Three-dimensional vibrations of multilayered hollow spheres submerged in a complex fluid

Abstract

Fluid–structure interaction is fundamental to the characteristics of the induced flows due to the motion of structures in fluids and also is crucial to the performance of submerged structures. This paper presents a three-dimensional analytical study of the intrinsic free vibration of an elastic multilayered hollow sphere interacting with an exterior non-Newtonian fluid medium. The fluid is assumed to be characterized by a compressible linear viscoelastic model accounting for both the shear and compressional relaxation processes. For small-amplitude vibrations, the equations governing the viscoelastic fluid can be linearized, which are then solved by introducing appropriate potential functions. The solid is assumed to exhibit a particular material anisotropy, i.e. spherical isotropy, which includes material isotropy as a special case. The equations governing the anisotropic solid are solved in spherical coordinates using the state-space formalism, which finally establishes two separate transfer relations correlating the state vectors at the innermost surface with those at the outermost surface of the multilayered hollow sphere. By imposing the continuity conditions at the fluid–solid interface, two separate analytical characteristic equations are derived, which characterize two independent classes of vibration. Numerical examples are finally conducted to validate the theoretical derivation as well as to investigate the effects of various factors, including fluid viscosity and compressibility, fluid viscoelasticity, solid anisotropy and surface effect, as well as solid intrinsic damping, on the vibration characteristics of the submerged hollow sphere. Particularly, our theoretically predicted vibration frequencies and quality factors of gold nanospheres with intrinsic damping immersed in water agree exceptionally well with the available experimentally measured results. The reported analytical solution is truly and fully three-dimensional, covering from the purely radial breathing mode to the torsional mode to any general spheroidal mode as well as being applicable to various simpler situations, and hence can be a broad-spectrum benchmark in the study of fluid–structure interaction.

Time-Domain Analysis for Fluid Damping of Acoustic Vibrations of Single Gold Nanorod in Water

“…The fluid damping of a gold nanorod in water arises from two mechanisms: (1) the propagation of energy into the surrounding fluid away from the vibrating particle through acoustic waves and (2) the viscous dissipation in the fluid. , To examine the role of each mechanism in the fluid damping of gold nanorod, a parametric FEM study on vibrational damping of gold nanorod in water has been conducted with the same model, material properties and parameters as those used in the above three-dimensional FEM simulations, except that the bulk or shear viscosity of fluid is purposely set to be zero.…”

“…An effective way of removing the inhomogeneous effect is to conduct the measurements on single particles . For example, the experiments on acoustic vibrations of single gold nanoparticles optically trapped in water and substrate-supported single gold nanorods in water have been reported. , Besides experiments, there have been many continuum-based studies on the acoustic vibrations of single noble metal nanoparticles in fluid, − for the quantitative comparisons to experimental results, and the damping mechanisms in nanoparticle vibrations as well. However, it is worth noting that the existing continuum analysis mostly was performed with the adoption of certain simplified and approximated theoretical models.…”

A novel smart hybrid multimorph piezoelectric spherical shell cloak for broadband near-perfect underwater acoustic camouflage applications

“…In particular, for an ideal non-viscous acoustic fluid, the fluid-loaded structural modes are known to expediently decouple into two independent classes of vibrations, namely, the first-class (torsional or toroidal) modes that are associated to equi-volumetric motion, and the second-class (spheroidal) modes that are directly impelled by the fluid loading. This way, as it has also been demonstrated in Refs., 74,75 only the second class modes of structural vibrations associated with ( V 2,n , v 2,n ; n = 0,1, 2,3, . .…”

Complex dynamics in non-Newtonian fluid-structure interaction

“…In 2019 Wu et al [38] presented a numerical study on interaction between elastic multilayered spheres and a non-Newtonian fluid. They analyzed gold nanospheres immersed in water and calculated theoretically the natural frequencies and the quality factors.…”