Required information
Problem 07.035 - Angular frequency of a two-disk shaft
Consider the two equations given below for the angular frequency of a two-disk shaft.
For three roots,
((1)/(\omega ^(2)))^(3)-(m_(1)\delta _(11)+m_(2)\delta _(22)+m_(3)\delta _(33))((1)/(\omega ^(2)))^(2)+dotsdots=0
The three roots of the equation (1) can be expressed as (1)/(\omega _(1)^(2)),(1)/(\omega _(2)^(2)) and (1)/(\omega _(5)^(2)).
Thus, the equation (1) can be written as follows:
((1)/(\omega ^(2))-(1)/(\omega _(1)^(2)))((1)/(\omega ^(2))-(1)/(\omega _(2)^(2)))((1)/(\omega ^(2))-(1)/(\omega _(5)^(2)))=0
or
((1)/(\omega ^(2)))^(3)-((1)/(\omega _(1)^(2))+(1)/(\omega _(2)^(2))+(1)/(\omega _(5)^(2)))((1)/(\omega ^(2)))^(2)+dots.=0
Note that the constants in these two equations are equal.
Problem 07.035.c - Second critical speed of the shaft
Estimate the second critical speed of the shaft shown below. The shaft has a diameter of 1.00 inch and a span of 31
inches. Consider the values of w_(1) and w_(2) to be 29.00 lbf and 45.53 lbf , respectively. Take the value of E to be
3.002\times 10^(7)lb(f)/(i)n.^(2) and the value of g to be 386.1in(.)/(s^(2)).
w_(1)=29.00lbf, and ,w_(2)=45.53lbf,.
