Three-dimensional free vibrations of piezoelectric spherical shells filled with non-Newtonian fluids

Abstract

The dynamic interaction between piezoelectric structures and complex fluids is critical due to their widespread use in devices operating within complex fluid environments. This study investigates the three-dimensional (3D) free vibration behavior of a piezoelectric spherical shell filled with a non-Newtonian fluid, accounting for both shear and compressional relaxation effects. The linearized generalized Navier–Stokes equations in spherical coordinates are solved analytically by introducing appropriate velocity potential functions. Based on linear piezoelectricity theory, the governing equations for torsional and spheroidal modes are decoupled via three displacement functions and solved using the generalized Frobenius power series method. By enforcing the interface continuity conditions of the fluid–structure coupling system, complex characteristic frequency equations for the two classes of free vibrations are ultimately formulated. The complex vibration frequencies are computed using the Muller iteration algorithm. The proposed methodology is validated through comparative analysis with existing literature. Numerical examples are presented to examine the influences of fluid viscosity, fluid viscoelasticity, and spherical shell size on the vibration frequency and quality factor. The 3D analytical solutions developed in this study provide a theoretical basis for analyzing the vibrations of piezoelectric spherical containers and resonators filled with complex fluids, with promising applications in engineering and biomedicine.