Question

A Rigid rotor is assumed as a mass less shaft carrying a disk at the midspan and supported on short bearings. It has a critical speed of 1000 rpm. When the mass is doubled and the short bearings are replaced with long bearings. The critical speed will

• A. Remains same
• B. $\text{Increase by}\sqrt{2}\text{times}$
  
• C. $\text{Decrease by}\frac{1}{\sqrt{2}}\text{times}$
  
• D. $\text{Decrease by}\frac{1}{2\sqrt{2}}\text{times}$
  

Answer 1

The correct option is B $\text{Increase by}\sqrt{2}\text{times}$


When the rotor was supported on short bearing,

${\omega }_{n1}=1000\text{rpm}$

${\omega }_{n1}=\sqrt{\frac{g}{{\delta }_1}},{\delta }_1=\frac{W{L}^3}{48EI}$


${\omega }_{n1}=\sqrt{\frac{48EI}{M{L}^3}}$

When the mass is doubled and short bearing is replaced by long bearing,

${\omega }_{n2}=\sqrt{\frac{g}{{\delta }_2}},{\delta }_{21}=\frac{2W{L}^3}{192EI}$

${\omega }_{n2}=\sqrt{\frac{96EI}{M{L}^3}}$

${\omega }_{n2}=\sqrt{2{\omega }_{n1}}$