Analytical approximations for multiple scattering in one-dimensional waveguides with small inclusions

• DOI: 10.48550/arxiv.2405.02587
• Publication Date: 2024-05-04
• Authors: Mario Lázaro; Richard Wiltshaw; Richard Vaughan C...; Lluís Miquel Garc...
• Keywords: Approximations of π

We propose a new model to approximate the wave response of waveguides containing an arbitrary number small inclusions. The theory is developed consider any one-dimensional waveguide (longitudinal, flexural, shear, torsional waves or combination them by mechanical coupling), inclusions with different material and/or sectional properties. exact problem modelled through formalism generalised functions, Heaviside function accounting for discontinuous jump in properties For asymptotically inclusions, solution shown be equivalent Green's function. hypothesize that these expressions are also valid when size comparison wavelength, allowing us inhomogeneities as regular perturbations empty-waveguide (the homogeneous absence scatterers) point source terms. By approximating solutions function, multiple scattering considerably simplified, develop general methodology which expressed elastic waveguide. advantage our approach that, expressing constitutive equations first order form matrix, can matrix form; therefore, it trivial models more degrees freedom and arrive at problems independent used. validated two numerical examples, where we perform error analysis demonstrate validity solutions, parameter quantifying expected errors approximation dependent upon parameters