Abstract:
This thesis is concerned, in general, with the study of the influence of rotatory
inertia on the dynamic response to moving concentrated masses of rectangular plates on a
non- Winkler elastic foundation. Specifically, the equation of motion is not governed by
the classical two-dimensional theory of flexural motions of thin plate where the effect of
rotatory inertia is neglected. In addition, the plate rests on a non-Winkler elastic
foundation, in particular, the Pasternak Subgrade. In order to solve this problem, the
property of the Dirac-delta function as an even function is used to express it in series
form and the versatile two dimensional generalized integral transforms is used to reduce
the fourth order partial differential equation with singular coefficients to a coupled
second order ordinary differential equation. For the solution of this equation, a
modification of the Struble's asymptotic technique is' employed. The analytical solutions
are analyzed and numerical results in plotted curves are then presented.
The results show that as the rotatory inertia correction factor increases the
response amplitudes of a rectangular plate resting on a Pasternak Subgrade and under the
actions of moving masses decrease. This result holds for both Simply Supported and
Simple-Clamped plate and for both moving force and moving mass problems.
Furthermore, it is found that the response amplitudes of a rectangular plate resting
on a Pasternak Subgrade decrease with an increase in the values of shear modulus G for
fixed values of foundation's stiffness K and rotatory inertia Rot. Similarly, as K increases
the response amplitudes decrease but effect of G is more noticeable than that of K.
Finally, for both Simply Supported and Simple-Clamped rectanr ulur plate, under
moving concentrated masses, for the same natural frequency, the critical speed for the moving mass problem is smaller than that of the moving force problem. Hence resonance
is reached earlier in the former.
