Long-wave dispersion phenomena in a layer subject to elastically restrained boundary conditions

2011 ◽  
Vol 63 (1) ◽  
pp. 171-188 ◽  
Author(s):  
R. R. Mukhomodyarov ◽  
G. A. Rogerson
Keyword(s):  
Boundary Conditions ◽  
Wave Dispersion ◽  
Long Wave ◽  
Elastically Restrained

scholarly journals Buckling Of The Stiffened Flange Of The Thin-Walled Member At Longitudinal Stress Variation

2015 ◽  
Vol 61 (3) ◽  
pp. 149-168
Author(s):  
A. Szychowski
Keyword(s):  
Boundary Conditions ◽  
Free Edge ◽  
Cantilever Plate ◽  
Longitudinal Stress ◽  
Stress Variation ◽  
Buckling Modes ◽  
Load Distributions ◽  
Edge Stiffener ◽  
Thin Walled ◽  
Elastically Restrained

AbstractBuckling of the stiffened flange of a thin-walled member is reduced to the buckling analysis of the cantilever plate, elastically restrained against rotation, with the free edge stiffener, which is susceptible to deflection. Longitudinal stress variation is taken into account using a linear function and a 2nd degree parabola. Deflection functions for the plate and the stiffener, adopted in the study, made it possible to model boundary conditions and different buckling modes at the occurrence of longitudinal stress variation. Graphs of buckling coefficients are determined for different load distributions as a function of the elastic restraint coefficient and geometric details of the stiffener. Exemplary buckling modes are presented.

Effects of inertia and stratification in incompressible ideal fluids: pressure imbalances by rigid confinement

2013 ◽  
Vol 726 ◽  
pp. 404-438 ◽  
Author(s):  
R. Camassa ◽  
S. Chen ◽  
G. Falqui ◽  
G. Ortenzi ◽  
M. Pedroni
Keyword(s):  
Euler Equations ◽  
Initial Conditions ◽  
Numerical Algorithms ◽  
Wave Dispersion ◽  
Variable Density ◽  
Density Variation ◽  
Fluid Inertia ◽  
Time Dynamics ◽  
Long Wave ◽  
Set Up

AbstractConsequences of density stratification are studied for an ideal (Euler) incompressible fluid, confined to move under gravity between rigid lids but otherwise free to move along horizontal directions. Initial conditions that generate horizontal pressure imbalances in a laterally unbounded domain are examined. The aim is to show analytically the existence of classes of initial data for which total horizontal momentum evolves in time, even though only vertical forces act on the fluid in this set-up. A simple class of such initial conditions, leading to momentum evolution, is identified by systematic asymptotic expansions of the governing inhomogeneous Euler equations in the small-density-variation limit. These results for Euler equations are compared and confirmed with long-wave asymptotic models, which can handle arbitrary density variations and provide closed-form mathematical expressions for limiting cases. In particular, the role of wave dispersion arising from the fluid inertia is captured by the long-wave models, even for short-time dynamics emanating from initial conditions outside the models’ asymptotic range of validity. These results are compared with direct numerical simulations for variable-density Euler fluids, which further validate the numerical algorithms and the analysis.

Effect of an elastically restrained boundary on SV-wave radiation patterns

1968 ◽  
Vol 58 (2) ◽  
pp. 497-520
Author(s):  
Y. T. Huang
Keyword(s):  
Boundary Condition ◽  
Wave Propagation ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Elastic Wave ◽  
Solid Earth ◽  
Elastic Constants ◽  
Wave Radiation ◽  
Free Boundary Conditions ◽  
Elastically Restrained

Abstract In the solution of elastic wave propagation equations applied to solid earth, it is customarily assumed that free boundary conditions are satisfied at a surface which is in contact with the atmosphere. Situations which depart from this boundary condition have now been studied for arbitrary combinations of the Lamé elastic constants. The solutions are given for a homogeneous, isotropic half space.

A model study of elastic waves in a layered sphere

1967 ◽  
Vol 57 (5) ◽  
pp. 959-981
Author(s):  
Victor Gregson
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Elastic Waves ◽  
Wave Dispersion ◽  
Flat Space ◽  
Dispersion Curves ◽  
Body Waves ◽  
Surface Wave Dispersion ◽  
Steel Sphere ◽  
Long Wave

abstract Elastic waves produced by an impact were recorded at the surface of a solid 12.0 inch diameter steel sphere coated with a 0.3 inch copper layer. Conventional modeling techniques employing both compressional and shear piezoelectric transducers were used to record elastic waves for one millisecond at various points around the great circle of the sphere. Body, PL, and surface waves were observed. Density, layer thickness, compressional and shear-wave velocities were measured so that accurate surface-wave dispersion curves could be computed. Surface-wave dispersion was measured as well as computed. Measured PL mode dispersion compared favorably with theoretical computations. In addition, dispersion curves for Rayleigh, Stoneley, and Love modes were computed. Measured surface-wave dispersion showed Rayleigh and Love modes were observed but not Stoneley modes. Measured dispersion compared favorably with theoretical computations. The curvature correction applied to dispersion calculations in a flat space has been estimated to correct dispersion values at long-wave lengths to about one per cent of correct dispersion in a spherical model. Measured dispersion compared with such flat space dispersion corrected for curvature proved accurate within one per cent at long wave lengths. Two sets of surface waves were observed. One set was associated with body waves radiating outward from impact. The other set was associated with body waves reflecting at the pole opposite impact. For each set of surface waves, measured dispersion compared favorably with computed dispersion.

scholarly journals An Exact Series Solution for the Vibration of Mindlin Rectangular Plates with Elastically Restrained Edges

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Xue Kai ◽  
Wang Jiufa ◽  
Li Qiuhong ◽  
Wang Weiyuan ◽  
Wang Ping
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Cross Sectional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
The Matrix ◽  
Elastically Restrained Edges ◽  
Elastically Restrained

An analysis method is proposed for the vibration analysis of the Mindlin rectangular plates with general elastically restrained edges, in which the vibration displacements and the cross-sectional rotations of the mid-plane are expressed as the linear combination of a double Fourier cosine series and four one-dimensional Fourier series. The use of these supplementary functions is to solve the possible discontinuities with first derivatives at each edge. So this method can be applied to get the exact solution for vibration of plates with general elastic boundary conditions. The matrix eigenvalue equation which is equivalent to governing differential equations of the plate can be derived through using the boundary conditions and the governing equations based on Mindlin plate theory. The natural frequencies can be got through solving the matrix equation. Finally the numerical results are presented to validate the accuracy of the method.

Comments on the use of the Korteweg-de Vries equation in the study of anharmonic lattices

1974 ◽  
Vol 339 (1616) ◽  
pp. 119-126 ◽  
Keyword(s):  
Differential Equation ◽  
Lattice Dynamics ◽  
Continuum Limit ◽  
Vries Equation ◽  
Wave Dispersion ◽  
Order Partial Differential Equation ◽  
Lennard Jones ◽  
Long Wave ◽  
De Vries ◽  
The Continuum

The use of the Korteweg-de Vries equation as the continuum limit of the equations describing the anharmonic motion of atoms in a lattice is examined in the light of the periodic solutions recently constructed by Askar (1973). It is shown that the Korteweg-de Vries equation does not exactly represent the behaviour of the nonlinear lattice in the limit of long waves and that a sixth-order partial differential equation gives a more accurate description of the lattice dynamics. The relative accuracies of two long wave dispersion relations derived from the Korteweg-de Vries equation are discussed and numerical results are presented for Morse, Born-Meyer and Lennard-Jones potentials. Askar’s paper contains several misprints and errors and the corrected forms of his equations are presented in the appendix.

Swash zone boundary conditions for long-wave models

2005 ◽  
Vol 52 (10-11) ◽  
pp. 971-976 ◽  
Author(s):  
Giorgio Bellotti ◽  
Maurizio Brocchini
Keyword(s):  
Boundary Conditions ◽  
Swash Zone ◽  
Zone Boundary ◽  
Long Wave ◽  
Wave Models

Vibrations and Power Flows in a Coupled Beam System

2007 ◽  
Vol 129 (5) ◽  
pp. 616-622 ◽  
Author(s):  
Wen L. Li ◽  
Murilo W. Bonilha ◽  
Jie Xiao
Keyword(s):  
Boundary Conditions ◽  
Analytical Method ◽  
Power Flow ◽  
Practical Interest ◽  
Current Method ◽  
Beam System ◽  
The Subject ◽  
Coupled Beams ◽  
Elastically Restrained ◽  
Excellent Accuracy

Vibrations of and power flow between coupled beams have been the subject of many investigations, and various techniques have been developed over the years. However, most of the existing methods will require a certain level of modifications or adaptations to account for the variations in the coupling and∕or boundary conditions. In this study, a general analytical method is developed for predicting the vibrations of and power flow between two-coupled beams. The coupling between the beams is generically represented by two (translational and rotational) springs of arbitrary stiffnesses. Thus, many rigid and nonrigid connectors of practical interest can be directly taken into account. In addition, because the beams are elastically restrained at each end, the current method can be universally applied to different boundary conditions by simply varying the stiffnesses of the boundary springs. Numerical results are presented to show the excellent accuracy of the proposed approach.

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