Torsional wave dispersion in a bi-layered hollow cylinder with inhomogeneous initial stresses caused by internal and external radial pressures

Surkay D. Akbarov,Emin T. Bagirov 국제구조공학회 2021 Structural Engineering and Mechanics, An Int'l Jou Vol.77 No.5

The present paper studies the influence of the inhomogeneous initial stresses in the bi-layered hollow cylinder and it is assumed that these stresses are caused by the hydrostatic pressures acting on the interior and outer free surfaces of the cylinder. The study is made by utilizing the version of the three-dimensional linearized theory of elastic waves in bodies with initial stresses for which the initial stress-strain state in bodies is determined within the scope of the classical linear theory of elasticity. For the solution to the corresponding eigenvalue problem, the discrete-analytical method is employed. Numerical results are presented and analyzed for concrete selected pairs of materials. According to these results and their analyses, it is established that, unlike homogeneous initial stresses, the influence of the inhomogeneous initial stresses on the torsional wave dispersion has not only quantitative but also qualitative character. For instance, in particular, it is established that as a result of the initial stresses caused by the hydrostatic pressure acting in the interior free surface of the cylinder, the cut-off frequency appears for the fundamental dispersive mode and the values of this frequency increase with the intensity of this pressure.

On the dispersion of waves propagating in "plate+fluid layer" systems

Akbarov, Surkay D.,Negin, Masoud Techno-Press 2021 Coupled systems mechanics Vol.10 No.2

The paper deals with the study of the dispersion of quasi-Lamb waves in a hydro-elastic system consisting of an elastic plate, barotropic compressible inviscid fluid, and rigid wall. The motion of the plate is described using the exact equations of elastodynamics, however, the flow of the fluid using the linearized equations and relations of the Navier-Stokes equations. The corresponding dispersion equation is obtained and this equation is solved numerically, as a result of which the corresponding dispersion curves are constructed. The main attention is focused on the effect of the presence of the fluid and the effect of the fluid layer thickness (i.e., the fluid depth) on the dispersion curves. The influence of the problem parameters on the dispersion curves related to the quasi-Scholte wave is also considered. As a result of the analyses of the numerical results, concrete conclusions are made about the influence of the fluid depth, the rigid wall restriction on the fluid motion, and the material properties of the constituents on the dispersion curves. During the analyses, the zeroth and the first four modes of the propagating waves are considered.

3D dynamics of the oscillating-moving load acting in the interior of the hollow cylinder surrounded with elastic medium

Surkay D. Akbarov,Mahir A. Mehdiyev 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.71 No.6

In the paper the dynamics of the oscillating moving load acting in the interior of the hollow cylinder surrounded with elastic medium is studied within the scope of the exact field equations of 3D elastodynamics. It is assumed that the oscillating load act on the certain arc of the internal circle of the cylinder's cross section and this load moves with constant velocity along the cylinder's axis. The corresponding 3D dynamic problem is solved by employing moving coordinate system, the exponential Fourier transform and the presentation these transforms with the Fourier series. The expressions of the transforms are determined analytically, however their originals are found numerically. Under the investigations carried out in the paper the main attention is focused on the so-called “gyroscopic effect”, according to which, the influence of the vibration frequency on the values of the critical velocity and interface stresses are determined. Numerical results illustrated this effect are presented and discussed. In particular, it is established how the non-axisymmetricity of the problem acts on the influence of the load oscillation on its critical velocity and on the interface stresses.

Attenuation of quasi-Lamb waves in a hydroelastic system “elastic plate+compressible viscous fluid+rigid wall”

Surkay D. Akbarov,Mesut Negin 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.81 No.4

The paper studies the dispersion and attenuation of propagating waves in the “plate+compressible viscous fluid layer” system in the case where the fluid layer flow is restricted with a rigid wall, and in the case where the fluid layer has a free face. The motion of the plate is described by the exact equations of elastodynamics and the flow of the fluid by the linearized Navier-Stokes equations for compressible barotropic Newtonian viscous fluids. Analytical expressions are obtained for the amplitudes of the sought values, and the dispersion equation is derived using the corresponding boundary and compatibility conditions. To find the complex roots of the dispersion equation, an algorithm based on equating the modulus of the dispersion determinant to zero is developed. Numerical results on the dispersion and attenuation curves for various pairs of plate and fluid materials under different fluid layer face conditions are presented and discussed. Corresponding conclusions on the influence of the problem parameters on the dispersion and attenuation curves are made and, in particular, it is established that the change of the free face boundary condition with the impermeability condition can influence the dispersion and attenuation curves not only in the quantitative, but also in the qualitative sense.

Dispersion of axisymmetric longitudinal waves in a “hollow cylinder + surrounding medium” system with inhomogeneous initial stresses

Surkay D. Akbarov,Emin T. Bagirov 국제구조공학회 2019 Structural Engineering and Mechanics, An Int'l Jou Vol.72 No.5

The paper studies the dispersion of the axisymmetric longitudinal wave propagating in the “hollow cylinder + surrounding medium” system with inhomogeneous initial stresses caused by the uniformly distributed radial compressional forces acting at infinity. Up to now in the world literature, there exist only a few investigations related to the wave dispersion in a hollow cylinder with inhomogeneous initial stresses. Therefore, this paper is one of the first attempts in this field in the sense of the development of investigations for the case where the cylinder is surrounded with an infinite medium. The three-dimensional linearized theory of elastic waves is used for describing the considered wave propagation problem and, for a solution to the corresponding mathematical problem, the discrete-analytical solution method is developed and employed. The corresponding dispersion equation is obtained and this equation is solved numerically and, as a result of this solution, the dispersion curves are constructed for the first and second modes. By analyzing these curves, the character of the influence of the inhomogeneous initial stresses on the dispersion curves is established. In particular, it is established that as a result of the inhomogeneity of the initial stresses both new dispersion curves and the “band gap” for the wave frequencies can appear.

Forced vibration of the hydro-elastic system consisting of the orthotropic plate, compressible viscous fluid and rigid wall

Akbarov, Surkay D.,Huseynova, Tarana V. Techno-Press 2019 Coupled systems mechanics Vol.8 No.3

This paper studies the forced vibration of the hydro-elastic system consisting of the anisotropic (orthotropic) plate, compressible viscous fluid and rigid wall within the scope of the exact equations and relations of elastodynamics for anisotropic bodies for describing of the plate motion, and with utilizing the linearized exact Navier-Stokes equations for describing of the fluid flow. For solution of the corresponding boundary value problem it is employed time-harmonic presentation of the sought values with respect to time and the Fourier transform with respect to the space coordinate on the coordinate axis directed along the plate length. Numerical results on the pressure acting on the interface plane between the plate and fluid are presented and discussed. The main aim in this discussion is focused on the study of the influence of the plate material anisotropy on the frequency response of the mentioned pressure. In particular, it is established that under fixed values of the shear modulus of the plate material a decrease in the values of the modulus of elasticity of the plate material in the direction of plate length causes to increase of the absolute values of the interface pressure. The numerical results are presented not only for the viscous fluid case but also for the inviscid fluid case.

Fluid flow profile in the "orthotropic plate+compressible viscous fluid+rigid wall" system under the action of the moving load on the plate

Akbarov, Surkay D.,Huseynova, Tarana V. Techno-Press 2020 Coupled systems mechanics Vol.9 No.3

The paper studies the fluid flow profile contained between the orthotropic plate and rigid wall under the action of the moving load on the plate and main attention is focused on the fluid velocity profile in the load moving direction. It is assumed that the plate material is orthotropic one and the fluid is viscous and barotropic compressible. The plane-strain state in the plate and the plane flow of the fluid is considered. The motion of the plate is described by utilizing the exact equations of elastodynamics for anisotropic bodies, however, the flow of the fluid by utilizing the linearized Navier-Stokes equations. For the solution of the corresponding boundary value problem, the moving coordinate system associated with the moving load is introduced, after which the exponential Fourier transformation is employed with respect to the coordinate which indicates the distance of the material points from the moving load. The exact analytical expressions for the Fourier transforms of the sought values are obtained, the originals of which are determined numerically. Presented numerical results and their analyses are focused on the question of how the moving load acting on the face plane of the plate which is not in the contact with the fluid can cause the fluid flow and what type profile has this flow along the thickness direction of the strip filled by the fluid and, finally, how this profile changes ahead and behind with the distance of the moving load.

Parametric study of the wave dispersion in the hydro-elastic system consisting of an inhomogeneously prestressed hollow cylinder containing compressible inviscid fluid

Surkay D. Akbarov,Gurbaneli J. Veliyev Techno-Press 2023 Coupled systems mechanics Vol.12 No.1

The present work is concerned with the study of the influence of inhomogeneous initial stresses in a hollow cylinder containing a compressible inviscid fluid on the propagation of axisymmetric longitudinal waves propagating in this cylinder. The study is carried out using the so-called three-dimensional linearized theory of elastic waves in bodies with initial stresses to describe the motion of the cylinder and using the linearized Euler equations to describe the flow of the compressible inviscid fluid. It is assumed that the inhomogeneous initial stresses in the cylinder are caused by the internal pressure of the fluid. To solve the corresponding eigenvalue problem, the discrete-analytic solution method is applied and the corresponding dispersion equation is obtained, which is solved numerically, after which the corresponding dispersion curves are constructed and analyzed. To obtain these dispersion curves, parameters characterizing the magnitude of the internal pressure, the ratio of the sound velocities in the cylinder material and in the fluid, and the ratio of the material densities of the fluid and the cylinder are introduced. Based on these parameters, the influence of the inhomogeneous initial stresses in the cylinder on the dispersion of the above-mentioned waves in the considered hydro-elastic system is investigated. Moreover, based on these results, appropriate conclusions about this influence are drawn. In particular, it is found that the character of the influence depends on the wavelength. Accordingly, the inhomogeneous initial stresses before (after) a certain value of the wavelength lead to a decrease (increase) of the wave propagation velocity in the zeroth and first modes.

Three-dimensional analysis of the natural vibration of the three-layered hollow sphere with middle layer made of FGM

Surkay D. Akbarov,Hatam H. Guliyev,Nazmiye Yahnioglu 국제구조공학회 2017 Structural Engineering and Mechanics, An Int'l Jou Vol.61 No.5

This paper is a continuation of the investigations started in the paper by Akbarov, S.D., Guliyev, H.H and Yahnioglu, N. (2016) "Natural vibration of the three-layered solid sphere with middle layer made of FGM: three-dimensional approach", Structural Engineering and Mechanics, 57(2), 239-263, to the case where the three-layered sphere is a hollow one. Three-dimensional exact field equations of elastodynamics are employed for investigation and the discrete-analytical method is employed for solution of the corresponding eigenvalue problem. The FGM is modelled as inhomogeneous for which the modulus of elasticity, Poison's ratio and density vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies are presented and discussed. These results are also compared with the corresponding ones obtained in the previous paper by the authors. In particular, it is established that for certain harmonics and for roots of certain order, the values of the natural frequency obtained for the hollow sphere can be greater (or less) than those obtained for the solid sphere.

The influence of initial stresses on energy release rate and total electro-mechanical potential energy for penny-shaped interface cracks in PZT/Elastic/PZT sandwich circular plate-disc

Surkay D. Akbarov,Fazile I. Cafarova,Nazmiye Yahnioglu 국제구조공학회 2018 Smart Structures and Systems, An International Jou Vol.22 No.3

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack’s edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, BaTiO3/Al/BaTiO3 and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.