B. L. Jiao
Theoret. Phys., Univ. des Saarlandes, D-6600 Saarbrucken, Germany
A modified variational procedure is presented for an efficient determination of dispersion curves and especially of normal modes of phonons in periodic, inhomogeneous materials with abrupt changes of material constants: The Bloch wave eigenvalue problem is solved by a Ritz method using expansion functions with discontinuous first derivatives for the displacements, which satisfy the boundary conditions for displacements and stresses. Explicit expressions are given for a threefold periodic arrangement of inclusions in a matrix. Questions of convergency and completeness of the expansion are discussed. A numerical comparison with results obtained with customary Fourier trial functions for structures inhomogeneous in one and two dimensions and with exact results for one dimensional inhomogeneities shows the great accuracy of the method.