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Figure 5.8. Abaqus results showing the deflection contour plot and legend for the dynamic
simulation test in m.
For a simply supported beam of length L and constant bending stiffness, subjected to
a dynamic load P(t) = P0sin(ωt), the theoretical deflection value is given by Equation (5.1)
and Equation (5.2) [61].
(
∑
) (
(
)
33
)
[ (
√
) ]
ρ is the density, A is the cross sectional area, I is the area moment of inertia, E is Young’s
modulus, ω1 is the first characteristic frequency of vibration, L is the length of the beam, and
a = L/2.
A MATLAB program was developed to calculate the theoretical deflection at the
center of a beam, a = L/2. The theoretical results were compared to the Abaqus results
obtained from FE models meshed with 2, 4, and 8 elements through the thickness and the
corresponding graphs are presented in Figure 5.9, Figure 5.10 and Figure 5.11.