Hydroelastic System Research Articles

Dispersion of axisymmetric longitudinal waves propagating in an inhomogeneous prestressed hollow cylinder immersed in an inviscid compressible fluid

The paper investigates the dispersion of axisymmetric waves in a cylinder with inhomogeneous initial stresses caused by the hydrostatic pressure of the compressible inviscid fluid in which this cylinder is immersed. In the context of this study, the motion of the cylinder is described by the three-dimensional linearized equations for elastic waves in bodies with initial stresses, but the flow of the fluid is described by the linearized Navier-Stokes equations for compressible (barotropic) inviscid fluids. The initial stresses in the cylinder, due to the action of hydrostatic pressure on the outer surface of the cylinder, are determined according to the well-known Lame formulas of classical linear elasticity theory. The corresponding eigenvalue problem for the dispersion of axisymmetric waves propagating in the hydro-elastic system under consideration is solved using the discrete-analytic method. The dispersion equation is obtained and solved numerically. Concrete numerical investigations are carried out for three pairs of materials: Soft Rubber + Glycerin, Lucite + Water and Steel + Water. The dispersion curves obtained for these pairs of materials are presented and discussed for different values of the intensity of the external pressure. In particular, it is found that the inhomogeneous initial stresses in the cylinder cause zero group velocity (ZGV) points to appear on the dispersion curves of the lowest modes. However, the ZGV points (or modes) appear on the dispersion curves of the higher modes as a result of the contact of the hollow cylinder with the fluid.

Frequencies and profiles of flexural-gravity waves

New results of experiments on the effect of a floating thin plate on the regularization of a standing Faraday gravity wave on the free surface of water in a rectangular vessel are presented. It is shown that an increase in the thickness of a floating plate significantly affects both the natural frequency of oscillations of the hydroelastic system and the shape of the profiles of the observed standing flexural-gravity waves. When the plate thickness is below the critical value, the waveform is described by the theory of non-linear gravity waves; at large thicknesses, the “dry beam” approximation should be used as approximating dependencies.

An application of data-driven modeling for hydroelasticity of an elastically supported semi-circular pipe conveying fluid

PurposeThe paper aims to develop an efficient data-driven modeling approach for the hydroelastic analysis of a semi-circular pipe conveying fluid with elastic end supports. Besides the structural displacement-dependent unsteady fluid force, the steady one related to structural initial configuration and the variable structural parameters (i.e. the variable support stiffness) are considered in the modeling.Design/methodology/approachThe steady fluid force is treated as a pipe preload, and the elastically supported pipe-fluid model is dealt with as a prestressed hydroelastic system with variable parameters. To avoid repeated numerical simulations caused by parameter variation, structural and hydrodynamic reduced-order models (ROMs) instead of conventional computational structural dynamics (CSD) and computational fluid dynamics (CFD) solvers are utilized to produce data for the update of the structural, hydrodynamic and hydroelastic state-space equations. Radial basis function neural network (RBFNN), autoregressive with exogenous input (ARX) model as well as proper orthogonal decomposition (POD) algorithm are applied to modeling these two ROMs, and a hybrid framework is proposed to incorporate them.FindingsThe proposed approach is validated by comparing its predictions with theoretical solutions. When the steady fluid force is absent, the predictions agree well with the “inextensible theory”. The pipe always loses its stability via out-of-plane divergence first, regardless of the support stiffness. However, when steady fluid force is considered, the pipe remains stable throughout as flow speed increases, consistent with the “extensible theory”. These results not only verify the accuracy of the present modeling method but also indicate that the steady fluid force, rather than the extensibility of the pipe, is the leading factor for the differences between the in- and extensible theories.Originality/valueThe steady fluid force and the variable structural parameters are considered in the data-driven modeling of a hydroelastic system. Since there are no special restrictions on structural configuration, steady flow pattern and variable structural parameters, the proposed approach has strong portability and great potential application for other hydroelastic problems.

Dispersion of the axisymmetric waves propagating in the hydro-elastic system consisting of the pre-strained highly elastic plate, compressible inviscid fluid, and rigid wall

Dispersion of the axisymmetric waves propagating in the hydro-elastic system consisting of the pre-strained highly elastic plate, compressible inviscid fluid, and rigid wall

Active sloshing control of a circular cylindrical container with FG GPL-RC

The main purpose of the current study is to design a control system for a sloshing system to suppress the vibration of functionally graded graphene platelet-reinforced composite (FG GPL-RC) on the top surface. A set of piezoelectric sensors and actuators are used for active control of fluid-structure coupling in transient seismic analysis of an inviscid liquid sloshing in a cylindrical tank. First, the top surface FG GPL-RC is optimized to satisfy maximum deformation, face failure, mid shear, and face wrinkling by changing the geometrical parameters and weight fraction distribution through the thickness. The nonlinear governing equations of nanocomposite panels with mechanical properties derived from the Halpin–Tsai model are solved by smoothed particle hydrodynamics (SPH) method. A parameter study counting the boundary condition effects, thickness-to-radius ratio, material distribution of the laminates, and dimensions of the sloshing tank on the FG GPL-RC natural frequencies are surveyed and explained in detail. Then, the frequency analysis of the plate with and without sloshing is performed while the inviscid fluid motion is modeled by SPH. The proposed method is validated with available data in the literature. Finally, the active control of the coupled system in response to the external disturbances is completed by a tuned proportional–integral–derivative (PID) controller which used the piezoelectric sheets on the top surface plate. The performance of the proposed control system is illustrated by a comparison of the controlled and uncontrolled transient responses of the coupled hydro-elastic system to the El-Centro seismic load.

К исследованию геоэкологических последствий производственной деятельности на нефтедобывающей морской платформе

At the present stage, in connection with a decrease in the level of hydrocarbon production on continental fields, offshore fields on the shelf should become the main source. Offshore platforms located in the open sea are exposed to various environmental factors, in turn, affect the geoecological medium of the continental shelf. The processes of development of hydrocarbon deposits are accompanied, as a rule, by an increase in the level of seismicity and, in particular, by the occurrence of man-made earthquakes. To study the dynamics of tension, the problem of vibration of a block hydroelastic system consisting of an ideal fluid layer on a deformable half-space is considered, which simulates the production process on an offshore oil platform. Vibration is caused by the action of a concentrated harmonic source located in a layer of ideal fluid. The problem of determining the contact stresses arising in the system between the liquid layer and the elastic foundation is solved. The nature of the distribution of contact stresses is determined by a set of system parameters: the intensity and frequency of vibrations, mechanical characteristics and density of the elastic medium and liquid, and the thickness of the liquid layer. The results obtained in this work can be useful to organizations monitoring deformation, geodynamic processes and seismicity of the territory to assess the possible increase in seismic intensity.

Mathematical modeling of the dynamics of a hydroelastic system—A hollow cylinder with inhomogeneous initial stresses and compressible fluid

This work attempts to present mathematical modeling of the dynamics of the hydroelastic system consisting of a hollow cylinder with inhomogeneous initial stresses and a compressible barotropic inviscid fluid which filled the interior of the cylinder. The motion of the cylinder is described with the 3D linearized theory of elastic waves in bodies with initial stresses; however, the flow of the fluid is described with the linearized Euler equations for compressible inviscid fluid. Formulations of the boundary conditions on the outer surface of the cylinder and compatibility conditions between the cylinder and fluid on the interior surface of the cylinder are presented. Concrete formulations are made for the axisymmetric case, and general aspects of the solution methods of the formulated problems are considered. Under these considerations, two types of problem are selected: (1) the axisymmetric longitudinal wave propagation and (2) fluid flow profile on the outer free surface of the cylinder—the “circular” radial moving load. Numerical results are presented and discussed for the first type of problem. In particular, it is established that the character of the influence of the inhomogeneous initial stresses on the wave propagation velocity in the hydroelastic system under consideration depends on the dimensionless wavenumber. The perspective of future investigations is also presented and discussed.

Study of the tension of a heterogeneous hydroelastic system

The purpose of the article is to analyze seismic-acoustic wave fields and stress-strain state in a complex heterogeneous seismogenic structure of the contact area of the continental and oceanic crust, taking into account two types of impact: technogenic and pressure of the oceanic water column. The study uses the theory of block structures and the block element method, developed on the basis of a topological approach. It is shown that the contact stress can be considered as a superposition of stress waves occurring at the interface between the liquid and elastic media. The number of waves, their amplitude and frequency are determined by the physical and geometric characteristics of the volume of the liquid, the elastic semi-bounded layer, the elastic foundation, as well as the oscillation frequency of the external harmonic load. The model can be useful in the design of a transport network, production facilities on the coastal territory, since it allows one to assess seismic risks before the start of the process, as well as the risks of associated hazardous exogenous phenomena - landslides, tsunamis, and volcanism activation.

On the influence of finite initial deformations on the surface instability of the incompressible elastic layer interacting with the half-space of an ideal fluid

The problem of the propagation of quasi-Lamb waves in a pre-deformed incompressible elastic layer that interacts with the half-space of an ideal compressible fluid is considered. The study is conducted on the basis of the three-dimensional linearized equations of elasticity theory of finite deformations for the incompressible elastic layer and on the basis of the three-dimensional linearized Euler equations for the half-space of an ideal compressible fluid. The problem is formulated, and the approach based on the utilization of representations of the general solutions of the linearized equations for an elastic solid and a fluid is developed. Applying the Fourier method, we arrive at two eigenvalue problems for the equations of motion of the elastic body and the fluid. Solving them, we find the eigenfunctions. Substituting the general solutions into the boundary conditions, we obtain a homogeneous system of linear algebraic equations for the arbitrary constants. From the condition for the existence of a nontrivial solution, we derive the dispersion equation. A dispersion equation, which describes the propagation of normal waves in the hydroelastic system, is obtained. The dispersion curves for quasi-Lamb waves over a wide range of frequencies are constructed. The effect of the finite initial deformations in an elastic layer, the thickness of the elastic layer, and the half-space of an ideal compressible fluid on the phase velocities and dispersion of quasi-Lamb modes are analyzed. It follows from the graphical material presented above that, in the case of compression with 0.54, i.e., with a 46 percent’s reduction in the length of the highly elastic incompressible body, the phase velocities of the surface waves (Stoneley waves and Rayleigh waves) vanish. This indicates that surface instability develops at 0.54 for a highly elastic incompressible non-Hookean body initially in a plane stress-strain state. We should point out that these figures agree with results obtained earlier in the theory of stability and correspond to the critical value of the contraction parameter. In the case of highly elastic incompressible bodies, the linearized wave theory makes it possible to study not only general and several specific wave processes, but also the conditions under which the surface instability begins in elastic bodies and hydroelastic systems. It also follows from the graphs that the ideal fluid slightly affects the surface instability of hydroelastic systems. The numerical results are presented in the form of graphs, and their analysis is given.

ПРОДОЛЬНО-РАДИАЛЬНЫЕ КОЛЕБАНИЯ УПРУГОЙ ЦИЛИНДРИЧЕСКОЙ ОБОЛОЧКИ С ВЯЗКОЙ СЖИМАЕМОЙ ЖИДКОСТЬЮ

In this paper, the longitudinal-radial vibrations of the elastic cylindrical shell filled with a viscous compressible fluid are studied using the mathematical model proposed. The general equations for the longitudinal-radial vibrations of the shell made of the homogeneous and isotropic material are derived. These equations can be used to obtain refined equations of vibrations. The proposed algorithm allows one to uniquely determine the stress-strain state of points in any section of the considered hydroelastic system using the field of the required functions in coordinates and time. The benchmark problem of harmonic oscillations in a cylindrical shell with a viscous fluid is solved. The dependences of the frequency on the wave number are obtained for various shell- fluid interaction cases.

Propagation of Waves in an Elastic Half-Space Interacting with a Viscous Liquid Layer

The problem of the propagation of acoustic waves in a layer of a compressible viscous fluid that interacts with an elastic half-space is solved using the three-dimensional linear equations of classical elasticity theory for the solid and the three-dimensional linearized Navier–Stokes equations for the compressible viscous fluid. The problem statement and approach based on the application of the general solutions of linear equations for elastic bodies and linearized equations for the fluid are employed. The dispersion equation describing the propagation of quasi-Lamb waves in the hydroelastic system is derived. Dispersion curves for normal waves in a wide frequency range are plotted. The effect of the thickness of the liquid layer on the phase velocities and attenuation coefficients of acoustic waves is analyzed. It is shown that the influence of fluid viscosity on the parameters of the wave process is associated with the properties of wave localization. Using the developed approach and obtained results, the limits of the applicability of the models of wave processes based on the model of an ideal fluid are established. The numerical results are presented in the form of graphs and analyzed.

ENERGY APPROACHTO THE SOLUTION OF THE HYDROELASTIC PROBLEM OF DIVERTICULUM GROWTH ON FUSIFORM ANEURYSM

This paper considers an energy approach to assessing the state of a cerebral aneurysm as a hydroelastic system consisting of an elastic vessel wall and incoming blood flow. Assuming that the elastic energy of a vessel with an aneurysm, combined with the bending and kinetic energies, is spent only in viscous flow dissipation in the structure, we performed a series of numerical calculations for fusiform aneurysm configuration models with and without a diverticulum of different sizes relative to the size of the aneurysm body. It is shown that pressure–velocity diagrams are in good agreement with clinical data. It is shown by numerical simulation that a small diverticulum has a significant effect on hemodynamics inside the aneurysm body, and at a large diverticulum size, the vortex induced inside the diverticulum is almost completely localized in it.

Hydroelastic responses of floating composite plates under moving loads using a hybrid moving element-boundary element method

Responses of floating plates with the impact of moving excitations have been previously studied by several scholars. Generally, such structures were often assumed to be isotropic. Nonetheless, the directional-dependent bending stiffness should be considered for designing practical floating structures, especially for very large floating structures. Accordingly, this article aims to analyze hydroelastic responses of floating composite plates subjected to moving loads for the first time. For this, a novel numerical approach as a combination of boundary element method and moving element method which is named the BEM–MEM is proposed. In the this approach, governing equations of motion, moving element, and fluid matrices are formulated in a relative coordinate system traveling with moving loads. Consequently, the suggested paradigm can effectively eliminate difficulties in addressing the bound of computational domain and tracking the location of contact points which often encounter in the traditional finite element method owing to utilizing a fixed coordinate system. Several numerical examples are exhibited to demonstrate the performance and ability of the boundary element method-moving element method . Gained results are compared with those by the Fourier transform method and the asymptotic expression to verify the accuracy of the proposed methodology. The outcomes indicate that the speed of moving loads considerably affects the plate deflection. In addition, as the speed is larger than the minimum celerity of the free surface of hydroelastic system ( Cmin), the influence of anisotropy on the deflection becomes significant.

Excitation and Damping Fluid Forces on a Cylinder Undergoing Vortex-Induced Vibration

In the context of flow-induced vibration, the component of the hydrodynamic coefficient in-phase with the velocity of an oscillating body, $C_v$, can be termed `positive excitation' or `negative damping' if $C_v>0$. While this empirical approach is of long standing in the literature it does not account for distinct physical mechanisms that can be associated with fluid excitation and fluid damping. In this work, we decompose the total hydrodynamic force into a drag component aligned with the time-dependent vector of the relative velocity of a cylinder oscillating transversely with respect to a free stream and a lift component normal to the drag component. The drag and lift components are calculated from laboratory measurements of the components of the hydrodynamic force in the streamwise and cross-stream directions combined with simultaneous measurements of the displacement of an elastically mounted rigid circular cylinder undergoing vortex-induced vibration. It is shown that the drag component only does negative work on the oscillating cylinder, i.e. it is a purely damping force as expected from theoretical considerations. In contrast to this the lift component mostly does positive work on an oscillating cylinder, i.e. it is the sole component providing fluid excitation. In addition, the new excitation (lift) coefficient, $C_L$ displays the same scaling as the linear theory predicts for the traditional excitation coefficient, $C_v$, even though $C_L$ is two orders of magnitude higher than $C_v$. More importantly, while $C_v$ depends on the mechanical properties of the hydro-elastic system, according to linear theory, we provide here evidence that $C_L$ depends solely on fluid-dynamical parameters. Finally, an effective drag is calculated that represents the dissipation of energy within the fluid, and it is found that the effective drag is not equal to the mean value of the drag component. The effective drag provides complementary information that characterizes the state of the wake flow. Its variation suggests that the wake can dissipate the kinetic energy most vigorously at the end of the initial branch.

On the Energy of a Hydroelastic System: Blood Flow in an Artery with a Cerebral Aneurysm

The energy approach to the study of a hydroelastic system consisting of an elastic blood vessel, viscous fluid flow, and an aneurysm has been developed to evaluate the various energy components of the system: viscous flow dissipation energy and the stretching and bending energies of the aneurysm wall. To calculate the total energy of the system, we have developed a computing complex including commercial and free software and self-developed modules. The performance of the complex has been tested on model geometric configurations and configurations corresponding to blood vessels with cerebral aneurysms of real patients and reconstructed by angiographic images. The calculated values of the Willmore functional characterizing the shell bending energy are consistent with theoretical data.

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

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.

On the Energy of a Hydroelastic System: Blood Flow in an Artery with Cerebral Aneurysm

On the Energy of a Hydroelastic System: Blood Flow in an Artery with Cerebral Aneurysm

Feedback stabilization of a linear hydro-elastic system

It is known that the linear Stokes-Lamé system can be stabilized by a boundary feedback in the form of a dissipative velocity matching on the common interface [5]. Here we consider feedback stabilization for a generalized linear fluid-elasticity interaction, where the matching conditions on the interface incorporate the curvature of the common boundary and thus take into account the geometry of the problem. Such a coupled system is semigroup well-posed on the natural finite energy space [13], however, the system is not dissipative to begin with, which represents a key departure from the feedback control analysis in [5]. We prove that a damped version of the general linear hydro-elasticity model is exponentially stable. First, such a result is given for boundary dissipation of the form used in [5]. This proof resolves a more complex version, compared to the classical case, of the weighted energy methods, and addresses the lack of over-determination in the associated unique continuation result. The second theorem demonstrates how assumptions can be relaxed if a viscous damping is added in the interior of the solid.

The influence of the initial strains of the highly elastic plate on the forced vibration of the hydro-elastic system consisting of this plate, compressible viscous fluid, and rigid wall

The hydro-elastic system consisting of a pre-stretched highly elastic plate, compressible Newtonian viscous fluid, and the rigid wall is considered and it is assumed that on the plate a lineal-located time-harmonic force acts. It is required to investigate the dynamic behavior of this system and determine how the problem parameters and especially the pre-straining of the plate acts on this behavior. The elasticity relations of the plate are described through the harmonic potential and linearized (with respect to perturbations caused by external time-harmonic force) form of these relations is used in the present investigation. The plane-strain state in the plate is considered and the motion of that is described within the scope of the three-dimensional linearized equations of elastic waves in elastic bodies with initial stresses. The motion of the fluid is described by the linearized Navier-Stokes equations and it is considered the plane-parallel flow of this fluid. The Fourier transform with respect to the space coordinate is applied for a solution to the corresponding boundary-value problem. Numerical results on the frequency response of the interface normal stress and normal velocity and the influence of the initial stretching of the plate on this response are presented and discussed. In particular, it is established that the initial stretching of the plate can decrease significantly the absolute values of the aforementioned quantities.

Active sloshing control in a smart flexible cylindrical floating roof tank

An exact three dimensional fully-coupled hydro-elastic analysis for transient liquid sloshing in a partially-filled vertically-standing flexible circular cylindrical shell container fitted with a freely floating smart piezo-sandwich thin elastic circular plate is presented. The problem formulation is based on the linear water wave theory, the classical (Kirchhoff/Sanders) thin plate and shell models, Maxwell's equations of electrodynamics, Stokes’ transformation, and eigen-function expansions in cylindrical coordinates. The control action is achieved by combined volume displacement and volume velocity feedbacks (VDF, VVF) implemented in a second order active damping (AD) compensator via two competent evolutionary heuristic optimization techniques that systematically tune the controller gain parameters while constraining the floating panel displacement and control voltage. The uncontrolled and controlled transient responses of the coupled hydro-elastic system under various external disturbances (i.e., a harmonic base excitation, a real seismic event, a severe launch vehicle liftoff event, and a distributed impulsive transverse load on the floating panel) are calculated by means of Durbin's numerical inverse Laplace transform scheme. Moreover, the free vibration characteristics of the coupled fluid/structure interaction (FSI) system are briefly studied. The superior performance of the proposed active floating roof control configuration in effective suppression of the key hydro-elastic parameters (panel displacement, and shell displacements/stresses) is demonstrated. It is also found that, in the current FSI control problem, the Multi-objective Particle Swarm Optimization (MOPSO)-based ADC outperforms the Non-dominated Sorting Genetic Algorithm (NSGA-II)-based method, in terms of convergence rate and computational effort. Limiting cases are examined and the precision of results is verified by comparisons with the existing data as well as with the results produced by a commercial finite element package.