<p>For an Euler–Bernoulli beam and a thin inextensible half-ring, it is shown that their Green’s function for normal forces and displacements can be zero in the presence of dissipative losses. The beam and half-ring are considered in two versions: with a simple support and movable seal at the ends. Solutions exist in wide frequency bands. For a half-ring with a movable seal, there are solutions for which the frequency derivative of the Green’s function is close to zero with a frequency-independent loss tangent. A vibration isolator in the form of a closed ring with four supports arranged at points corresponding to one of these solutions will have both theoretically infinite vibration isolation at one frequency and large vibration isolation in a wide band of neighboring frequencies.</p>