So do you mean, without the value of Thickness, we cannot find frequencies analytically..right?
If you don't mean this, then what is the analytical approach or formulas to find those frequencies?

Without thickness, we can find frequencies in ANSYS Workbench. The only thing we need to do is convert 2D behaviour of Geometry to 'Plain Strain'. So Ansys workbench does not require Thickness of the geometry.