A capacitive pressure sensor uses a steel diaphragm ( , ) clamped around its rim of radius

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Buckling, plates and elastic foundations

Problem

A capacitive pressure sensor uses a steel diaphragm (E=200 GPaE = 200\,\mathrm{GPa}, ν=0.3\nu = 0.3) clamped around its rim of radius a=8.0 mma = 8.0\,\mathrm{mm}. The diaphragm must deflect at its centre by exactly w0=5.0 μmw_0 = 5.0\,\mathrm{\mu m} when a uniform pressure q=2.0 kPaq = 2.0\,\mathrm{kPa} is applied. ((a)) Find the flexural rigidity DD the diaphragm must have. ((b)) Find the thickness hh required. ((c)) Check the ratio w0/hw_0/h and comment on whether the linear plate theory used to derive w0=qa4/64Dw_0 = qa^4/64D is still trustworthy.

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