ok, fine. As I already stated, IMHO under these condition the “purpose” of the random vibration analysis is not existent. Your idealization of the body will just not move (better: it will not amplify the vibration that it is excited with). Try to think so: you shake a very stiff beam (say a stell beam fixed on both sides, with a section of 20 cm x 20 cm, 1 m long) with a shaker that can reach 30 Hz. What do you think it will happen? Nothing, the beam will shake exactly like your shaking table: input = ouput, no need of FEM.
As soon as at least a small bit of PSD energy is contained above the first natural frequency (f1), than the results are of some interest. But until the whole area under the PSD stays well under f1, you do not need any analysis, because any result of interest can be computed with formulas or with a static equivalent analysis.
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