Biharmonic function
A mathematical function is called biharmonic in a domain if it has the biharmonic equation
fulfilled for all points ; is the Laplace operator .
The biharmonic equation is thus a partial differential equation of the fourth order of .
In practice this equation occurs e.g. B. in continuum mechanics with plates . The deformation of a plate at a point obeys the inhomogeneous biharmonic equation as a first approximation :
Here is the force (density) that is being exerted on the plate.
Harmonic functions are always biharmonic functions; however, the reverse does not have to apply.
Web links
- Eric W. Weisstein : Biharmonic Equation . In: MathWorld (English).