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I am trying to do a vibration analysis of a cantilever beam in contact with earth (in ABAQUS). Now I need to match these results with the analytiocal solution.

Could any of you guide me any paper or book where this klind of a problem is solved. So basically im looking for the solution of the vibration problem with equation (with friction term):

mx''+cx'+kx = F(t)

where ' is the derivative with respect to time and F(t) is a sinusoidal external load applied on the cantilever end.

Thanks in advance.

Ira