Effective wave motion in periodic discontinua near spectral singularities at finite frequencies and wavenumbers

We consider the effective wave motion, at spectral singularities such as corners of the Brillouin zone and Dirac points, in periodic continua intercepted by compliant interfaces that pertain to e.g. masonry and fractured materials. We assume the Bloch-wave form of the scalar wave equation (describing anti-plane shear waves) as a point of departure, and we seek an asymptotic expansion about a reference point in the wavenumber-frequency space...