Why is the Navier-Cauchy equation (as given here https://en.wikipedia.org/wiki/Linear_elasticity) a second order wave equation? How can I proof this?
2026-04-03 12:30:53.1775219453
Navier-Cauchy-equation
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You do not need to prove it. It is a matter of definition. The equation of motion involves a second derivative of displacement with respect to time. In that equation, the components of the stress tensor must be replaced by linear combinations of the components of the strain tensor, which are in turn expressed through partial derivatives of the displacement. The final outcome is a set of equations containing, on one side, the second partials of displacements w.r.t. time and, on the other, second partial derivatives with respect to spatial coordinates. Such equations describe wave propagation, just like the standard wave equation but the waves are more complex, like spherical waves for example.