A rubber-like pad in a vibration mount under a machine carries only the machine's…

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 Non-Newtonian and viscoelastic fluids

Problem

A rubber-like pad in a vibration mount under a machine carries only the machine's oscillating load; a steel spring beside it carries the static weight, which a Maxwell fluid could not hold without creeping. The pad is modelled as a Maxwell fluid with shear modulus

G = 2\,\mathrm{MPa}

and viscosity

\eta = 200\,\mathrm{kPa\,s}

. The machine vibrates the mount sinusoidally at

f = 5\,\mathrm{Hz}

. ((a)) Find the Maxwell relaxation time

\tau_M

of the mount. ((b)) Compute the storage modulus

G'

and loss modulus

G''

at this frequency. ((c)) Using the loss factor

\eta_L = G''/G'

and Chapter 6's relation

Q = 1/\eta_L

, find

Q

for the mount at

5\,\mathrm{Hz}

. That relation was derived for a small loss factor; say how far to trust it here.

Browse the problem library