GATE-2018 (24) :Wyllie – Time average equation

94. For a homogenous ,isotropic elastic medium, the ratio${\frac{\lambda}{\mu}}$ of the Lame’s constants for Poisson ratio$(\nu)$=0.3 will be

(Thanks to Saroja)

solution: 

 

${\frac{\lambda}{\mu}} $= ?

Poisson ratio $(\upsilon) $= 0.3

Formulas:

$ \lambda = \frac{\nu E}{(1+\nu)(1-2\nu)}$

$ \mu = \frac{E}{2(1+\nu)}$

$ \frac{\lambda}{\mu}=\frac{\frac{\nu E}{(1+\nu)(1-2\nu)}}{\frac{E}{2(1+\nu)}}$

         =$\frac{2\nu}{(1-2\nu)}$

         =$\frac{2*0.3}{(1-(2*0.3))}$

         =$\frac{0.6}{1-0.6}$

         =$\frac{0.6}{0.4}$

$\frac{\lambda}{\mu}$= 1.5

Reference : Fundamentals of Geophysics by William Lowrie.