On The Dynamic Stability of Functionally Graded Material Beams Under Parametric Excitation

By: Rout, TrilochanContributor(s): Mohanty, S C [Supervisor] | Dash, R R [Supervisor] | Department of Mechanical EngineeringMaterial type: TextTextLanguage: English Publisher: 2012Description: 144 pSubject(s): Engineering and Technology | Mechanical Engineering | Structural AnalysisOnline resources: Click here to access online Dissertation note: Thesis (Ph.D)- National Institute of Technology, Rourkela Summary: The dynamic stability of functionally graded material (FGM) beams subjected to parametric excitation is studied using finite element method. First order shear deformation theory (Timoshenko beam theory) is used for the analysis of the beams. The shape functions for the beam element are established from the differential equation of static equilibrium. Floquet’s theory is used to establish the stability boundaries. A steel-alumina functionally graded ordinary (FGO) beam with steel-rich bottom is considered for the analysis. For the analysis of functionally graded sandwich (FGSW) beam, alumina and steel are chosen as top and bottom skin respectively and the core is FGM with steel and alumina as constituent phases. The material properties in the direction of thickness of FGM are assumed to vary as per power law and exponential law. The effect of property distribution laws on critical buckling load, natural frequencies and parametric instability of the beams is investigated. Also, the effect of variation of power law index on the critical buckling load, natural frequencies and dynamic stability of beams is determined. It is found that the property variation as per exponential law ensures better dynamic stability than property variation as per power law. Increase in the value of power law index is found to have detrimental effect on the dynamic stability of the beams. Influence of the elastic foundations on the dynamic stability of the beams is studied. Pasternak elastic foundation is found to have more enhancing effect on the dynamic stability of the beam than Winkler elastic foundation. The dynamic stability of FGO and FGSW beams used in high temperature environment is investigated. It is observed that increase in environmental temperature has an enhancing effect on the instability of the beams. The effect of beam geometry, rotary inertia, hub radius and rotational speed on natural frequencies as well as on the parametric instability of iv rotating FGO and FGSW cantilever beams is studied. It is observed that increase in rotational speed enhances the dynamic stability of the beams. Parametric instability of a pre-twisted FGO cantilever beam is investigated. The effect of property distribution laws and pre-twist angle on critical buckling load, natural frequencies and parametric instability of the beam is studied. The increase in the value of power law index is found to have enhancing effect on the parametric instability of the beam. The increase in pre-twisting of the beam reduces the chance of parametric instability of the beam with respect to the first principal instability region. But the increase in pre-twist angle has a detrimental effect on the stability of the beam for second principal instability region.
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Thesis (Ph.D)- National Institute of Technology, Rourkela

The dynamic stability of functionally graded material (FGM) beams
subjected to parametric excitation is studied using finite element method. First
order shear deformation theory (Timoshenko beam theory) is used for the
analysis of the beams. The shape functions for the beam element are
established from the differential equation of static equilibrium. Floquet’s theory
is used to establish the stability boundaries. A steel-alumina functionally
graded ordinary (FGO) beam with steel-rich bottom is considered for the
analysis. For the analysis of functionally graded sandwich (FGSW) beam,
alumina and steel are chosen as top and bottom skin respectively and the
core is FGM with steel and alumina as constituent phases. The material
properties in the direction of thickness of FGM are assumed to vary as per
power law and exponential law.
The effect of property distribution laws on critical buckling load, natural
frequencies and parametric instability of the beams is investigated. Also, the
effect of variation of power law index on the critical buckling load, natural
frequencies and dynamic stability of beams is determined. It is found that the
property variation as per exponential law ensures better dynamic stability than
property variation as per power law. Increase in the value of power law index
is found to have detrimental effect on the dynamic stability of the beams.
Influence of the elastic foundations on the dynamic stability of the
beams is studied. Pasternak elastic foundation is found to have more
enhancing effect on the dynamic stability of the beam than Winkler elastic
foundation.
The dynamic stability of FGO and FGSW beams used in high
temperature environment is investigated. It is observed that increase in
environmental temperature has an enhancing effect on the instability of the
beams.
The effect of beam geometry, rotary inertia, hub radius and rotational
speed on natural frequencies as well as on the parametric instability of
iv
rotating FGO and FGSW cantilever beams is studied. It is observed that
increase in rotational speed enhances the dynamic stability of the beams.
Parametric instability of a pre-twisted FGO cantilever beam is
investigated. The effect of property distribution laws and pre-twist angle on
critical buckling load, natural frequencies and parametric instability of the
beam is studied. The increase in the value of power law index is found to
have enhancing effect on the parametric instability of the beam. The increase
in pre-twisting of the beam reduces the chance of parametric instability of the
beam with respect to the first principal instability region. But the increase in
pre-twist angle has a detrimental effect on the stability of the beam for second
principal instability region.

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