A hybrid numerical-analytical approach for the simulation of antiplane vibrations of multilayered elastic waveguides with multiple inhomogeneities

Abstract

Computer simulation of the excitation, propagation and scattering of elastic waves holds promise in designing structural health monitoring systems, in developing new ultrasonic non-destructive testing methods, in seismic sounding and sensorics and in other applications. This paper presents a further development of the hybrid numerical-analytical approach that allow analysis of the wave structure of the solution of dynamic boundary value problems in multilayer elastic waveguides with multiple local inhomogeneities, vibration sources and sensors. The approach is based on a grid solution of the corresponding dynamic problem in local domains with obstacles, which subsequently couples with the expansion in the form of traveling waves in homogeneous parts of the waveguide. In this form, the hybrid approach allows to construct solutions for complex geometries and defects, and it uses analytical representations to obtain a physically clear insight into the wave process for homogeneous parts of the waveguide. The proposed computational scheme is described for the problem of SH-wave propagation in a 2-D multilayer waveguide with single or multiple obstacles, and it can be generalized to the case of oscillations of isotropic and orthotropic materials. The hybrid approach is numerically verified based on comparison with the solutions of the considered problems obtained by other methods. The possibility of optimizing the developed computational scheme in the case of waveguides with multiple regions with inhomogeneities in order to reduce computational costs is indicated. The problem of diffraction of the SH-waves on a stringer, which were excited by a surface source of vibrations and measured by a piezoelectric sensor, is considered as an example of the use of a hybrid approach for parametric analysis of wave processes.