In this study, the hydrostatic vibration analysis of an isotropic rectangular microplate in
partial contact with a bounded fluid is studied. Modified couple stress theory based on the
Kirchhoff plate assumptions are used to mathematically model the problem. The extended
Hamilton's principle is employed to drive the governing differential equation of motion and
the corresponding boundary conditions. The transverse displacement of the microplate is
approximated by a set of admissible functions which must satisfy the geometric boundary …