Dynamic Stress Response Analysis of Circular Inclusions in Inhomogeneous Media With Trigonometric Variations in Modulus and Density Under Shear Horizontal Waves

Functionally gradient materials (FGMs) are widely used in nuclear, military, automotive, and aerospace fields due to the excellent properties. The mechanical properties and stability analysis of functionally graded structures are particularly significant; this study closely links the design theory and research on the physical mechanism of FGMs by proposing an analytical method for the investigation of the propagation of elastic waves in inhomogeneous media with modulus and density variations (including composite media with homogeneous inclusions); this method uses the design theory for special functional materials based on the theory and method for modeling elastic wave propagation in homogeneous media. As an example, the dynamic stress response caused by homogeneous circular inclusions contained in an inhomogeneous medium with trigonometric variation in the modulus and density is analyzed under shear horizontal waves. The effects of the inhomogeneity parameters, reference wavenumber of the substrate, and properties of the circular inclusion relative to those of the substrate on the dynamic stress concentration factor (DSCF) around the circular inclusion are investigated; the results show that the inhomogeneity of the substrate is the primary factor affecting the degree of dynamic stress concentration at the boundary of the inclusion and may lead to a DSCF value of up to several hundred; this work not only helps to advance the fundamental understanding of the structure–response relationships of FGMs, but also provides theoretical reference for the structure design.