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Free vibration analysis of FGM stepped nanostructures using nonlocal dynamic stiffness model

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A nonlocal Dynamic Stiffness Model (DSM) for free vibration analysis of Functionally Graded Material (FGM) stepped nanostructures based on the Nonlocal Elastic Theory (NET) is proposed. An exact solution to the equation of motion of a nanobeam element according to the Timoshenko beam theory, NET, and taking into account position of the neutral axis is constructed. Nondimensional frequencies and mode shapes of complete FGM stepped nanostructures are easily obtained using the nonlocal DSM. Numerical results are presented to show significance of the material distribution profile, nonlocal effect, and boundary conditions on free vibration of nanostructures.
Słowa kluczowe
Rocznik
Strony
279--292
Opis fizyczny
Bibliogr. 25 poz., rys., tab.
Twórcy
  • Hanoi University of Civil Engineering, Vietnam
  • Fujita Corporation, Vietnam
  • Hanoi University of Civil Engineering, Vietnam
  • Le Quy Don Technical University, Vietnam
Bibliografia
  • 1. Aria A., Friswell M., 2019, A nonlocal finite element model for buckling and vibration of functionally graded nanobeams, Composites Part B: Engineering, 166, 233-246.
  • 2. Banerjee J., Ananthapuvirajah A., 2018, Free vibration of functionally graded beams and frameworks using the dynamic stiffness method, Journal of Sound and Vibration, 422, 34-47.
  • 3. Chakraverty S., Behera L., 2015, Free vibration of non-uniform nanobeams using Rayleigh-Ritz method, Physica E: Low-Dimensional Systems and Nanostructures, 67, 38-46.
  • 4. Ebrahimi F., Nasirzadeh P., 2015, A nonlocal Timoshenko beam theory for vibration analysis of thick nanobeams using differential transform method, Journal of Theoretical and Applied Mechanics, 53, 4, 1041-1052.
  • 5. Ebrahimi F., Salari E., 2015, A semi-analytical method for vibrational and buckling analysis of functionally graded nanobeams considering the physical neutral axis position, CMES – Computer Modeling in Engineering and Sciences, 105, 2, 151-181.
  • 6. Eltaher M., Alshorbagy A., Mahmoud F., 2013a, Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams, Composite Structures, 99, 193-201.
  • 7. Eltaher M., Alshorbagy A.E., Mahmoud F., 2013b, Vibration analysis of Euler-Bernoulli nanobeams by using finite element method, Applied Mathematical Modelling, 37, 7, 4787-4797.
  • 8. Eringen A.C., 2002, Nonlocal Continuum Field Theories, Springer Science & Business Media.
  • 9. Ghavanloo E., Rafii-Tabar H., Fazelzadeh S.A., 2019, Computational Continuum Mechanics of Nanoscopic Structures, Springer.
  • 10. Jena S.K., Chakraverty S., 2018, Free vibration analysis of variable cross-section single layered graphene nano-ribbons (SLGNRs) using differential quadrature method, Frontiers in Built Environment, 4, 63.
  • 11. Karličić D., Murmu T., Adhikari S., McCarthy M., 2015, Non-Local Structural Mechanics, John Wiley & Sons.
  • 12. Li X.-F., Wang B.-L., 2009, Vibrational modes of Timoshenko beams at small scales, Applied Physics Letters, 94, 10, 101903.
  • 13. Lien T.V., Ngo D.T., Nguyen K.T., 2019, Free and forced vibration analysis of multiple cracked FGM multi span continuous beams using dynamic stiffness method, Latin American Journal of Solids and Structures, 16, 2.
  • 14. Malikan M., Wiczenbach T., Eremeyev V.A., 2021, Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect, Continuum Mechanics and Thermodynamics, 1-16.
  • 15. Mechab I., El Meiche N., Bernard F., 2016, Free vibration analysis of higher-order shear elasticity nanocomposite beams with consideration of nonlocal elasticity and Poisson effect, Journal of Nanomechanics and Micromechanics, 6, 3, 04016006.
  • 16. Narendar S., Gopalakrishnan S., 2011, Spectral finite element formulation for nanorods via nonlocal continuum mechanics, Journal of Applied Mechanics, 78, 6, 061018.
  • 17. Rahmani O., Pedram O., 2014, Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory, International Journal of Engineering Science, 77, 55-70.
  • 18. Reddy J., 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45, 2-8, 288-307.
  • 19. Şimşek M., Yurtcu H., 2013, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Composite Structures, 97, 378-386.
  • 20. Su H., Banerjee J., 2015, Development of dynamic stiffness method for free vibration of functionally graded Timoshenko beams, Computers and Structures, 147, 107-116.
  • 21. Taima M.S., El-Sayed T.A., Farghaly S.H., 2020, Free vibration analysis of multistepped nonlocal Bernoulli-Euler beams using dynamic stiffness matrix method, Journal of Vibration and Control, 27, 7-8, 774-789.
  • 22. Trinh L.C., Vo T.P., Thai H.-T., Nguen T.-K., 2018, Size-dependent vibration of bi-directional functionally graded microbeams with arbitrary boundary conditions, Composites Part B: Engineering, 134, 225-245.
  • 23. Usharani R., Uma G., Umapathy M., Choi S.-B., 2018, A novel piezoelectric energy harvester using a multi-stepped beam with rectangular cavities, Applied Sciences, 8, 11, 2091.
  • 24. Uymaz B., 2013, Forced vibration analysis of functionally graded beams using nonlocal elasticity, Composite Structures, 105, 227-239.
  • 25. Wang C., Zhang Y., He X., 2007, Vibration of nonlocal Timoshenko beams, Nanotechnology, 18, 10, 105401.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c188dab8-e1ba-4335-9575-52e1267d66ac
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