The driving-point mechanical impedance describing the steady-state characteristics of mechanical vibratots are considered. When a mechanical vibrator is driven by such a force which is in certain distribution and which is changing sinusoidally with time, the drivint point impedance is defined by the ratio of the total force to the mean velocity at the driving position. If the equation of motion, describing the steady state displacement of the vibrator driven by a concentrated force be solved, and the steady state solution under this condition be obtained, then the driving point impedance is formally calculated according to definition. But this gives sometimes an incorrect value, for the steady state solution with a point source (Green's function or Green's tensor of the problem) may have some singularities in the neibourhood of its source point. The behavior of the solutions in the neighborhood of the source points, and singulalities of the driving-point impedances are considered for various vibrators, namely, stretched strings, longitudinally or torsionally vibrating bars, stretched membranes, laterally vibrating bars, thin plates, stretched plates, etc. All of these solutions are continuous and driving-point impedances have no singularity except the only case of stretched membranes. In the case of the vibrator with an isotropic elastic material however, the driving-point impednce of such a vibrator with a point source terminal or a line or curve source terminal has serious singularities and its value becomes identically equal to zero, because of the singularities of the Green's tensor (diadic) of elastic waves at its source point.
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