Numerical Computation And Theoretical Analysis For Elastic Waves In Nonhomogeneous Spherical Shell Structures

Spherical shell structures which as a common structure are widely used in many industrial fields, and the safety assurance technologies for such large scale equipments are always the focus concerned in academic circle. At the same time, when the structure is subjected to dynamic loading, the inclusion (cavity) in the structure will lead to the scattering of elastic waves and the dynamic stress concentration. which will greatly affect the strength and life of the structure. The researches of the paper are mainly on the detection, safety evaluation and material property test of large spherical shell structures. The main research contents are as follows:(1) The propagation characteristics of elastic wave in the spherical shell with viscoelastic coating are studied, and the influence of the thickness and the damping factor of the viscoelastic coating on the propagation properties are examined. The viscoelastic layer is described by the standard linear solid viscoelastic, then the dispersion curves and the attenuation curves for various thicknesses and damping factors are calculated.(2) The dispersion characteristics of elastic waves in a spherical shell of exponentially FGM are calculated. According to the particular material properties, the analytical solution of displacement components by a new variables separation technique. The dispersion curves of parametric gradient coefficients are calculated separately from dispersion equations of non-dimensional form to reveal the the influences of the coefficients, furthermore, the distribution of displacement and stress components in the radial direction is investigated.(3) Three-dimensional scattering and dynamic stress concentration of elastic waves around a spherical inclusion (inhomogeneity and a cavity) in a thick spherical shell are investigated theoretically and numerically. Two spherical coordinates, located at the spherical shell center and the inclusion center, are established to express the incident wave and scattered wave of expansion form of spherical wave functions.