An analytical method for predicting the dynamic effective properties of coated nanocomposites subjected to P- and SV-waves

The propagation characteristic of elastic waves in composite materials is a key problem that affects the dynamic properties of material structures. When the elastic wave propagates in the structure, the elastic wave scattering phenomenon will occur due to the sudden change of material properties and geometric discontinuity. The elastic dynamic constant plays an important role in the ultrasonic nondestructive evaluation of structural composites. Compared with traditional composites, nanocomposites have higher interfacial volume ratio and interfacial energy, which makes the propagation and dynamic mechanical behavior of elastic waves in nanocomposites more complicated. Based on the Gurtin–Murdoch surface/interface elasticity theory, elastic wave theory and generalized self-consistent method, a dynamic micromechanical model was established to study the in-plane dynamic modulus of nanocoated fiber composites, and the scattering problem of steady-state incident P-wave and SV-wave on nanoscale-coated fiber composites was studied. The in-plane dynamic effective properties of nanocoated fiber composites subjected to plane waves (P-wave and SV-wave) were investigated theoretically. The non-classical boundary conditions of displacement and stress at the interface between fiber, coating and substrate are derived by considering the theory of surface/interface elasticity. According to the wave equation, the displacement potential of P-wave and SV-wave in the material is given, and then, the displacement and stress expressions are obtained. The phase velocity, attenuation, in-plane effective bulk modulus and effective shear modulus of P-wave and SV-wave are obtained by non-classical boundary conditions and iterative process of multiple scattering methods. The phase velocity and attenuation of wave propagation of nanocoated fiber composites and the dynamic effective properties of nanocoated fiber composites with interface properties and coating parameters were analyzed.