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 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 Added Mass of Fluid and Fundamental Frequencies of a Horizontal Elastic Circular Plate Vibrating in Fluid of Constant Depth

2017 ◽  
Vol 64 (3-4) ◽  
pp. 163-186
Author(s):  
Kazimierz Szmidt ◽  
Benedykt Hedzielski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Fluid Motion ◽  
Added Mass ◽  
Free Vibrations ◽  
Constant Depth ◽  
Infinite Layer ◽  
Pressure Load ◽  
Fundamental Frequencies ◽  
Elastic Circular Plate

AbstractThe paper deals with free vibrations of a horizontal thin elastic circular plate submerged in an infinite layer of fluid of constant depth. The motion of the plate is accompanied by the fluid motion, and thus, the pressure load on this plate results from displacements of the plate in time. The plate and fluid motions depend on boundary conditions, and, in particular, the pressure load depends on the gap between the plate and the fluid bottom. In theoretical description of this 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. This coupling leads to the so-called co-vibrating (added) mass of fluid, which significantly changes the fundamental frequencies (eigenfrequencies) of the plate. In formulation of the problem, a linear theory of small deflections of the plate is employed. At the same time, one assumes the potential fluid motion with the potential function satisfying Laplace’s equation within the fluid domain and appropriate boundary conditions at fluid boundaries. In order to solve the problem, the infinite fluid domain is divided into sub-domains of simple geometry, and the solution of problem equations is constructed separately for each of these domains. Numerical experiments have been 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.

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.

Vibration of an Infinitely Extending Plate Resting on an Elastic Foundation

1963 ◽  
Vol 30 (3) ◽  
pp. 355-362 ◽  
Author(s):  
Kazuyosi Ono
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Infinite Number ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
The Other ◽  
Damped Oscillation

Free vibrations and forced vibrations of an infinitely extending plate resting on an elastic foundation and carrying a mass are solved. Then the amplitudes of the free vibrations produced by an impulse applied to the mass on the plate are determined, and it is found that two kinds of vibration are produced in the plate: One is a free vibration and the other is a special vibration, which consists of an infinite number of free vibrations and resembles a damped oscillation.

scholarly journals Far-Field Characteristics of Linear Water Waves Generated by a Submerged Landslide over a Flat Seabed

2020 ◽  
Vol 8 (3) ◽  
pp. 196
Author(s):  
Haixiao Jing ◽  
Yanyan Gao ◽  
Changgen Liu ◽  
Jingming Hou
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Water Waves ◽  
Wave Model ◽  
Linear Wave ◽  
Far Field ◽  
Constant Depth ◽  
Low Froude Number ◽  
Dispersive Model ◽  
Wave Models

Understanding the propagation of landslide-generated water waves is of great help against tsunami hazards. In order to investigate the effects of landslide shapes on the far-field leading wave generated by a submerged landslide at a constant depth, three linear wave models with different degrees of dispersive properties are employed in this study. The linear fully dispersive model is then validated by comparing the results against the experimental data available for landslides with a low Froude number. Three simplified shapes of landslides with the same volume, which are unnatural for a body of incoherent material, are used to investigate the effects of landslide shapes on the far-field properties of the generated leading wave over a flat seabed. The results show that the far-field leading crest over a constant depth is independent of the exact landslide shape and is invalid at a shallow water depth. Therefore, the most popular non-dispersive model (also called the shallow water wave model) cannot be used to reproduce the phenomenon. The weakly dispersive wave model can predict this phenomenon well. If only the leading wave is considered, this model is accurate up to at least μ = h0/Lc = 0.6, where h0 is the water depth and Lc denotes the characteristic length of the landslide.

The Effect of Viscosity on the Forced Vibrations of a Fluid-Filled Elastic Shell

1983 ◽  
Vol 50 (3) ◽  
pp. 517-524 ◽  
Author(s):  
T. C. Su
Keyword(s):  
Essential Feature ◽  
Elastic Shell ◽  
Energy Dissipation Rate ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
External Forcing ◽  
Fluid Loading ◽  
Response Curves ◽  
Frequency Spectra ◽  
Resonant Frequencies

The effect of viscosity on the axisymmetric, forced vibrations of a fluid-filled, elastic, spherical shell is studied analytically. Necessary theory, using boundary layer approximation for the fluid as developed in a previous paper for free vibrations, has been extended to incorporate an external forcing excitation. Shell response, fluid loading, and energy dissipation rate are computed for radial, tangential, and combined force excitations. The essential feature of the modal and the total responses is determined by resonant frequencies and various vibration-absorbing frequencies. Frequency spectra for such frequencies, as well as various response curves, are presented in dimensionless forms to illustrate the characteristics of the solution.

An Asymptotic Method to Analyze the Vibrations of an Elastic Layer

1969 ◽  
Vol 36 (1) ◽  
pp. 65-72 ◽  
Author(s):  
J. D. Achenbach
Keyword(s):  
Power Series ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Wave Number ◽  
Dimensionless Wave Number ◽  
Analogous Manner ◽  
Independent Variable ◽  
Thickness Variable

The displacement components for both free and forced vibrations are sought as power series of the dimensionless wave number ε, where ε = 2π × layer thickness/wavelength. For the free vibration problem the object is to determine the frequencies, which are also sought as power series of the dimensionless wave number. The displacement and frequency expansions are substituted in the displacement equations of motion and in the boundary conditions. By collecting terms of the same order εn, a system of second-order, inhomogeneous, ordinary differential equations of the Helmholtz type is obtained, with the thickness variable as independent variable, and with associated boundary conditions. For free vibrations, subsequent integration yields the coefficients of εn for the displacements and the frequencies for all modes, and in the whole range of frequencies, but in a range of dimensionless wave numbers 0 < ε < ε* < 1, where ε* increases as more terms are retained in the expansions. For forced vibrations, the amplitudes are determined in an analogous manner if the external surface tractions are of sinusoidal dependence on the in-plane coordinates and on time. The response to surface tractions of more general spatial dependence is obtained by Fourier superposition.

Forced Vibrations of Viscoelastic Timoshenko Beams

1976 ◽  
Vol 98 (3) ◽  
pp. 820-826 ◽  
Author(s):  
C. C. Huang ◽  
T. C. Huang
Keyword(s):  
Boundary Conditions ◽  
Laplace Transform ◽  
Attenuation Factor ◽  
Equations Of Motion ◽  
Bending Moment ◽  
Expansion Method ◽  
Free Vibrations ◽  
Forced Vibrations ◽  
Mode Shapes ◽  
Timoshenko Beams

In a previous paper, the correspondence principle has been applied to derive the differential equations of motion of viscoelastic Timoshenko beams with or without external viscous damping. To study free vibrations these equations are solved by Laplace transform and boundary conditions are applied to obtain the attenuation factor and the frequency of the damped free vibrations and mode shapes. The present paper continues to analyze this subject and deals with the responses in deflection, bending slope, bending moment and shear for forced vibrations. Laplace transform and appropriate boundary conditions have been applied. Examples are given and results are plotted. The solution of forced vibrations of elastic Timoshenko beams obtained as a result of reduction from viscoelastic case and by eigenfunction expansion method concludes the paper.

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