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Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams

Tang, A.-Y. ; Wu, J.-X. ; Li, X.-F. ; Lee, K.Y.

International journal of mechanical sciences, 2014-12, Vol.89, p.1-11 [Periódico revisado por pares]

Elsevier Ltd

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  • Título:
    Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams
  • Autor: Tang, A.-Y. ; Wu, J.-X. ; Li, X.-F. ; Lee, K.Y.
  • Assuntos: Critical frequencies ; Density ; Exact solutions ; Exponential gradient ; Free vibration ; Frequency equation ; Functionally graded materials ; Functionally gradient materials ; Mathematical analysis ; Natural frequency ; Timoshenko beam ; Timoshenko beams ; Vibration
  • É parte de: International journal of mechanical sciences, 2014-12, Vol.89, p.1-11
  • Notas: ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
    content type line 23
  • Descrição: Free vibration of non-uniform functionally graded beams is analyzed via the Timoshenko beam theory. Bending stiffness and distributed mass density are assumed to obey a unified exponential law. For various boundary conditions, exact frequency equations are derived in closed form. These frequency equations can reduce to those for classical Timoshenko beams if the gradient index disappears. Moreover, the frequency equations of exponentially graded Rayleigh, shear, and Euler–Bernoulli beams can be obtained as special cases of the present. The gradient index has a strong influence on the natural frequencies. For Timoshenko beams, there exist two critical frequencies depending on the gradient index. Harmonic vibration cannot be excited for frequencies less than the lower critical frequency. The obtained results can serve as a benchmark for examining the accuracy of numerical frequencies based on other approaches for analyzing transverse vibration of non-uniform axially graded Timoshenko beams. The results also apply to bending vibration of rectangular Timoshenko beams with constant thickness and exponentially decaying/amplifying width. •Free vibration of functionally graded Timoshenko beams is analyzed.•Exact frequency equations of exponentially graded Timoshenko beams are obtained.•Effect of end constraints of functionally graded Timoshenko beams is examined.•Natural frequencies depend on the gradient index and admit jump property.•Natural frequencies for graded beams using Euler–Bernoulli, shear, Rayleigh, and Timoshenko theories are compared.
  • Editor: Elsevier Ltd
  • Idioma: Inglês
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