Adiabatic normal modes in a slowly irregular elastic waveguide resting on a Winkler foundation

Asymptotic expansion for normal modes in an elastic layer resting on the Winkler foundation is constructed. Parameters of the layer slowly and smoothly vary in the lateral direction. Equations of elastodynamics are written in the form of the Schroedinger-type equation and the analogy with the derivation of the adiabatic approximation for Quantum Mechanics is applied. Adiabatic expansion may fail in the vicinity of the degeneration point, i.e., near the section, where two or more propagation constants coincide. The size of this vicinity is estimated.