Investigating dynamic free vibration response of isotropic thin rectangular plate resting
on two-parameter elastic foundation is of interest in the field of geotechnics, structure,
highway, railway and mechanical engineering. This study employs analytical approach
to the investigation of free vibration analysis of isotropic rectangular plate submerged
in fluid and resting on combined elastic foundations under different support
conditions. The nonlinear partial differential equation of the system is transformed into
nonlinear ordinary differential equation using the Galerkin method of separation. The
resulting ordinary differential equation is solved using Adomian decomposition
method (ADM). The reliability of the solutions obtained is validated with numerical and
existing results as reported in the literature. Also, the bending moment and stress are
analysed. The analytical solutions are used for the investigation of dynamic behaviour
of plates in fluid, effect of aspect ratio, effect of elastic foundation parameters on
natural frequency and effect of bending moment and stress on the mode of the
vibrating plate. From the results, it is observed that the increase in elastic foundation
parameter increases the natural frequency. Increasing the aspect ratio increases the
natural frequency. Increasing the combined elastic foundation parameters increases
the natural frequency. Natural frequency of plates reduces when submerged in fluid
with the mode shapes not significantly affected. The node and antinodes of the mode
shapes are affected by moment and stress. It is expected that the present study will
add to the existing knowledge in the field of vibration of plates.