Dynamic stability and buckling of viscoelastic plates and nanobeams subjected to distributed axial forces.
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Date
2016
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Abstract
Plates and beams are typical examples of structures that must be analyzed and understood.
Buckling and vibration represent for such structures a potential source of fatigue and damage.
Damage and fatigue are often caused by axial forces. The current research uses differential
quadrature method to study the stability of viscoelastic plate subjected to follower forces in one
hand, and the Rayleigh-Ritz method to analyze the buckling of Carbone nanotubes subjected to
point and axial load in other hand.
For plate, the 3D relation of viscoelastic is used to derive the equation of vibration of
viscoelastic rectangular plate subjected to follower force. This equation is solved numerically by
differential quadrature method, then the dynamic stability analysis is done by plotting the
eigenvalues versus the follower force.
We employ the Euler Bernoulli beam theory and the nonlocal theory to derive the equation of
equilibrium of Carbone nanotubes subjected to point and axial loads. Rayleigh-Ritz method is
used to calculate buckling loads, and the effects of equation's parameters on that buckling loads
are analysed properly.
Frequencies of vibration of viscoelastic plates and critical load obtained by using differential
quadrature method are compared to other results with good satisfaction. The same satisfaction is
observed when the buckling load values of Carbone nanotubes obtained using the Rayleigh-Ritz
methods are compared to those existing in the literature.
The cantilever viscoelastic plate undergoes flutter instability only and the delay time appears
to influence that instability more than other parameters. The SFSF plate undergoes divergence
instability only. The both types of instability are observed CSCS plate subjected to uniformly
follower load but the flutter instability disappears in presence of triangular follower load. The
values of the mentioned critical loads increase with triangular follower load for all boundary
conditions. The aspect ratio has a large influence on the divergence and flutter critical load
values and little influence on the instability quality. The laminar friction coefficient of the
flowing fluid increases the critical fluid velocity but its effect on the stability of viscoelastic
plate behavior is minor.
The nonlocal parameter appears to decrease buckling load considerably. Buckling is more
sensitive to the magnitude of the tip load for the clamped-free boundary conditions. The
application of the present theory to a non-uniform nanocone shows that the buckling loads
increases with radius ratio and decreases with small scale constants.
Description
Doctor of Philosophy in Mechanical Engineering. University of KwaZulu-Natal, Durban 2016.