The hand calcs are only calculating the resonant frequencies in a certain plane. The FEA calculates vibration modes in general 3D space.
So make sure you are filtering through the modes to find the vibration modes corresponding to vibration in the correct plane. You may need to increase the number of frequencies the study is solving for because of this. Then I would expect them to match within a reasonable margin.
There are also validation examples available for similar problem setups in SOLIDWORKS, under Help -> SOLIDWORKS Simulation - > Validation -> Verification Problems
Ryan is right.
Change the settings to request more modes and re-run. Inspect the plots to determine which modes are relevant (contain vertical movement only). A visual inspection is quite easy, but you could also just look at which modes contain significant mass participation in the Y direction.
Alternatively you could put a sliding constraint on one side of the beam, thus allowing only modes that are planer.
Your solid mesh is way, way finer than it needs to be. The default values SW assigns would be a good starting point. (But even this is far finer than required). A beam mesh is an option to simplify things more.
The gravity load isn't included in your hand calculations, so it needn't be included in the FEA. Removing it allows you to use the FFEPlus solver, which is also way faster.
In any case the beam is a little stubby. You'll get closer matches between FEA and hand calcs if you make the beam 100 inches long instead of 10.