- #1
MiSo
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Hello to everybody,
I am solving some examples related to wave equation of shear horizontal wave in cylindrical coordinates (J.L Rose: Ultrasolic Waves in Solid Media, chapter 6), which is expressed as follows:
∇2u=1/cT2⋅∂2u/∂t2
The Laplace operator in cylindrical coordinates can can be derived in the form of (which I have verified to myself):
∇2=∂2/∂r2+1/r⋅∂/∂r+1/r2⋅∂2/∂θ2+∂2/∂x2
Prof. Rose uses in his book following expression of Laplace operator:
∇2=1/r⋅∂/∂r⋅(r⋅∂/∂r)+1/r2⋅∂/∂θ2+∂2/∂x2
Can anyone please give be an explanation how to get such an expression? I am quite confused.
Mike
I am solving some examples related to wave equation of shear horizontal wave in cylindrical coordinates (J.L Rose: Ultrasolic Waves in Solid Media, chapter 6), which is expressed as follows:
∇2u=1/cT2⋅∂2u/∂t2
The Laplace operator in cylindrical coordinates can can be derived in the form of (which I have verified to myself):
∇2=∂2/∂r2+1/r⋅∂/∂r+1/r2⋅∂2/∂θ2+∂2/∂x2
Prof. Rose uses in his book following expression of Laplace operator:
∇2=1/r⋅∂/∂r⋅(r⋅∂/∂r)+1/r2⋅∂/∂θ2+∂2/∂x2
Can anyone please give be an explanation how to get such an expression? I am quite confused.
Mike