Hydroelastic Problem Research Articles

Modeling on Vibration of Sandwich Plate Possessing a Compressible Core and Interacting with Viscous Fluid

The paper proposed a mathematical model for analyzing the dynamic response of a three-layered channel wall with a compressible core. The narrow channel formed by two parallel walls is considered. The bottom channel wall was a simply supported three-layered plate. The upper channel wall was considered to be absolutely rigid. The channel was filled with a viscous incompressible liquid with pulsating pressure due to a given harmonic law of pressure pulsation at the channel edges. Longitudinal and transverse vibrations of the three-layered channel wall were studied. The dynamic response of the three-layered channel wall was determined on the basis of hydroelastic oscillations problem solution. The frequency-dependent distribution functions of longitudinal and transverse elastic displacements amplitudes of the three-layered channel wall were constructed. These functions make it possible to obtain amplitude-frequency characteristics of the three-layered channel wall in fixed channel cross-sections. The study was supported by Russian Foundation for Basic Research (projects № 18-01-00127-a and № 19-01-00014-a).

Energy Approach to the Solution of the Hydroelastic Problem of the Growth of a Diverticulum of a Fusiform Aneurysm

Energy Approach to the Solution of the Hydroelastic Problem of the Growth of a Diverticulum of a Fusiform Aneurysm

NON-STATIONARY PROBLEM OF THE PLANE OBLIQUE PRESSURE WAVE DIFFRACTION ON THIN SHELL IN THE SHAPE OF PARABOLIC CYLINDER

A non-stationary plane problem of the dynamics of thin elastic shell in the form of parabolic cylinder immersed in the fluid under the impact of the plane oblique pressure wave is considered. To solve this problem, a system of equations in the related formulation is constructed. Herewith, the hydroelasticity problems are reduced to the equations of the shell dynamics, the damping effect of fluid is taken into account by introducing an integral convolution type operator in the time domain which in the first approximation allows for accounting the capillary porosity of the shell material. The operator core is a surface transition function of the auxiliary problem of the plane acoustic pressure wave diffraction on a convex surface. The problem is solved approximately based on the thin layer hypothesis. The integral and differential equations of shell motion are solved numerically based on the difference discretization of differential operators and the representation of the integral operator by sum using the trapezium rule.

Rankine source method analysis for nonlinear hydroelastic responses of a container ship in regular oblique waves

Abstract In this study, some numerical solutions for the hydroelastic problems of bodies are studied by means of Rankine source method. Firstly, Rankine source method is generalised to the elastic modes. The difference method is used to obtain the source strength. In order to eliminate the errors in solving process, a damping correction factor is applied. Secondly, the numerical predictions of the nonlinear hydroelastic responses of a 13000-TEU container ship are presented. In the hydrodynamic part, the nonlinear hydrostatic restoring force and nonlinear incident wave force caused by instantaneous wetted surface as well as slamming force are considered. In the structure part, the finite element method is used to solve vertical and horizontal oscillation modes. Finally, the hydroelastic method is extended to the oblique waves by adopting an autopilot model to consider the rudder force/moment. Variation of the different load components with wave direction is studied. The present numerical results show acceptable agreement with previous experimental results.

Axially Symmetric Vibrations of Elastic Annular Bases and a Perfect Two-Layer Liquid in a Rigid Annular Cylindrical Vessel

We deduce a frequency equation for the natural coupled axially symmetric vibrations of elastic bases (in the form of annular plates) and a heavy two-layer incompressible perfect liquid in a rigid annular cylindrical vessel. We consider different limiting cases: the case of degeneration of annular plates into membranes, the case of absolutely rigid or circular plates, and the case of absence of the upper plate (liquid with free surface). For a broad range of parameters of the analyzed mechanical system, we investigate the frequency spectra and obtain a series of mechanical effects in the problem of hydroelasticity.

Parametric analysis on hydroelastic behaviors of hydrofoils and propellers using a strongly coupled finite element/panel method

This paper analyzed the hydroelastic behaviors of hydrofoils and marine propellers immersed in incompressible, inviscid and irrotational fluids. Strongly coupled fluid–structure interaction analyses were performed using a three-dimensional (3-D) potential-based panel method in conjunction with a 3-D finite element method. The present method is developed for hydroelastic analyses of geometrically complex-shaped propeller blades, and the application of the method to the hydroelastic problems of hydrofoils is straightforward. The parameters dominating the added-mass and -damping matrices of the hydrofoils and propellers are examined. The effects of the translational motion of the hydrofoil and the rotational motion of the propeller on the added-mass and -damping matrices are compared based on different non-penetration boundary conditions and distributions of the inflow velocity. It is found that for hydroelastic analyses of propellers, the reduced frequency, i.e., the ratio of excitation frequency to rotational frequency, is a key parameter for determining the added-mass and -damping matrices of the propellers. The effect of the advance ratio on the added-mass and -damping matrices of the propeller blade depends upon the ratio of excitation frequency to rotational frequency. For hydrofoils, the added-damping matrix is significantly affected by the ratio of the excitation frequency multiplied by chord length and divided by axial inflow velocity.

Numerical analysis of violent hydroelastic problems based on a mixed MPS-mode superposition method

The traditional potential-flow-based hydroelasticity computation is unable to directly simulate the violent free surface deformation and slamming, and has a lack of mutual interactions between rigid-body and flexible motion parts. In this paper, the modified MPS (Moving Particle Semi-implicit) and modal superposition methods are used for the time-domain hydroelasticity computation of cylindrical shell and non-uniform beam structures involving violent free surface deformation and slamming. The improved modal superposition technique is revisited and extended to derive the time-domain governing equations for flexible shell and non-uniform beam motions, which couples rigid-body and flexible modes and considers the mutual interaction between them. The modified MPS method developed by the authors previously is first validated by the rigid cylinder water problem, and then the flexible cylindrical shell water entry and ship hull structure slamming are simulated. Relatively good agreement has been obtained between current results and the available numerical and experimental data, which shows the feasibility of the proposed model for the hydroelasticity computation involving violent free surface deformation.

Hydroelastic response of three-layered beam resting on winkler foundation

The hydroelastic oscillations problem of the sandwich beam resting on elastic foundation and interacting with the pulsating fluid layer was investigated. The three-layered beam with an incompressible lightweight filler was considered. The broken normal hypothesis for the three-layered beam and the model of viscous incompressible fluid, as well as Winkler model for elastic foundation, was chosen to study hyroelastic problem. A mathematical model of the considered mechanical system consists of dynamic equations of the three-layered beam with incompressible lightweight filler and the Navier-Stokes equations with continuity equation for the pulsating viscous fluid layer. The no-slip conditions and pressure coincidence at the edges with the given pressure into edges cavities were selected as boundary ones. The plane problem of hydroelastic beam bending oscillations for the regime of steady harmonic ones were considered. The solution of the hydroelastic problem was carried out by the perturbations method using proposed small parameters of the hydroelastic problem. As a result, the laws of three-layered beam elastic deflections and the hydrodynamic parameters of pulsating viscous fluid layer were obtained.

Computer simulating the forced vibrations of structure elements interacting with liquid under harmonic, impulse and seismic excitations

The method for simulating forced vibrations of structure elements, which interact with water medium during service is developed. Harmonic, impulse and seismic loadings are accounted for. It is assumed that the fluid surrounding the structure element is an ideal and incompressible one, and its movement caused by the vibrations of the element in question is vortex-free. Therefore the velocity potential that satisfies the Laplace equation exists. To determine the fluid pressure on the surfaces contacting with the liquid the Cauchy-Lagrange integral is used. The velocity potential is determined by solving the Neumann boundary value problem for the Laplace equation on an open surface. The potential of the double layer is used as an integral representation. This potential satisfies the Laplace equation and the conditions for vanishing velocity at infinity. The non-penetration condition leads to the necessity of solving the hypersingular integral equation for the pressure drop. To solve the boundary value problem of hydroelasticity the method of given forms is applied. The unknown displacements and potential are represented as series with unknown coefficients. The basic functions in these series are the modes of vibrations of the element without liquid. The frequencies of the structure element vibrations in fluid are evaluated taking the added masses into account. For simulating forced vibrations the system of second order differential equations relatively to the unknown time-dependent coefficients is obtained. The vibrations of a rigidly clamped square plate are examined as an example. The behavior of the maximum stress intensity is analyzed in dependence with the loading parameters. The estimations for critical values of load parameters are provided.

Liquid Induced Vibrations of Truncated Elastic Conical Shells with Elastic and Rigid Bottoms

A method of estimating natural modes and frequencies of vibrations for elastic shells of revolution conveying a liquid is proposed. The vibration modes of the liquid-filled elastic shells are presented as linear combinations of their own vibration modes without liquid. The explicit expression for fluid pressure is defined using Bernoulli’s integral and potential theory suppositions. Non-penetration, kinematic, and dynamic boundary conditions are applied at the shell walls and on a free liquid surface, respectively. The solution of the hydro-elasticity problem is found out using an effective technique based on coupled finite and boundary element methods. Computational vibration analysis of elastic truncated conical shells with different fixation conditions is accomplished. Sloshing and elastic walls frequencies and modes of liquid-filled truncated conical tanks are estimated. Both rigid and elastic bottoms of shells are considered. Some examples of numerical estimations are provided to testify the efficiency of the developed method

Fully coupled time domain solution for hydroelastic analysis of a floating body

A numerical method is developed to study the ship hydroelasticity problem in time domain. Boundary – Element Method (BEM) with three-dimensional transient free-surface Green function and Neumann – Kelvin approximation is used for the solution of the hydrodynamic part. The structural domain is modeled by finite element method (FEM) using 1D beam element in time domain. The coupling between BEM and FEM is made through body boundary condition in the hydrodynamic solution. Furthermore, direct integration scheme, i.e. Newmark –β method is used for obtaining the structural velocity and deformation. The efficiency and robustness of the proposed method are validated with available published results. Three different barge type structures and a large container ship are taken for the analysis. A good correspondence is observed between the proposed and reported numerical and experimental results. Also, it is observed that structural flexibility plays an important role while calculating structural deflection, shear force, bending moment etc. The developed numerical method seems to be robust, efficient and a very useful tool in predicting the hydrodynamic loads, structural deflections, shears force, bending moment etc. for flexible structure.

Vibrations of Elastic Shells of Revolution Partially Filled with Ideal Liquid

We propose an algorithm for the numerical analyses of vibrations of elastic shells of revolution partially filled with ideal incompressible liquids. In the solution of this problem, the wave motions of liquid on its free surface are taken into account. The solution of the problem of hydroelasticity is based on the application of the method of decomposition of the domain of integration of equations of the theory of shells with the use of the variational statement of the problem and on the approximate construction of the operator inverse to the operator of the hydrodynamic part of the problem. We construct a generalized functional of displacements of the shell for which the role of conditions of matching for the solutions in different subdomains is played by the natural boundary conditions. The obtained numerical results are compared with the existing exact solutions of the analyzed problem for a shell in the form of a straight circular cylinder.

Mathematical Modeling of Hydroelastic Oscillations of the Stamp and the Plate, Resting on Pasternak Foundation

The forced oscillations of the elastic fixed stamp and the plate, resting on Pasternak foundation are studied. The oscillations are caused by pressure pulsation in liquid layer between the stamp and the plate. Pasternak model is chosen as an elastic foundation. The laws of the stamp movement, the plate deflection and pressure in the liquid are discovered on the basis of hydroelasticity problem analytical solution. The functions of amplitude deflection distribution and liquid pressure along the plate are constructed, as well as the stamp amplitude-frequency characteristic. The obtained mathematical model allows to investigate the dynamics of hydroelastic interaction of the stamp with the plate, resting on elastic foundation, to define resonance frequencies of the plate and the stamp and corresponding deflections amplitudes, as well as liquid presser amplitudes.

Hydroelastic Oscillations of a Circular Plate, Resting on Winkler Foundation

The forced hydroelastic oscillations of a circular plate resting on elastic foundation are investigated. The oscillations are caused by a stamp vibration under interaction with a plate through a thin layer of viscous incompressible liquid. The axis-symmetric problem for the regime of the steady-state harmonic oscillations is considered. On the basis of hydroelasticity problem solution the laws of plate deflection and pressure in the liquid are found. The functions of the amplitudes deflection distribution and liquid pressure along the plate are constructed. The presented mathematical model provides for investigating viscous liquid layer interaction dynamics with a circular plate resting on an elastic foundation. The above-mentioned model makes it possible to define the plate oscillations resonance frequencies and the corresponding amplitudes of deflection and liquid pressure, as well.

Periodic traveling interfacial hydroelastic waves with or without mass

We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of spatially periodic traveling waves on infinite depth. Our traveling wave formulation uses a parameterized curve, in which the waves are able to have multi-valued height. This formulation and the presence of the elastic bending terms allows for the application of an abstract global bifurcation theorem of "identity plus compact" type. We furthermore perform numerical computations of these families of traveling waves, finding that, depending on the choice of parameters, the curves of traveling waves can either be unbounded, reconnect to trivial solutions, or end with a wave which has a self-intersection. Our analytical and computational methods are able to treat in a unified way the cases of positive or zero mass density along the sheet, the cases of single-valued or multi-valued height, and the cases of single-fluid or interfacial waves.

Wave motion in a fluid under an inhomogeneous ice cover

This paper studies steady waves in fluid and in semi-infinite ice cover generated by a constant pressure distribution with a rectangular planform moving uniformly along the edge of ice cover at fixed distance. This load simulates the air-cushion vehicle (ACV). We consider two cases: (i) the surface of fluid is free outside of ice sheet, (ii) fluid is bounded by a solid vertical wall and the edge of ice cover can be either clamped or free. The fluid is assumed to be ideal incompressible and of finite depth. The ice sheet is modelled by elastic thin plate. The solution of linear hydroelastic problem is obtained by two methods: the Wiener-Hopf technique and matched eigenfunction expansions. The deflection of ice sheet and free surface elevation, as well as wave forces acting on ACV are investigated for different speeds of motion.

Scattering of flexural–gravity waves by a group of elastic plates floating on a stratified fluid

A hydroelastic problem of flexural–gravity wave scattering by a demarcation between two floating elastic plates is investigated within the frame of linear potential-flow theory, where the method of matched eigenfunction expansions is employed for analysis. The formulations are subsequently generalized to the case of multiple elastic plates on a stratified fluid with multiple layers, which is helpful to the study of the hydrodynamic behaviors of inhomogeneous floating covers as well as the effects of density stratification in seawater. The eigenfunction expansions are numerically calculated by an inner product technique, in which an orthogonal definition involving an explicit differential term exhibits the effectiveness in dealing with the multi-layer matching relations between adjacent regions covered by different elastic plates. By use of Green’s theorem, an energy conversation relation is deduced to assure the convergence of the calculation. The high converging rates are exhibited afterwards. The correctness of numerical results are also verified by comparing with a previous analytical method. The details of the hydrodynamic responses of the generalized extension, especially the impact of the fluid stratification on the inner forces of the elastic plates, are discussed for different situations.

Hydroelastic oscillation of a plate resting on Pasternak foundation

The bending oscillations of the plate, resting in Pasternak foundation and interacting with a vibrating stamp through a thin layer of viscous incompressible liquid, are investigated. On the basis of hydroelasticity problem solution, the laws of the plate deflections and pressure in the liquid are found. The functions of the deflections amplitude distribution and liquid pressure along the channel are constructed. The obtained results allow to define oscillations resonance frequencies and to study viscous liquid interaction with elastic plates, resting on Pasternak foundation.

The negative-differential-resistance (NDR) mechanism of a hydroelastic microfluidic oscillator

A microfluidic oscillator is of interest because it converts a stable laminar flow to oscillatory flow, especially in view of the fact that turbulence is typically absent in miniaturized fluidic devices. One important design approach is to utilize hydroelastic effect-induced autonomous oscillations to modify the flow, so to reduce the reliance on external controllers. However, as complex fluid-structure interactions are involved, the prediction of its mechanism is rather challenging. Here, we present a simple equivalent circuit model and investigate the negative-differential-resistance (NDR) mechanism of a hydroelastic microfluidic oscillator. We show that a variety of complex flow behaviors including the onset of oscillation, formation of different oscillation patterns, collapse of the channel, etc can be well explained by this model. It provides a generic approach for construction of microfluidic NDR oscillators, following which a new design is also proposed. Relevant findings give more insights into the hydroelastic instability problems in microfluidics, and enrich the study of microfluidic flow control devices based on the electric circuit theory.

Hydroelasticity of a 3D floating body using a semi analytic approach in time domain

A semi analytic three dimensional time domain method is developed to predict the hydroelastic effect due to wave induced loads on a floating body. An Euler–Bernoulli beam with analytically defined mode shapes is taken into consideration to represent the structural response. The hydrodynamic forces are obtained in time domain through impulse response function, and the Duhamel integral is employed in order to get the structural deflections; velocity etc. The hydrodynamic and structural part is then fully coupled in time domain through modal analysis for the solution of the hydroelastic problem. A rectangular barge with zero forward speed is taken for analysis. To check the effect of structural stiffness in force and moment calculations, structural responses, shear forces and bending moments are calculated for different stiffness factors. It is seen that structural flexibility plays an important role for calculations of shear force and bending moment. For validation, the computed results have been compared with other published and available results obtained by different numerical methods and satisfactory agreement is found. The present semi analytic technique appears to be time efficient, robust and could be a very useful tool in predicting the hydroelastic effects in shear force, bending moment, structural deflection at initial design stage.