scholarly journals Flow-induced Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Finite Depth

2019 ◽  
Vol 66 (3-4) ◽  
pp. 101-130
Author(s):  
Kazimierz Szmidt ◽  
Benedykt Hedzielski
Keyword(s):  
Boundary Conditions ◽  
Water Waves ◽  
Fluid Pressure ◽  
Plate Motion ◽  
Thin Elastic Plate ◽  
Infinite Domain ◽  
Elastic Band ◽  
Pressure Load ◽  
Coupled Problem ◽  
Starting Point

AbstractThe paper deals with forced vibrations of a horizontal thin elastic plate submerged in a semi-infinite layer of fluid of constant depth. The pressure load on this plate is induced by water waves arriving at the plate. This load is accompanied by pressure resulting from the motion of the plate. The plate and fluid motions depend on boundary conditions, and, in particular, the pressure load depends on the width of the gap between the plate and the bottom. In theoretical description of the phenomenon, we deal with a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surfaces. The main attention is focused on transient solutions of the problem, which correspond to fluid (and plate) motion starting from rest. In formulation of this problem, a linear theory of small deflections of the plate is employed. In order to calculate the fluid pressure, a solution of Laplace’s equation is constructed in a doubly connected fluid domain. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in the finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of boundary conditions of the coupled problem considered, the fluid domain is divided into sub-domains of simple geometry, and the solutions of the problem equations are constructed separately in each of these domains. Numerical experiments have been conducted to illustrate the formulation developed in this paper.

scholarly journals Vibrations of a Horizontal Elastic Band Plate Submerged in Fluid of Constant Depth

2016 ◽  
Vol 63 (2-3) ◽  
pp. 191-213
Author(s):  
Kazimierz Szmidt ◽  
Benedykt Hedzielski
Keyword(s):  
Water Waves ◽  
Fluid Pressure ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Thin Elastic Plate ◽  
Constant Depth ◽  
Infinite Domain ◽  
Elastic Band ◽  
Infinite Layer ◽  
Pressure Load

AbstractThe paper deals with free and forced vibrations of a horizontal thin elastic plate submerged in an infinite layer of fluid of constant depth. In free vibrations, the pressure load on the plate results from assumed displacements of the plate. In forced vibrations, the fluid pressure is mainly induced by water waves arriving at the plate. In both cases, we have a coupled problem of hydrodynamics in which the plate and fluid motions are coupled through boundary conditions at the plate surface. At the same time, the pressure load on the plate depends on the gap between the plate and the fluid bottom. The motion of the plate is accompanied by the fluid motion. This leads to the so-called co-vibrating mass of fluid, which strongly changes the eigenfrequencies of the plate. In formulation of this problem, a linear theory of small deflections of the plate is employed. In order to calculate the fluid pressure, a solution of Laplace’s equation is constructed in the doubly connected infinite fluid domain. To this end, this infinite domain is divided into sub-domains of simple geometry, and the solution of the problem equation is constructed separately for each of these domains. Numerical experiments are conducted to illustrate the formulation developed in this paper.

scholarly journals Nonlinear Interactions between Gravity Waves in Water of Constant Depth

2015 ◽  
Vol 62 (1-2) ◽  
pp. 3-25
Author(s):  
Kazimierz Szmidt ◽  
Benedykt Hedzielski
Keyword(s):  
Water Waves ◽  
Fluid Motion ◽  
Power Series Expansion ◽  
Nonlinear Boundary Conditions ◽  
Constant Depth ◽  
Infinite Domain ◽  
Starting Point ◽  
Transient Solutions ◽  
Nonlinear Character ◽  
Approximate Formulation

AbstractThe paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.

scholarly journals Transformation of Long Waves in a Canal of Variable Section

2016 ◽  
Vol 63 (1) ◽  
pp. 3-18
Author(s):  
Kazimierz Szmidt ◽  
Benedykt Hedzielski
Keyword(s):  
Water Waves ◽  
Fluid Motion ◽  
Finite Domain ◽  
Infinite Domain ◽  
Initial Value ◽  
One Dimensional ◽  
Starting Point ◽  
Transient Solutions ◽  
Variable Section ◽  
Laboratory Flume

Abstract The paper deals with long water waves propagating in a straight canal of constant depth and variable section. In the formulation of this problem, a simplified, one-dimensional model is considered that is based on the assumption of a “columnar” fluid motion. To this end, a system of material coordinates is employed as independent variables in the description of this phenomenon. The main attention is focused on transient solutions corresponding to a fluid motion starting from rest.With respect to the initial value problem considered,we confine our attention to a finite domain fluid motion induced by a piston-type generator placed at the beginning of the canal. For a finite elapse of time, measured from the starting point, the solution in the finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. The main goal of our investigations is to describe the evolution of the free surface (the wave height) at the smallest section of the canal. Numerical examples are provided to illustrate the model formulation developed in this paper. The accuracy of this approximate description is assessed by comparing its results with data obtained in hydraulic experiments performed in a laboratory flume.

scholarly journals From metaphors to equations: How can we find the good ones?

2000 ◽  
Vol 23 (3) ◽  
pp. 409-410
Author(s):  
Gottfried Mayer-Kress
Keyword(s):  
Boundary Conditions ◽  
Forest Fire ◽  
Water Waves ◽  
Standing Waves ◽  
Musical Instruments ◽  
Oscillator Model ◽  
Mechanical Oscillator ◽  
Target Article ◽  
Mechanical Oscillators

Among the metaphors used in the target article are “musical instruments,” “water waves,” and other types of mechanical oscillators. The corresponding equations have inertial properties and lead to standing waves that depend on boundary conditions. Other, physiologically relevant quantities like refractory times are not contained in the mechanical oscillator model but occur naturally, for instance, in biological forest fire metaphors.

ANOMALY FREE SUPERGRAVITY IN D=10: I) THE BIANCHI IDENTITIES AND THE BOSONIC LAGRANGIAN

1988 ◽  
Vol 03 (04) ◽  
pp. 953-1021 ◽  
Author(s):  
RICCARDO D’AURIA ◽  
PIETRO FRÉ ◽  
MARIO RACITI ◽  
FRANCO RIVA
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Variational Equation ◽  
Second Order ◽  
Effective Theory ◽  
Spin Connection ◽  
Bianchi Identities ◽  
First Order ◽  
Interaction Terms ◽  
Starting Point

Using a theorem by Bonora-Pasti and Tonin on the existence of a solution for D=10N=1 Bianchi identities in the presence of a Lorentz Chern Simons term, we find an explicit parametrization of the superspace curvatures. Our solution depends only on one free parameter which can be reabsorbed in a field redefinition of the dilaton and of the gravitello. We emphasize that the essential point which enables us to obtain a closed form for the curvature parametrizations and hence for the supersymmetry transformation rules is the use of first order formalism. The spin connection is known once the torsion is known. This latter, rather than being identified with Hµνρ as it is usually done in the literature, is related to it by a differential equation which reduces to the algebraic relation Hµνρ = - 3Tµνρ e4/3σ only at γ1=0 (γ1 being proportional to κ/g2). The solution of the Bianchi identities exhibited in this paper corresponds to a D=10 anomaly free supergravity (AFS). This theory is unique in first order formalism but corresponds to various theories in second order formalism. Indeed the torsion equation is a differential equation which, in order to be solved must be supplemented with boundary conditions. One wonders whether supplemented with a judicious choice of boundary conditions for the torsion equation, AFS yields all the interaction terms found in the effective theory of the heterotic string (ETHS). In this respect two remarks are in order. Firstly it appears that solving the torsion equation iteratively with Tµνρ = -1/3Hµνρ e-4/3σ as starting point all the terms of ETHS except those with a ζ(3) coefficient show up. (Whether the coefficient agree is still to be checked.) Secondly, as shown in this paper the rheonomic solution of the super Poincaré Bianchi identities is unique. Hence additional interaction terms can be added to the Lagrangian only by modifying the rheonomic parametrization of the [Formula: see text]-curvature. The only assumption made in our paper is that [Formula: see text] has at most ψ∧ψ∧V components (sector (1,2)). Correspondingly the only room left for a modification of the present theory is the addition of a (0, 3) part in the rheonomic parametrization of [Formula: see text]. When this work was already finished a conjecture was published by Lechner Pasti and Tonin that such a generalization of AFS might exist and be responsible for the ζ(3) missing term. Indeed if we were able to solve the [Formula: see text]-Bianchi with this new (0, 3)-part then the torsion equation would be modified via new terms which, in second order formalism, lead to additional gravitational interactions. The equation of motion of Anomaly Free Supergravity can be worked out from the Bianchi identities: we indicate through which steps. The corresponding Lagrangian could be constructed with the standard procedures of the rheonomy approach. In this paper we limit ourselves to the bosonic sector of such a Lagrangian and we show that it can indeed be constructed in such a way as to produce the relation between Hµνρ and Tµνρ as a variational equation.

Distribution of the preferred clothing pressure over the whole body

2018 ◽  
Vol 89 (11) ◽  
pp. 2187-2198 ◽  
Author(s):  
Tamaki Mitsuno ◽  
Ayaka Kai
Keyword(s):  
Nervous System ◽  
Autonomic Nervous System ◽  
Hydrostatic Pressure ◽  
Body Part ◽  
Whole Body ◽  
Elastic Band ◽  
Autonomic Nervous ◽  
Pressure Load ◽  
Calibration Methods ◽  
Clothing Pressure

A system for measuring clothing pressure employing a renewed hydrostatic pressure-balancing method was examined using three calibration methods. All methods revealed an almost perfectly linear Y = X relation for the pressure load (X) and the reading of the system (Y). In the application, the distributions of elastic band pressure were examined on 21 planes from head to foot. The preferred elastic band pressures of the leg and arm were significantly higher than those of the neck and abdomen. These results are due to the large presence of the autonomic nervous system at the surfaces of the neck and abdomen. In the area of the abdomen, the preferred elastic band pressure was higher from the mammilla to the shoulder than for the anteroposterior midlines. The development of compression ware must consider appropriate tightening for each body part.

scholarly journals SPH Simulation of Interior and Exterior Flow Field Characteristics of Porous Media

Water ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 918 ◽  
Author(s):  
Shijie Wu ◽  
Matteo Rubinato ◽  
Qinqin Gui
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Flow Field ◽  
Boundary Conditions ◽  
Water Waves ◽  
Flow Behavior ◽  
Simulation Method ◽  
Interface Problem ◽  
Ocean Engineering ◽  
Flow Field Characteristics

At the present time, one of the most relevant challenges in marine and ocean engineering and practice is the development of a mathematical modeling that can accurately replicate the interaction of water waves with porous coastal structures. Over the last 60 years, multiple techniques and solutions have been identified, from linearized solutions based on wave theories and constant friction coefficients to very sophisticated Eulerian or Lagrangian solvers of the Navier-Stokes (NS) equations. In order to explore the flow field interior and exterior of the porous media under different working conditions, the Smooth Particle Hydrodynamics (SPH) numerical simulation method was used to simulate the flow distribution inside and outside a porous media applied to interact with the wave propagation. The flow behavior is described avoiding Euler’s description of the interface problem between the Euler mesh and the material selected. Considering the velocity boundary conditions and the cyclical circulation boundary conditions at the junction of the porous media and the water flow, the SPH numerical simulation is used to analyze the flow field characteristics, as well as the longitudinal and vertical velocity distribution of the back vortex flow field and the law of eddy current motion. This study provides innovative insights on the mathematical modelling of the interaction between porous structures and flow propagation. Furthermore, there is a good agreement (within 10%) between the numerical results and the experimental ones collected for scenarios with porosity of 0.349 and 0.475, demonstrating that SPH can simulate the flow patterns of the porous media, the flow through the inner and outer areas of the porous media, and the flow field of the back vortex region. Results obtained and the new mathematical approach used can help to effectively simulate with high-precision the changes along the water depth, for a better design of marine and ocean engineering solutions adopted to protect coastal areas.

A new Boussinesq method for fully nonlinear waves from shallow to deep water

2002 ◽  
Vol 462 ◽  
pp. 1-30 ◽  
Author(s):  
P. A. MADSEN ◽  
H. B. BINGHAM ◽  
HUA LIU
Keyword(s):  
Laplace Equation ◽  
Infinite Series ◽  
Deep Water ◽  
Water Waves ◽  
Modulational Instability ◽  
Surface Boundary ◽  
Nonlinear Water Waves ◽  
Finite Series ◽  
Starting Point ◽  
Highly Nonlinear

A new method valid for highly dispersive and highly nonlinear water waves is presented. It combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain. The starting point is an exact solution to the Laplace equation given in terms of infinite series expansions from an arbitrary z-level. We replace the infinite series operators by finite series (Boussinesq-type) approximations involving up to fifth-derivative operators. The finite series are manipulated to incorporate Padé approximants providing the highest possible accuracy for a given number of terms. As a result, linear and nonlinear wave characteristics become very accurate up to wavenumbers as high as kh = 40, while the vertical variation of the velocity field becomes applicable for kh up to 12. These results represent a major improvement over existing Boussinesq-type formulations in the literature. A numerical model is developed in a single horizontal dimension and it is used to study phenomena such as solitary waves and their impact on vertical walls, modulational instability in deep water involving recurrence or frequency downshift, and shoaling of regular waves up to breaking in shallow water.

Numerical Simulation of Nonlinear Water Wave Propagation Over Rippled Bed

2007 ◽  
Author(s):  
Gerasimos A. Kolokythas ◽  
Athanassios A. Dimas
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Waves ◽  
Stokes Equations ◽  
Surface Flow ◽  
Surface Boundary ◽  
Computational Domain ◽  
Time Step ◽  
Outflow Boundary ◽  
Rippled Bed

In the present study, numerical simulations of the free-surface flow, developing by the propagation of nonlinear water waves over a rippled bottom, are performed assuming that the corresponding flow is two-dimensional, incompressible and viscous. The simulations are based on the numerical solution of the Navier-Stokes equations subject to the fully-nonlinear free-surface boundary conditions and the suitable bottom, inflow and outflow boundary conditions. The equations are properly transformed so that the computational domain becomes time-independent. For the spatial discretization, a hybrid scheme with finite-differences and Chebyshev polynomials is applied, while a fractional time-step scheme is used for the temporal discretization. A wave absorption zone is placed at the outflow region in order to efficiently minimize reflection of waves by the outflow boundary. The numerical model is validated by comparison to the analytical solution for the laminar, oscillatory, current flow which develops a uniform boundary layer over a horizontal bottom. For the propagation of finite-amplitude waves over a rigid rippled bed, the case with wavelength to water depth ratio λ/d0 = 6 and wave height to wavelength ratio H0/λ = 0.05 is considered. The ripples have parabolic shape, while their dimensions — length and height — are chosen accordingly to fit laboratory and field data. Results indicate that the wall shear stress over the ripples and the form drag forces on the ripples increase with increasing ripple height, while the corresponding friction force is insensitive to this increase. Therefore, the percentage of friction in the total drag force decreases with increasing ripple height.

scholarly journals 4D Travel-Time Tomography as a Tool for Tracking Fluid-Driven Medium Changes in Offshore Oil–Gas Exploitation Areas

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5878
Author(s):  
Grazia De Landro ◽  
Ortensia Amoroso ◽  
Guido Russo ◽  
Aldo Zollo
Keyword(s):  
Seismic Velocity ◽  
Fluid Pressure ◽  
Time Lapse ◽  
Velocity Model ◽  
Target Volume ◽  
Fluid Injection ◽  
Pressure Perturbation ◽  
Operational Conditions ◽  
Starting Point ◽  
Velocity Changes

The monitoring of rock volume where offshore exploitation activities take place is crucial to assess the corresponding seismic hazard. Fluid injection/extraction operations generate a pore fluid pressure perturbation into the volume hosting the reservoir which, in turn, may trigger new failures and induce changes in the elastic properties of rocks. Our purpose is to evaluate the feasibility of reconstructing pore pressure perturbation diffusion in the host medium by imaging the 4D velocity changes using active seismic. We simulated repeated active offshore surveys and imaged the target volume. We constructed the velocity model perturbed by the fluid injection using physical modeling and evaluated under which conditions the repeated surveys could image the velocity changes. We found that the induced pressure perturbation causes seismic velocity variations ranging between 2–5% and 15–20%, depending on the different injection conditions and medium properties. So, in most cases, time-lapse tomography is very efficient in tracking the perturbation. The noise level characterizing the recording station sites is a crucial parameter. Since we evaluated the feasibility of the proposed 4D imaging strategy under different realistic environmental and operational conditions, our results can be directly applied to set up and configure the acquisition layout of surveys aimed at retrieving fluid-induced medium changes in the hosting medium. Moreover, our results can be considered as a useful starting point to design the guidelines to monitor exploitation areas.

Sign in / Sign up

Export Citation Format

Share Document