Figure 1

(a) Cutout cavity on mount. The cavity is represented by the light gray shaded area. The support “yokes” are shown in white. Spacer length, $99.8\mathrm{mm}$; diameter, $60\mathrm{mm}$; axial bore diameter, $21.5\mathrm{mm}$; vent-hole diameter $4\mathrm{mm}$. The mirrors are $31\mathrm{mm}$ in diameter and $8\mathrm{mm}$ thick. The parameters relevant to the design, the cut depth $c$ and the support coordinates $x$ and $z$ are indicated. (b) Details of the support point in cross section. The black shaded areas represent rubber tubes and spheres. Case A: Diamond stylus set into a cylindrical ceramic mount, cushioned on all sides by a rubber tube, and from below by a rubber sphere. The stylus digs into the underside of the cavity, and can be considered to be in rigid contact with it. Case B: 3-mm-diam rubber sphere recessed into a cylindrical hole in the yoke.Reuse & Permissions

Figure 2

(Color online) Plot showing the deformation of a quarter section of the cavity. The point $O$ marks the center of the mirror surface. $c=18.45\mathrm{mm}$, $x=22\mathrm{mm}$, and $z=17\mathrm{mm}$. The scale of the distortion is amplified by a factor of ${10}^7$ and a uniform downward displacement of $10\mathrm{nm}$ is subtracted. The white (black) lines indicate the outline of the loaded (unloaded) geometry.Reuse & Permissions

Figure 3

Plot of axial displacement at the center of the mirror surface, $w_O$, as a function of $z$ for various $c$ and $x$.Reuse & Permissions

Figure 4

Schematic of experimental setup for measuring vibration response. PD: photodiode; f-V: frequency-to-voltage converter. The thicker lines indicate beam paths; the thinner lines indicate electronic signal paths.Reuse & Permissions

Figure 5

Plot of experimental response of cutout cavity to vertical acceleration as a function of the support position. $c=18.45\mathrm{mm}$, $x=22\mathrm{mm}$, and $z=17\mathrm{mm}$. The response predicted by the model is also shown. This is calculated by converting the displacement to the frequency change this would induce, taking into account that the center points of the two mirrors are displaced by equal and opposite amounts.Reuse & Permissions