Nonlinear forced vibration response of smart two-phase nano-composite beams to external harmonic excitations

Soraya Mareishi; Hamed Kalhori; Mohammad Rafiee; Seyedeh Marzieh Hosseini

Curved and Layered Structures (2015)

  • Volume: 2, Issue: 1
  • ISSN: 2353-7396

Abstract

top
This paper presents an analytical solution for nonlinear free and forced vibration response of smart laminated nano-composite beams resting on nonlinear elastic foundation and under external harmonic excitation. The structure is under a temperature change and an electric excitation through the piezoelectric layers. Different distribution patterns of the single walled aligned and straight carbon nanotubes (SWCNTs) through the thickness of the beam are considered. The beam complies with Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. The nonlinearity is due to the mid-plane stretching of the beam and the nonlinear stiffness of the elastic foundation. The Multiple Time Scales perturbation scheme is used to perform the nonlinear dynamical analysis of functionally graded carbon nanotube-reinforced beams. Analytical expressions of the nonlinear natural frequencies, nonlinear dynamic response and frequency response of the system in the case of primary resonance have been presented. The effects of different parameters including applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the carbon nanotubes on the nonlinear natural frequencies and frequency-response curves are presented. It is found that the volume fractions of SWCNTs as well as their distribution pattern significantly change the behavior of the system.

How to cite

top

Soraya Mareishi, et al. "Nonlinear forced vibration response of smart two-phase nano-composite beams to external harmonic excitations." Curved and Layered Structures 2.1 (2015): null. <http://eudml.org/doc/276880>.

@article{SorayaMareishi2015,
abstract = {This paper presents an analytical solution for nonlinear free and forced vibration response of smart laminated nano-composite beams resting on nonlinear elastic foundation and under external harmonic excitation. The structure is under a temperature change and an electric excitation through the piezoelectric layers. Different distribution patterns of the single walled aligned and straight carbon nanotubes (SWCNTs) through the thickness of the beam are considered. The beam complies with Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. The nonlinearity is due to the mid-plane stretching of the beam and the nonlinear stiffness of the elastic foundation. The Multiple Time Scales perturbation scheme is used to perform the nonlinear dynamical analysis of functionally graded carbon nanotube-reinforced beams. Analytical expressions of the nonlinear natural frequencies, nonlinear dynamic response and frequency response of the system in the case of primary resonance have been presented. The effects of different parameters including applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the carbon nanotubes on the nonlinear natural frequencies and frequency-response curves are presented. It is found that the volume fractions of SWCNTs as well as their distribution pattern significantly change the behavior of the system.},
author = {Soraya Mareishi, Hamed Kalhori, Mohammad Rafiee, Seyedeh Marzieh Hosseini},
journal = {Curved and Layered Structures},
keywords = {Nonlinear forced response; nano-composite; harmonic excitation; multiple time scales},
language = {eng},
number = {1},
pages = {null},
title = {Nonlinear forced vibration response of smart two-phase nano-composite beams to external harmonic excitations},
url = {http://eudml.org/doc/276880},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Soraya Mareishi
AU - Hamed Kalhori
AU - Mohammad Rafiee
AU - Seyedeh Marzieh Hosseini
TI - Nonlinear forced vibration response of smart two-phase nano-composite beams to external harmonic excitations
JO - Curved and Layered Structures
PY - 2015
VL - 2
IS - 1
SP - null
AB - This paper presents an analytical solution for nonlinear free and forced vibration response of smart laminated nano-composite beams resting on nonlinear elastic foundation and under external harmonic excitation. The structure is under a temperature change and an electric excitation through the piezoelectric layers. Different distribution patterns of the single walled aligned and straight carbon nanotubes (SWCNTs) through the thickness of the beam are considered. The beam complies with Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. The nonlinearity is due to the mid-plane stretching of the beam and the nonlinear stiffness of the elastic foundation. The Multiple Time Scales perturbation scheme is used to perform the nonlinear dynamical analysis of functionally graded carbon nanotube-reinforced beams. Analytical expressions of the nonlinear natural frequencies, nonlinear dynamic response and frequency response of the system in the case of primary resonance have been presented. The effects of different parameters including applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the carbon nanotubes on the nonlinear natural frequencies and frequency-response curves are presented. It is found that the volume fractions of SWCNTs as well as their distribution pattern significantly change the behavior of the system.
LA - eng
KW - Nonlinear forced response; nano-composite; harmonic excitation; multiple time scales
UR - http://eudml.org/doc/276880
ER -

References

top
  1. [1] Rajoria H., Jalili N., Determination of strength and damping characteristics of carbon nanotube-epoxy composites. In: Proc. 2004 ASME Int. Mech. Eng. Congress Exposition Anaheim: CA, 2004. 
  2. [2] Hosseini M., Mareishi S., Kalhori H., Large Amplitude Free and Forced Oscillations of Functionally Graded Beams, Mech. Adv. Mater. Struct., 2014, 21, 255-262.[Crossref][WoS] 
  3. [3] Liang Ke L., Yang J., Kitipornchai S., An analytical study on the nonlinear vibration of functionally graded beams, Meccanica, 2010, 45, 743-752.[WoS][Crossref] Zbl1258.74104
  4. [4] Rafiee M., Yang J., Kitipornchai S., Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers, Compos. Struct., 2013, 96, 716-725. 
  5. [5] Rafiee M., Yang J., Kitipornchai S., Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams. Comput. Math. Appl., 2013, 66, 1147-1160.[Crossref][WoS] 
  6. [6] Heshmati M., Yas M.H., Vibrations of non-uniform functionally graded MWCNTs-polystyrene nanocomposite beams under action of moving load, Mater. Des., 2013, 46, 206-218.[WoS][Crossref] 
  7. [7] Heshmati M., Yas M.H., Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load, Appl. Math. Model., 2012, 36, 1371-1394.[Crossref][WoS] Zbl1243.74098
  8. [8] Long Y., Qu X., Le H., Meng G., A variational formulation for dynamic analysis of composite laminated beams based on a general higher-order shear deformation theory, Compos. Struct., 2013, 102, 175-192. 
  9. [9] Yas M.H., Samadi N., Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation, Int. J. Pres. Ves. Pip., 2012, 98, 119-128.[WoS] 
  10. [10] Kanani A.S., Niknam H., Ohadi A.R., Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam, Compos. Struct., 2014, 115, 60-68. 
  11. [11] Shen H.S., Xiang Y., Nonlinear analysis of nanotube-reinforced composite beams resting on elastic foundations in thermal environments, Eng. Struct., 2013, 56, 698-708.[Crossref] 
  12. [12] Boyaci H., Vibrations of stretched damped beams under nonideal boundary conditions, Sadhana, 2006, 31, 1-8. Zbl1101.74034
  13. [13] Kamali Eigoli A., Ahmadian M.T., Nonlinear vibration of beams under nonideal boundary conditions, Acta Mech., 2011, 218, 259-267.[WoS] Zbl05912853
  14. [14] Ke L.L., Yang J., Kitipornchai S., Nonlinear free vibration of functionally graded carbon nanotube reinforced composite beams, Compos. Struct., 2010, 92, 676-683. 
  15. [15] Mahmoodi S.N., Khadem S.E., Jalili N., Theoretical development and closed-form solution of nonlinear vibrations of a directly excited nanotube-reinforced composite cantilever beam, Arch. Appl. Mech., 2006, 75, 153-163. Zbl1119.74422
  16. [16] Rafiee M., Mareishi S., Mohammadi M., An investigation on primary resonance phenomena of elastic medium based carbon nanotubes, Mech. Res. Commun., 2012, 44, 51-56.[WoS] 
  17. [17] Shen H.S., Xiang Y., Nonlinear vibration of nanotube-reinforced composite cylindrical shells in thermal environments, Comput. Methods Appl. Mech. Engng., 2012, 213-216, 196-205.[WoS] Zbl1243.74059
  18. [18] Tornabene F., Fantuzzi N., Bacciocchi M., Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories, Compos. Part B-Eng., 2014, 67, 490-509.[WoS] 
  19. [19] Rafiee M., He X.Q., Mareishi S., Liew K.M., Modeling and stress analysis of smart CNTs/fiber/polymer multiscale composite plates, Int. J. Appl. Mech., 2014, 6, 1450025-1-23.[Crossref] 
  20. [20] Ke L.L., Yang J., Kitipornchai S., Xiang Y., Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials, Mech. Adv. Mater. Struct., 2009, 16, 488-502.[Crossref][WoS] 
  21. [21] Ke L.L., Yang J., Kitipornchai S., Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening, Compos. Struct., 2009, 90, 152-160.[WoS] 
  22. [22] Hosseini S.M., Mareishi S., Kalhori H., Rafiee M., Large amplitude free and forced oscillations of functionally graded beams, Mech. Adv. Mater. Struct., 2014, 21, 255-262.[Crossref][WoS] 
  23. [23] Shooshtari A., Rafiee M., Nonlinear forced vibration analysis of clamped functionally graded beams, Acta Mech., 2011, 221, 23-38. Zbl1277.74033
  24. [24] Mareishi S., Mohammadi M., Rafiee M., An Analytical Study on Thermally Induced Vibration Analysis of FG Beams Using Different HSDTs, Appl. Mech. Mat., 2013, 249, 784-791. 
  25. [25] Hosseini Hashemi SH., Nazemnezhad R., An Analytical Study on the nonlinear free vibration of functionally graded nanobeams incorporating surface effects, Compos. Part B-Eng., 2013, 52,199-206.[Crossref][WoS] 
  26. [26] Shooshtari A., Hoseini S.M., Mahmoodi S.N., Kalhori H., Analytical solutions for nonlinear free vibrations of viscoelastic microcantilevers covered with a piezoelectric layer, SmartMater. Struct., 2012, 21, 075015.[Crossref] 
  27. [27] Mahmoodi S.N., Jalili N., Nonlinear vibrations and frequency response analysis of piezoelectrically driven microcantilevers, Int. J. Nonlin. Mech., 2007, 42, 577-587.[Crossref] 
  28. [28] Mahmoodi S.N., Daqaq M., Jalili N., On the nonlinear-flexural response of piezoelectrically-driven microcantileversensors, Sensor. Actuat. A-Phys., 2009, 153, 171-179. 
  29. [29] Rafiee M., Mohammadi M., Sobhani Aragh B., Yaghoobi H., Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells: Part I: Theory and analytical solutions, Compos. Struct., 2013, 103, 179-187. 
  30. [30] Rafiee M., Mohammadi M., Sobhani Aragh B., Yaghoobi H., Nonlinear free and forced thermo-electro-aero-elastic vibration and dynamic response of piezoelectric functionally graded laminated composite shells: Part II: Numerical results, Compos. Struct., 2013, 103, 188-196. 
  31. [31] Hadjiloizi D.A., Kalamkarov A.L., Metti C., Georgiades A.V., Analysis of Smart Piezo Magneto-Thermo-Elastic Composite and Reinforced Plates: Part I-Model Development, Curved Layer. Struct., 2014, 1, 11-31. 
  32. [32] Hadjiloizi D.A., Kalamkarov A.L., Metti C., Georgiades A.V., Analysis of Smart Piezo-Magneto-Thermo-Elastic Composite and Reinforced Plates: Part II-Applications, Curved Layer. Struct., 2014, 1, 32-58. 
  33. [33] Rafiee M., Liu X.F., He X.Q., Kitipornchai S., Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates, J. Sound Vib., 2014, 333, 3236-3251.[WoS] 
  34. [34] Rafiee M., He X.Q., Liew K.M., Non-linear dynamic stability of piezoelectric functionally graded carbon nanotube-reinforced composite plates with initial geometric imperfection. Int. J. Nonlin. Mech., 2014, 59, 37-51.[Crossref][WoS] 
  35. [35] Hariri H., Bernard Y., Razek A., A two dimensional modeling of non-collocated piezoelectric patches bonded on thin structure, Curved Layer. Struct., 2015, 2, 15-27. 
  36. [36] Tornabene F., Fantuzzi N., Viola E., Batra R.C., Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory, Compos. Struct., 2015, 119, 67-89.[WoS] 
  37. [37] Fu Y.M., Wang J.Z., Mao Y.Q., Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment, Appl. Math. Model., 2011, 36, 4324-4340.[Crossref][WoS] Zbl1252.74013
  38. [38] Rafiee M., He X.Q., Liew K.M., Nonlinear analysis of piezoelectric nanocomposite energy harvesting plates, Smart Mater. Struct., 2014, 23, 065001.[Crossref][WoS] 
  39. [39] Fantuzzi N., Tornabene F., Strong formulation finite element method for arbitrarily shaped laminated plates- Part I. Theoritical analysis, Adv. Aircraft Spacecraft Sci., 2014, 1, 125-143. 
  40. [40] Fantuzzi N., Tornabene F., Strong formulation finite element method for arbitrarily shaped laminated plates- Part II. Numerical analysis, Adv. Aircraft Spacecraft Sci., 2014, 1,145-175. 
  41. [41] Viola E., Miniaci M., Fantuzzi N., Marzani A., Vibration analysis of multi-stepped and multi-damaged parabolic arches using GDQ, Curved Layer. Struct., 2015, 2, 28-49. 
  42. [42] Shi D.L., Feng X.Q., Huang Y.Y., Hwang K.C., Gao H.J., The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites, J. Eng. Mater.-T. ASME, 2004, 126, 250-257. 
  43. [43] Esawi A.M.K., Farag M.M., Carbon nanotube reinforced composites: Potential and current challenges, Mater. Des., 2007, 28, 2394-2401.[Crossref] 
  44. [44] Reddy J.N., Mechanics of laminated composite plates and shells: theory and analysis, 2nd ed., CRC Press, Boca Raton, 2004. Zbl1075.74001
  45. [45] Nayfeh A.H., Mook D.T., Nonlinear oscillations, John Wiley, New York, 1979. 
  46. [46] Nayfeh A.H., Perturbation Methods, Wiley, New York, 1973. Zbl0265.35002
  47. [47] Kevorkian J., Cole J.D., Perturbation methods in applied mathematics, Springer, Berlin, 1981. Zbl0456.34001
  48. [48] Ece M.C., Aydogdu M., Taskin V., Vibration of a variable cross-section beam. Mech. Res. Commun., 2007, 34, 78-84.[WoS] Zbl1192.74169

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.