Effect of Embedding Medium Viscoelasticity on the Transient Response to Plane Waves of Arbitrarily Thick Circular Cylinders

1967 ◽  
Vol 34 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Jacques Crouzet-Pascal ◽  
Hyman Garnet ◽  
Allan Pifko
Keyword(s):  
Transient Response ◽  
Surrounding Medium ◽  
Plane Waves ◽  
Time History ◽  
Circular Cylinders ◽  
Method Of Solution ◽  
Unstrained State ◽  
Embedding Medium ◽  
State Of Rest ◽  
Incident Waves

The transient response of a circular cylinder of arbitrary thickness, embedded in a viscoelastic medium and impinged upon by plane waves, is obtained. Dilatational and shear incident waves are considered. The solution is valid within the scope of the linear theories of elasticity and viscoelasticity. The method of solution, which circumvents the difficulties encountered in the customary transform approaches, relies upon (a) the construction of a train of incident pulses from steady-state components, where each pulse represents the time history of the transient stress in the incident wave and (b) the existence of a physical mechanism that, between pulses, restores the disturbed particles of the cylinder and the surrounding medium to an unstrained state of rest. The influence on the major stress and displacement response of variations in the viscoelastic properties of the medium is investigated for the case of incident step waves. The results for the viscoelastic media are compared with corresponding results for the limiting cases of elastic-unrelaxed and elastic-relaxed media.

Transient Response of a Circular Cylinder of Arbitrary Thickness, in an Elastic Medium, to a Plane Dilatational Wave

1966 ◽  
Vol 33 (3) ◽  
pp. 521-531 ◽  
Author(s):  
Hyman Garnet ◽  
Jacques Crouzet-Pascal
Keyword(s):  
Elastic Medium ◽  
Incident Wave ◽  
Surrounding Medium ◽  
Time History ◽  
Theory Of Elasticity ◽  
Published Data ◽  
Arbitrary Thickness ◽  
Unstrained State ◽  
History Of ◽  
State Of Rest

The response of a hollow cylinder of arbitrary thickness, embedded in an elastic medium, to a transient plane pressure wave is presented. The solution is valid within the scope of the linear theory of elasticity. The technique for obtaining the solutions relies upon (a) the construction of a train of incident pulses from steady-state components, where each pulse represents the time history of the transient stress in the incident wave, and (b) the existence of a physical mechanism which, between pulses, restores the disturbed particles of the cylinder and the surrounding medium to an unstrained state of rest. The validity of the technique is demonstrated by (a) comparisons with published data for limiting cases and (b) results obtained for a broad range of values of cylinder and surrounding medium parameters. The influence on the cylinder response of liner thickness and cylinder-medium impedance mismatch, when the incident wave is a step pulse, is investigated.

Stationary and Transient Response of Cylindrical Shells Under Random Excitation

1988 ◽  
Vol 110 (2) ◽  
pp. 205-209
Author(s):  
A. V. Singh
Keyword(s):  
Transient Response ◽  
Random Vibration ◽  
Time History ◽  
Wide Band ◽  
Random Excitation ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
History Of ◽  
The Mean ◽  
Random Vibration Analysis

This paper presents the random vibration analysis of a simply supported cylindrical shell under a ring load which is uniform around the circumference. The time history of the excitation is assumed to be a stationary wide-band random process. The finite element method and the condition of symmetry along the length of the cylinder are used to calculate the natural frequencies and associated mode shapes. Maximum values of the mean square displacements and velocities occur at the point of application of the load. It is seen that the transient response of the shell under wide band stationary excitation is nonstationary in the initial stages and approaches the stationary solution for large value of time.

Transient Interaction of a Circular Plate and a Fluid Medium

1979 ◽  
Vol 46 (1) ◽  
pp. 26-30 ◽  
Author(s):  
J. W. Berglund
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Fluid Medium ◽  
Fluid Field ◽  
Elastic Circular Plate ◽  
Unstrained State ◽  
State Of Rest ◽  
Acoustic Fluid

The transient dynamic response of an elastic circular plate subjected to a suddenly applied pressure is determined for several edge boundary conditions. The plate boundary is attached to a semi-infinite, radially rigid tube which is filled with an acoustic fluid, and pressure is applied to the in-vacuo side of the plate. The transient solution is determined by using a technique in which the plate is subjected to a periodic pressure function constructed of appropriately signed and time-shifted Heaviside step functions, and by relying on a physical mechanism which returns the plate and fluid near the plate to an unstrained state of rest between pulses. The plate response is presented for a number of radius-to-thickness ratios and edge boundary conditions when interacting with water. Comparisons are also made with solutions obtained using a plane wave approximation to the fluid field.

Large amplitude waves in bounded media I. Reflexion and transmission of large amplitude shockless pulses at an interface

1973 ◽  
Vol 273 (1234) ◽  
pp. 261-313 ◽  
Keyword(s):  
Large Amplitude ◽  
Sea Water ◽  
Surrounding Medium ◽  
Interface Energy ◽  
Elastic Materials ◽  
Stress Strain ◽  
Single Interface ◽  
Isentropic Flow ◽  
Curve Fit ◽  
Unstrained State

Techniques which can be used to analyse the interaction of large amplitude elastic waves in a bounded medium are described. Although presented in the context of uniaxial stretching deformations in an elastic string or bar, these techniques can be used to analyse the behaviour of any system whose response is described by the nonlinear one-dimensional wave equation. In this first paper the bounded medium is contained between two parallel planes which separate it from other similar media. These are of semi-infinite extent along the axis of propagation which is normal to the interfaces. The paper is in two parts. In the first part the reflexion and transmission of an incident pulse when it arrives at an interface with a semi-infinite medium is described and the ideas of nonlinear impedance, reflexion coefficient and transmission coefficient are introduced. The results are quite general: no special forms for the stress-strain relations of either elastic materials is assumed. The results for a single interface are used to analyse the decay of a pulse as it moves back and forth between two interfaces. This decay occurs because at each contact with the interface energy is radiated across the interface to the surrounding medium. The algorithm s obtained have simple graphical interpretations. The general theory is used to discuss the decay of a pulse in a layer of saturated soil which is bounded from above by sea water and from below by rock. This pulse is triggered by a seismic disturbance deep inside the rock. The theory is also used to analyse the decay in the oscillation which occurs in a shock tube w hen a diaphragm separating air at high pressure from air at atmospheric pressure is ruptured. The bound gas is contained between the closed end of the tube and the contact discontinuity which is generated w hen the diaphragm bursts. In the second part of the paper a more detailed account is given of what happens when a pulse is partially reflected and partially transmitted at an interface. This is achieved by noting that the responses of m any elastic materials can be correlated, both qualitatively and quantitatively, by a family of stress-strain laws for which the governing nonlinear equations for this problem can be solved exactly. These laws are sufficiently general to locally curve fit any prescribed stress-strain law to an error 0 ([stra in ]4) in some vicinity of the unstrained state. They can also be used to fit the response of a polytropic gas during isentropic flow to within an error of 1 % as the density changes by a factor of ten! The reflexion of a large amplitude pulse from rigid and perfectly free interfaces is given special emphasis as is the reflexion from an interface with a Hookean material.

FREQUENCY AND TRANSIENT RESPONSES OF ELECTROMAGNETIC FIELDS CREATED BY CURRENTS IN CONFINED CONDUCTORS

Geophysics ◽  
1978 ◽  
Vol 43 (5) ◽  
pp. 1002-1010 ◽  
Author(s):  
A. Kaufman
Keyword(s):  
Magnetic Field ◽  
Transient Response ◽  
Surrounding Medium ◽  
Low Frequency ◽  
Infinite Dimensions ◽  
Transient Responses ◽  
Inductive Methods ◽  
Conducting Bodies ◽  
The Relationship ◽  
The Magnetic Field

This paper considers the behavior of the frequency and transient responses of the magnetic field created by currents in conducting bodies. It is assumed that the surrounding medium is an insulator. The relationship between the low‐frequency part of the frequency spectrum and the late stage of the transient response depends on the type of conductor. These responses and the distribution of the spectrum poles differ for conductors having finite and infinite dimensions. The dependence of various components of the field on conductivity differs, which is important for understanding the resolving capabilities of the inductive methods.

TWO VERSIONS OF QUASI-NEWTON METHOD FOR MULTIDIMENSIONAL INVERSE SCATTERING PROBLEM

1993 ◽  
Vol 01 (02) ◽  
pp. 197-228 ◽  
Author(s):  
SEMION GUTMAN ◽  
MICHAEL KLIBANOV
Keyword(s):  
Newton Method ◽  
Inverse Scattering ◽  
Born Approximation ◽  
Scattering Problem ◽  
Plane Waves ◽  
Inverse Scattering Problem ◽  
Circular Cylinders ◽  
Iterative Sequence ◽  
Scattering Field ◽  
Quasi Newton

Suppose that a medium with slowly changing spatial properties is enclosed in a bounded 3-dimensional domain and is subjected to a scattering by plane waves of a fixed frequency. Let measurements of the wave scattering field induced by this medium be available in the region outside of this domain. We study how to extract the properties of the medium from the information contained in the measurements. We are concerned with the weak scattering case of the above inverse scattering problem (ISP), that is, the unknown. spatial variations of the medium are assumed to be close to a constant. Examples can be found in the studies of the wave propagation in oceans, in the atmosphere, and in some biological media. Since the problems are nonlinear, the methods for their linearization (the Born approximation) have been developed. However, such an approach often does not produce good results. In our method, the Born approximation is just the first iteration and further iterations improve the identification by an order of magnitude. The iterative sequence is defined in the framework of a Quasi-Newton method. Using the measurements of the scattering field from a carefully chosen set of directions we are able to recover (finitely many) Fourier coefficients of the sought parameters of the model. Numerical experiments for the scattering from coaxial circular cylinders as well as for simulated data are presented.

scholarly journals Exact Matrix Representation of the Transverse Magnetic Multiple Scattering of Obliquely Incident Plane Waves by the Diffraction Grating of Penetrable Cylinders

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Ömer Kavaklıoğlu ◽  
Roger Henry Lang
Keyword(s):  
Multiple Scattering ◽  
Diffraction Grating ◽  
Plane Waves ◽  
Transverse Magnetic ◽  
Circular Cylinders ◽  
Scattering Coefficients ◽  
Obliquely Incident ◽  
Incident Plane ◽  
Inversion Procedure ◽  
Exact Matrix

“An exact matrix conformation model” associated with the equations describing the exact behavior of the Fourier-Bessel multiple scattering coefficients of the diffraction grating consisting of an infinite number of infinitely long parallel penetrable circular cylinders, corresponding to the obliquely incident transverse-magnetic plane waves in “Twersky-Wait-Kavaklıoğlu representation,” originally excogitated in (Kavaklıoğlu, 2000), is acquired, and the exact solution for “the Fourier-Bessel multiple scattering coefficients of the diffraction grating at oblique incidence” is obtained by a matrix inversion procedure.

Exact Transient Response of an Elastic Half Space Loaded Over a Rectangular Region of Its Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 516-522 ◽  
Author(s):  
F. R. Norwood
Keyword(s):  
Half Space ◽  
Real Axis ◽  
Transient Response ◽  
Plane Waves ◽  
Elastic Half Space ◽  
Impulsive Loading ◽  
Rectangular Region ◽  
The Real ◽  
Algebraic Expressions ◽  
Straight Lines

The response of an elastic half space to a normal impulsive loading over one half and also over one quarter of its bounding surface is considered. By a simple superposition the solution is obtained for a half space loaded on a finite rectangular region. In each case the solution was found to be a superposition of plane waves directly under the load, plus waves emanating from bounding straight lines and the corners of the loaded region. The solution was found by Cagniard’s technique and by extending the real transformation of de Hoop to double Fourier integrals with singularities on the real axis of the transform variables. Velocities in the interior of the half space are given for arbitrary values of Poisson’s ratio in terms of single integrals and algebraic expressions.

Transient Response of a Rigid Spherical Inclusion in an Elastic Medium

1965 ◽  
Vol 32 (3) ◽  
pp. 637-642 ◽  
Author(s):  
C. C. Mow
Keyword(s):  
Exact Solution ◽  
Elastic Medium ◽  
Transient Response ◽  
Integral Method ◽  
Spherical Inclusion ◽  
Time History ◽  
Fourier Integral ◽  
Incident Pulse ◽  
History Of

The transient response of a rigid spherical inclusion of arbitrary density embedded in an elastic medium owing to an incident pulse is examined in this paper. The Fourier-integral method is used, and an exact solution of the response is obtained. It is found that the acceleration and velocity of the inclusion are substantially different from those of the medium. A slight difference in the time history of the displacement between the inclusion and the medium is also noted.

Effect of Reynolds Number on Local Scour Around a Monopile in Steady Current

2019 ◽  
Author(s):  
Xiaofan Lou ◽  
Kaibing Zhang ◽  
Zhenhong Chen
Keyword(s):  
Reynolds Number ◽  
Time Scale ◽  
Time History ◽  
Local Scour ◽  
Circular Cylinders ◽  
Scour Depth ◽  
Clear Water ◽  
Number Range ◽  
Steady Current ◽  
Equilibrium Scour Depth

Abstract The effect of Reynolds number (Re) on the local scour around a monopile encountering steady current was investigated experimentally in a water flume. The experiment was performed using circular cylinders with different diameters under two different freestream velocities, covering both clear-water and live-bed scours and a Reynolds number range of approximately 9,000–60,000. The time-series of the scour depth was recorded during the whole scour process and the scour pit was scanned after the scour process reached equilibrium. Results are presented in terms of the equilibrium scour depth, the time-scale of the scour process and the three-dimensional scour profile at different Reynolds numbers. For both clear-water and live-bed scours, the time history of the scour process indicate that the time-scale becomes larger as Re increases. It is also found that the normalized equilibrium scour depth, as well as the normalized scour radius, decrease with the increasing Re. An empirical equation of the equilibrium scour depth is derived as a function of Reynolds number based on the experimental results so as to better account for Re effect in the scour design.

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