ELASTIC BLOCH WAVES IN COMPOSITE-MATERIALS - VARIATIONAL-METHODS AND BOUNDARY-CONDITIONS

A modified variational procedure is presented, which allows an efficie nt determination of dispersion curves and especially of normal modes o f phonons in periodic, inhomogeneous materials with abrupt changes of material constants. The Bloch wave eigenvalue problem is solved by a R itz method using expansion functions with discontinuous first derivati ves for the displacements, which satisfy the interface conditions for displacements and stresses. An explicit derivation is given for threef old periodic arrangements of inclusions in a matrix. Questions of conv ergence are discussed. A numerical comparison with results obtained wi th customary Fourier trial functions for structures inhomogeneous in o ne and two dimensions and with exact results for one-dimensional (laye r) structures shows the great accuracy of the method.