Question $12$

A device for vibration$-$testing has an electromagnetic actuator driving a round table $($see

figure$),$ at a constant operating amplitude $($ A $)$ and frequency $($ w $)$ significantly less than the

resonance frequency of the table $(C_1=1$ in this condition$).$ Also, it is important to prevent the

table from flexing to much under load $($F$),$ for that reason the vertical deformation $(y)$ should

be less than an admissible vertical deflection $[$y$]$ with given value.

Power consumed by the table: $P=C_1*m*A^2*{}^3$

Mass of the table: $m=*r^2*t*$

Admissible vertical deflection: $[y]=\frac{F*r^2}{6*E*c^3}$

Where:

$E=$ Modulus of elasticity of the table.

$r=$ Density of the material of the table.

The following materials are being considered:

$1-$ Zinc alloy.

$2-$ Ti alloy,

$3-$ Mg alloy.

$4-$ Steel

Using the Ashby chart $($figure $2-24)$ and Material Index, select the order from highest to

lowest in material preference considering the best material to minimize the power $($P$)$

consumption of the table.

Zinc alloy

Ti alloy

Mg alloy