, pp.1493–1498.
- [18] Sarkar, K., and Ganguli, R., (2014)."Closed-Form Solutions for Axially Functionally Graded Timoshenko Beams Having Uniform Cross-Section And Fixed–Fixed Boundary Condition", Composites: Part B, vol.58, pp.361–370.
- [19]Li,L., and Zhang. D., (2015) ."Dynamic Analysis of Rotating Axially FG Tapered Beams Based on A New Rigid–Flexible Coupled Dynamic Model Using The B-Spline Method", Composite Structures, vol.124, pp. 357–367.
- [20]Pradhan, K.K., and Chakraverty, S., (2013)."Free Vibration Of Euler And Timoshenko Functionally Graded Beams By Rayleigh–Ritz Method," Composites: Part B, vol. 51, pp.175–184.
- [21]Wang, C.M., Ke, L.L., Roy Chowdhury, A.N., Yang, J., Kitipornchai, S., and, Fernando D., (2017). "Critical Examination of Midplane And Neutral Plane Formulations for Vibration Analysis of FGM Beams", Engineering Structures, vol.130,pp.275–281.
- [22]Çalım, F.F., (2016). " Free and Forced Vibration Analysis of Axially Functionally Graded Timoshenko Beams on Two-Parameter Viscoelastic Foundation",Composites Part B,vol.103, pp.98-112.
- [23]Çalım, F.F., (2016)."Transient Analysis Of Axially Functionally Graded Timoshenko Beams with Variable Cross-Section", Composites Part B,vol. 98, pp.472-483.
- [24]Aslan, T.A.,Noori, A.R., Temel, B., (2017). "Forced Vibration of Out Of Plane Loaded Stepped Circular Rods", International Conference on Civil and Enviromental Engineering, 2017 May 8-10, p.2062-2074.
- [25]Temel, B., Aslan, T.A., and Noori, A.R.,(2017)."An Efficient Dynamic Analysis of Planar Arches", European Mechanical Science, vol. 1(3), pp. 82-88
- [26]Durbin, F., (1974)."Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate’s Method", Comput. J., vol.17, pp.371 – 376.
- [27] Temel, B., Çalim, F.F. And Tütüncü, N., (2004)."Quasi-Static and Dynamic Response of Viscoelastic Helical Rods", J. Sounds Vib., vol. 271, pp.921 - 935.
- [28] ANSYS, Inc Release 15.0 (2013), Canonsburg, PA.
Year 2018,
Volume: 2 Issue: 2, 37 - 45, 20.06.2018
Timuçin Alp Aslan
,
Ahmad Reshad Noori
,
Beytullah Temel
References
- [1] Elıshakoff, I. and Guede, Z., (2004)."Analytical Polynomial Solutions For Vibrating Axially Graded Beams", Mechanics of Advanced Materials and Structures, vol.11, pp.517–533
- [2] Aydogdu, M. and Taskin V., (2007)."Free Vibration Analysis of Functionally Graded Beams with Simply Supported Edges", Materials and Design vol.28, pp.1651–1656
- [3] Aydogdu, M., "Semi-inverse Method for Vibration and Buckling of Axially Functionally Graded Beams", Journal of Reinforced Plastics and Composites, DOI: 10.1177/0731684407081369 http://www.sagepublications.com
- [4] Li X. F., (2008). "A Unified Approach for Analyzing Static and Dynamic Behaviors Of functionally Graded Timoshenko and Euler–Bernoulli Beams.", J Sound Vib.;vol.318, pp.1210–29.
- [5] Sina, S. A., Navazi H. M.,and Haddadpour H., (2009)."An Analytical Method For Free Vibration Analysis of Functionally Graded Beams", Materials and Design, vol.30(3) pp.741–747.
- [6] Simsek M, and Kocaturk T., (2009)."Free and Forced Vibration Of A Functionally Graded Beam Subjected To A Concentrated Moving Harmonic Load " Composite Structures , vol.90(4),pp.465–73.
- [7] Huang, Y.,and X.F.Li., (2010)."A New Approach for Free Vibration of Axially Functionally Graded Beams with Non-Uniform Cross-Section", Journal of Sound and Vibration, vol.329, pp.2291–2303.
- [8] Filipich, C. P.,and Piovana, M. T., (2010)."The Dynamics of Thick Curved Beams Constructed with Functionally Graded Materials", Mechanics Research Communications, vol.37, pp.565–570.
- [9] Malekzadeh, P., (2009)."Two-Dimensional In-Plane Free Vibrations of Functionally Graded Circular Arches with Temperature-Dependent Properties", Composite Structures vol. 91, pp. 38–47.
- [10] Yousefi, A., and Rastgoo, A., (2011)."Free Vibration of Functionally Graded Spatial Curved Beams", Composite Structures, vol.93, pp.3048–3056.
- [11]Atmane, H. A., Tounsi, A., Meftah, S. A., and Belhadj, H. A., (2011)."Free Vibration Behavior of Exponential Functionally Graded Beams with Varying Cross-section", Journal of Vibration and Control, vol.17(2), pp.311–318.
- [12] H., Hein, Feklistova, L., (2011)."Free Vibrations of Non-Uniform And Axially Functionally Graded Beams Using Haar Wavelets", Engineering Structures, vol. 33, pp. 3696–3701.
- [13]Piovan, M.T., Domini, S., Ramirez, J.M., (2012)."In-Plane and Out-Of-Plane Dynamics And Buckling Of Functionally Graded Circular Curved Beams", Composite Structures, vol.94, pp.3194–3206.
- [14]Shahba, A. and Rajasekaran, S., (2012)."Free Vibration And Stability of Tapered Euler–Bernoulli Beams Made of Axially Functionally Graded Materials", Applied Mathematical Modelling, vol. 36, pp.3094–3111.
- [15]Bambill, D., V., Rossit, C. A.,and Felix, D. H., (2014). "Free Vibrations of Stepped Axially Functionally Graded Timoshenko Beams", Meccanica, DOI 10.1007/s11012-014-0053-4.
- [16]Li, X.-F., Kang, Y.-A., and Wu, J.-X., (2013)."Exact Frequency Equations of Free Vibration of Exponentially Functionally Graded Beams", Applied Acoustics, vol 74, pp.413–420.
- [17]Huang, Y., Yang L. E., and Luo, Q. Z., (2013)."Free Vibration of Axially Functionally Graded Timoshenko Beamswith Non-Uniform Cross-Section", Composites: Part B, vol.45, pp.1493–1498.
- [18] Sarkar, K., and Ganguli, R., (2014)."Closed-Form Solutions for Axially Functionally Graded Timoshenko Beams Having Uniform Cross-Section And Fixed–Fixed Boundary Condition", Composites: Part B, vol.58, pp.361–370.
- [19]Li,L., and Zhang. D., (2015) ."Dynamic Analysis of Rotating Axially FG Tapered Beams Based on A New Rigid–Flexible Coupled Dynamic Model Using The B-Spline Method", Composite Structures, vol.124, pp. 357–367.
- [20]Pradhan, K.K., and Chakraverty, S., (2013)."Free Vibration Of Euler And Timoshenko Functionally Graded Beams By Rayleigh–Ritz Method," Composites: Part B, vol. 51, pp.175–184.
- [21]Wang, C.M., Ke, L.L., Roy Chowdhury, A.N., Yang, J., Kitipornchai, S., and, Fernando D., (2017). "Critical Examination of Midplane And Neutral Plane Formulations for Vibration Analysis of FGM Beams", Engineering Structures, vol.130,pp.275–281.
- [22]Çalım, F.F., (2016). " Free and Forced Vibration Analysis of Axially Functionally Graded Timoshenko Beams on Two-Parameter Viscoelastic Foundation",Composites Part B,vol.103, pp.98-112.
- [23]Çalım, F.F., (2016)."Transient Analysis Of Axially Functionally Graded Timoshenko Beams with Variable Cross-Section", Composites Part B,vol. 98, pp.472-483.
- [24]Aslan, T.A.,Noori, A.R., Temel, B., (2017). "Forced Vibration of Out Of Plane Loaded Stepped Circular Rods", International Conference on Civil and Enviromental Engineering, 2017 May 8-10, p.2062-2074.
- [25]Temel, B., Aslan, T.A., and Noori, A.R.,(2017)."An Efficient Dynamic Analysis of Planar Arches", European Mechanical Science, vol. 1(3), pp. 82-88
- [26]Durbin, F., (1974)."Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate’s Method", Comput. J., vol.17, pp.371 – 376.
- [27] Temel, B., Çalim, F.F. And Tütüncü, N., (2004)."Quasi-Static and Dynamic Response of Viscoelastic Helical Rods", J. Sounds Vib., vol. 271, pp.921 - 935.
- [28] ANSYS, Inc Release 15.0 (2013), Canonsburg, PA.