Approximation of the eigenfrequencies of a triangular grid of bars

A rectangular plate is approximated by a regular triangular grid of bars. It is shown that the low-frequency spectrum of the plate is close to that of the grid. The difference between the eigenvalues of the continual and discrete problems is estimated in terms of the periodicity cell. The proof of the main result is based on a finite difference analogue of the Laplacian and on certain facts from the theory of differential equations on graphs.