A note on the spheroidal modes vibration of an elastic sphere in linear viscoelastic fluid

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing, and also to investigate the materials mechanical properties. An analytical approach based on the exact theory has been developed in this paper, to establish a new accurate and simple generalized frequency equation to predict spheroidal vibration of an elastic nanosphere, in a compressible viscoelastic fluid using linear Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. Thus, the obtained frequency equation can be very useful to interpret the experimental measurements of vibrational dynamics of nanospheres and can serve as benchmark solution in design of liquid sensors

Elasto-Acoustic Coupling Between Two Circular Cylinders and Dense Fluid

This paper describes a theoretical method for free vibration analysis of two elastic and isotropic cylinders filled with a dense fluid. The free vibration of two cylinders is studied on the basis of the linear three-dimensional elasticity theory. The compressible fluid is assumed to be nonviscous and isotropic which satisfy the acoustic wave equation. In this paper, the coupled dispersion equations of longitudinal, flexural and lobar modes are deduced and analytically solved. The finite element results computed by the Comsol Multiphysics software are compared with the present method for validation and an acceptable match between them was obtained. It is shown that the results from the proposed method are in good agreement with the numerical solutions. With this method, the effects of the cylinder parameters, such as the circumferential wave, the axial wavenumber, the thickness-to-radius and the length-to-radius on the coupled frequencies are investigated

Vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid

The vibrational frequency analysis of finite elastic tube filled with compressible viscous fluid has received plenty of attention in recent years. To apply frequency analysis to defect detection for example, it is necessary to investigate the vibrational behavior under appropriate boundary conditions. In this paper, we present a detailed theoretical study of the three dimensional modal analysis of compressible fluid within an elastic cylinder. The dispersion equations of flexural,torsional and longitudinal modes are derived by elastodynamic theory and the unsteady Stokes equation. The symbolic software Mathematica is used in order to find the coupled vibration frequencies. The dispersion equation is deduced and analytically solved. The finite element results are compared with the present method for validation and an acceptable match between them are obtained

Mathematical modelling of Love waves propagation in viscoelastic waveguide loaded with complex fluids

Love waves propagation in a viscoelastic waveguide loaded on its surface with viscoelastic fluids of finite thickness is investigated in this paper. The Maxwell and Kelvin-Voigt constitutive equations are employed in order to describe the fluid viscoelasticity. By solving the equations of motion in the different media (viscoelastic fluid, viscoelastic waveguide and elastic substrate) and imposing the suitable boundary conditions, an accurate and simple generalized complex dispersion equation is established for Love waves. Subsequently, a comparison is made with the published complex dispersion equations in the literature in some particular cases, and a very good agreement is showed. A detailed study was conducted by varying key parameters such as operating frequency, waveguide thickness and fluid thickness. The waveguide surface was subjected to various glycerol concentrations, with a wide range of dynamic viscosity, representing both Newtonian and viscoelastic behaviors. Theoretical analysis shows that to reasonably predict the characteristics responses of Love waves, the Maxwell fluid is more appropriate for low glycerol concentration and, the Kelvin-Voigt fluid is more suitable for high glycerol concentration and at high frequency. Results also evaluated the influence of layer thickness on the dispersion curves. The obtained results can be very useful in the design and optimization of Love wave fluid sensors

Prediction of Vibration Behavior of Micro-Circular Disks at Low Reynolds Number Regime

In the current study, a theoretical method is developed to predict the vibrational behavior of micro-circular disks filled with viscous fluids and numerical results are presented to validate the model. Vibrations with two outer boundary conditions, rigid and deformable vessel, are studied. The coupled governing equations of both rigid and deformable vessel vibration are solved by the analytical procedure, taking fluid–structure interaction into account. The fluid gap effect on the coupled eigenfrequencies is also considered. The frequency spectrum plots of the first several eigenfrequencies are presented in a wide range of fluid gap and elasticity ratio. The correctness of results is demonstrated using a commercial finite element software. It is shown that the obtained results through the proposed method reveal very good agreement with the numerical solution

Transverse vibration analysis of Euler-Bernoulli beam carrying point masse submerged in fluid media

In the present paper, an analytical method is developed to investigate the effects of added mass on natural frequencies and mode shapes of Euler-Bernoulli beams carrying concentrated masse at arbitrary position submerged in a fluid media. A fixed-fixed beams carrying concentrated masse vibrating in a fluid is modeled using the Bernoulli-Euler equation for the beams and the acoustic equation for the fluid. The symbolic software Mathematica is used in order to find the coupled vibration frequencies of a beams with two portions. The frequency equation is deduced and analytically solved. The finite element method using Comsol Multiphysics software results are compared with present method for validation and an acceptable match between them were obtained. In the eigenanalysis, the frequency equation is generated by satisfying all boundary conditions. It is shown that the present formulation is an appropriate and new approach to tackle the problem with good accuracy

Correlation between the toroidal modes of an elastic sphere and the viscosity of liquids

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing and also to investigate materials and mechanical properties. An analytical approach has been developed in this paper to accurately predict toroidal vibrations of an elastic nanosphere in water–glycerol mixture. The Maxwell and Kelvin–Voigt models are used to describe the viscoelasticity of this fluid. The influence of key parameters such as glycerol mass fraction, sphere radius, and angular mode number are studied. We demonstrate that the sphere radius plays a significant role on the quality factor. Results also highlight three behavior zones: viscous fluid, transition, and elastic solid. In addition, these investigations can serve as benchmark solution in design of liquid sensors

Correlation between the toroidal modes of an elastic sphere and the viscosity of liquids

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing and also to investigate materials and mechanical properties. An analytical approach has been developed in this paper to accurately predict toroidal vibrations of an elastic nanosphere in water–glycerol mixture. The Maxwell and Kelvin–Voigt models are used to describe the viscoelasticity of this fluid. The influence of key parameters such as glycerol mass fraction, sphere radius, and angular mode number are studied. We demonstrate that the sphere radius plays a significant role on the quality factor. Results also highlight three behavior zones: viscous fluid, transition, and elastic solid. In addition, these investigations can serve as benchmark solution in design of liquid sensors

Bleustein-Gulyaev waves in a finite piezoelectric material loaded with a viscoelastic fluid

A generalized analytical approach for the propagation of Bleustein–Gulyaev wave in a piezoelectric material loaded on its surface with a viscoelastic fluid is established in this paper. The Bleustein–Gulyaev waveguide surface is subjected to various glycerol concentrations. The Maxwell and Kelvin–Voigt models are used to describe the viscoelasticity of this fluid. Exact dispersion equation is obtained in the cases of both electrically short circuit and open circuit by solving the equilibrium equations of piezoelectric materials and the Stokes equation of viscoelastic fluid. The effect on the phase velocity and attenuation for several frequencies is highlighted. The influence of key parameters such as substrate thickness and fluid thickness is also studied. These investigations can serve as benchmark solution in design of Bleustein–Gulyaev wave sensors

Surface wave in a Maxwell liquid-saturated poroelastic layer

An analytical approach of the propagation and attenuation of Love waves in a viscoelastic liquidsaturated poroelastic layer has been considered in this paper. The equations of motion have been formulated separately for different media under suitable boundary conditions at the interface of viscoelastic liquid, poroelastic layer and elastic substrate. Following Biot’s theory of poroelasticity, a new accurate and simple generalized dispersion equation has been established to design Love wave liquid sensors. The effect of liquid shear viscosity on the Love waves velocity has been studied. The influence of thickness and porosity of the waveguide layer has also been shown on the Love waves velocity and attenuation. The various investigations results can serve as benchmark solutions in design of liquid sensors and nondestructive testing