Is there any typical frequencies range which mechanical systems resonant at ?
Yea, its natural frequency.
So what is the frequencies range ?
It is impossible to give a frequency range for a general mechanical system since the resonant frequency is specific to a particular mechanical system and is dependent on a large number of parameters.
I can't imagine mechanical system resonant at frequencies of GHz, But i can imagine electrical systems resonant at frequencies of MHz for example.
So there is no order of magnitude for it?
Well, 1-100,000 is five orders of magnitude, but there is probably an upper limit based on materials properties. Amplitude has to go down as frequency goes up to avoid having the inertial forces tear apart the object or device.
The equation for natural frequency is w^2=k/m
Nanomechanical resonators can have a resonance frequency of tens of MHz, large structures (buildings etc) less than 0.1 Hz.
So the "typical " frequency range for mechanical resonance covers at least 8 orders of magnitude.
Plus the (primary) resonance is usually quite broad due to dissipative processes. And there will be multiple resonances for different modes- compression, torsion, different axes, differences depending on where the exciter is and what direction it's operating.. on and on and on...
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