Title page for ETD etd-08222008-063748
|Type of Document
||Vibration of a nonlinear shear deformable beam by numerical simulation
||Master of Science
|Heller, Robert A.
|Kraige, Luther Glenn
|Date of Defense
The vibration of a uniform geometrically nonlinear shear deformable beam
subjected to a transverse harmonic excitation is investigated by the method of numerical
simulation. Rotatory and axial inertia are included in the model. The beam is simply
supported with supports a fixed distance apart. The nonlinear partial differential equations
of motion are discretized in space by the Rayleigh-Ritz method, resulting in a set of
nonlinear ordinary differential equations in time. The ordinary differential equations are
integrated numerically to produce a time history of the solution of the equations.
Transverse displacement, axial displacement, and cross sectional rotation are
approximated by series of the corresponding linear natural mode shapes of the beam.
Solutions of the equations of motion are compared to corresponding solutions where
shear deformation and rotatory inertia are neglected. The effect of slenderness on the
difference between the shear deformable case and the non shear deformable case is
investigated by considering two beam configurations.
In the simulations considered, the difference between the shear deformable model
and the non shear deformable model increases as excitation frequency is increased and the
length to thickness ratio of the beam is decreased.
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