Abstract:
This thesis studies the influence of axial force on the dynamic response to
moving concentrated masses of rectangular plate incorporating rotatory inertia
correction factor. The responses of the elastic structures to moving concentrated
forces are special cases of such dynamical problems.
The governing equation 0 f this problem is a fourth order partial differential
equation. The solution technique is based on the use of the property of the Diracdelta
function as an even function to express it in series form. the versatile two dimensional
generalized integral transform with the normal modes of the plate as
the kernel of transformation and a modification of the Struble's asymptotic
technique. By the use of this technique, one is able to obtain closed form solutions
for all variants of classical end conditions for this class of problems. The closed
form solutions are analysed and numerical analyses in plotted curves are
presented.
The results show that as the axial force (prestress), Nx and Ny, foundation
moduli K and rotatory inertia Ro increase, the response amplitudes of the
dynamical system decrease for both illustrative examples. However, higher values
of N; Ny, K and Ro are required for a more noticeable effect in the case of simple clamped
boundary conditions than those. of simply supported boundary conditions.
It is also found that for both illustrative examples, the moving force solution is 110t
an upper bound for the accurate solution of the moving mass problem of a
VII
rectangular plate under the action or a concentrated moving load. This important
result also agrees with the result of similar problems in literature.
Finally, in all the illustrative examples considered, 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 moving mass
problem.
