Abstract:
The dynamic behaviour under moving distributed masses of orthotropic rectangular
plates resting on bi-parametric elastic foundation is investigated in this dissertation. The
problem is investigated for both cases of plates resting on bi-parametric elastic founda-
tion with stiffness variation. The governing equation is a fourth order partial differential
equation. Approximate analytical solutions are obtained for problem under investiga-
tion. In order to solve this problem, a technique based on separation of variables is used
to tackle the governing fourth order partial differential equations with variable and sin-
gular co-efficients and reduce it to a system of coupled second order ordinary differential
equations. For the solutions of these resulting equations, a modification of the Struble’s
technique in conjunction with the methods of integral transformation techniques and
convolution theory are employed. Numerical calculations in plotted curves are then pre-
sented. From the analytical solution, it is observed that as the rotatory inertia correction
factor (R o ) increases, the amplitudes of plates decrease for both cases of moving force
and moving mass problems. As the flexural rigidities along both the x-axis (D x ) and
y-axis (D y ) increase, the deflection amplitudes of the plates decrease for both cases of
moving force and moving mass problems. As the shear modulus (G o ) and foundation
modulus (K o ) increase, the deflection amplitudes of the plates decrease for both cases of
moving force and moving mass problems for all variants of classical boundary condi-
tions considered. It is shown further from the results that for fixed values of rotatory in-
ertia correction factor, shear modulus and foundation modulus , flexural rigidities along
both x-axis and y-axis, the amplitude for the moving mass problem is greater than that
of the moving force problem which implies that resonance is attained earlier in moving
mass problem than in moving force problem of vibration of moving distributed masses
of orthotropic rectangular plate resting on a variable elastic bi-parametric foundation.
Finally, the analyses show that, for the same natural frequency, the critical speed for the
moving mass problem is smaller than that of the moving force problem. Resonance is
attained earlier in the moving mass system than in the moving force system. That is
vto say, the moving force solution is not an upper bound for the accurate solution of the
moving mass problem.
