EIGENPAIR DERIVATIVE WITH RESPECT TO BOUNDARY SHAPE

This work focuses on how changes of boundary shapes affect eigenvalues and eigenfunctions in continuous systems. The governing equation, plu s its boundary conditions for the eigenpair derivatives, is derived us ing the delta-function method, which can facilitate the differentiatio n of boundary conditions with respect to boundary shapes. Even though the eigenproblem equation with its corresponding boundary conditions i s homogeneous, the governing equation with its boundary conditions for the eigenpair derivatives may be nonhomogeneous. A transformation met hod is proposed to transform the differential equation with nonhomogen eous boundary conditions into a new problem with homogeneous boundary conditions so that the eigenfunctions form a complete set for this new problem,The explicit results for the eigenpair derivatives are given, and an example is presented to illustrate the method and its validity .