Enhanced grid scheme for one-dimensional integro-differential Volterra equation in the time domain

2002 ◽  
Vol 50 (4) ◽  
pp. 492-499
Author(s):  
I.V. Scherbatko ◽  
A.G. Nerukh ◽  
S. Iezekiel
Keyword(s):  
Time Domain ◽  
Volterra Equation ◽  
One Dimensional ◽  
Grid Scheme ◽  
The Time Domain

Vibrations of beams with a breathing crack and large amplitude displacements

2015 ◽  
Vol 230 (1) ◽  
pp. 34-54 ◽  
Author(s):  
Gonçalo Neves Carneiro ◽  
Pedro Ribeiro
Keyword(s):  
Time Domain ◽  
Equations Of Motion ◽  
Shape Functions ◽  
Breathing Crack ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Time Histories ◽  
Linear Effects ◽  
Fourier Spectra ◽  
The Time Domain

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

Wrap‐around removal from one‐dimensional synthetic seismograms

Geophysics ◽  
1989 ◽  
Vol 54 (7) ◽  
pp. 911-915 ◽  
Author(s):  
Hans Thybo
Keyword(s):  
Frequency Domain ◽  
Computational Methods ◽  
Time Domain ◽  
Synthetic Seismograms ◽  
Seismic Exploration ◽  
One Dimensional ◽  
Borehole Logs ◽  
The Time Domain ◽  
Layered Models

One‐dimensional (1-D) synthetic seismograms are important tools in seismic exploration. They play an important role in the correlation of recorded seismograms with borehole logs and also permit the estimation of delay‐type attenuation in finely layered models. Existing computational methods for computing 1-D seismograms can be grouped according to whether the calculations are performed in the time domain or in the frequency domain.

Numerical methods for solving one‐dimensional cochlear models in the time domain

1987 ◽  
Vol 82 (5) ◽  
pp. 1655-1666 ◽  
Author(s):  
Rob J. Diependaal ◽  
H. Duifhuis ◽  
H. W. Hoogstraten ◽  
Max A. Viergever
Keyword(s):  
Numerical Methods ◽  
Time Domain ◽  
One Dimensional ◽  
The Time Domain

scholarly journals Nonlinear Modal Analysis of a One-Dimensional Bar Undergoing Unilateral Contact via the Time-Domain Boundary Element Method

2017 ◽  
Author(s):  
Jayantheeswar Venkatesh ◽  
Anders Thorin ◽  
Mathias Legrand
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Time Domain ◽  
Domain Boundary ◽  
Unilateral Contact ◽  
Dimensional System ◽  
One Dimensional ◽  
The Time Domain ◽  
Element Method

Finite elements in space with time-stepping numerical schemes, even though versatile, face theoretical and numerical difficulties when dealing with unilateral contact conditions. In most cases, an impact law has to be introduced to ensure the uniqueness of the solution: total energy is either not preserved or spurious high-frequency oscillations arise. In this work, the Time Domain Boundary Element Method (TD-BEM) is shown to overcome these issues on a one-dimensional system undergoing a unilateral Signorini contact condition. Unilateral contact is implemented by switching between free boundary conditions (open gap) and fixed boundary conditions (closed gap). The solution method does not numerically dissipate energy unlike the Finite Element Method and properly captures wave fronts, allowing for the search of periodic solutions. Indeed, TD-BEM relies on fundamental solutions which are travelling Heaviside functions in the considered one-dimensional setting. The proposed formulation is capable of capturing main, subharmonic as well as internal resonance backbone curves useful to the vibration analyst. For the system of interest, the nonlinear modeshapes are piecewise-linear unseparated functions of space and time, as opposed to the linear modeshapes that are separated half sine waves in space and full sine waves in time.

Numerical Modeling and Simulation of Random Road Surface Using IFFT Method

2011 ◽  
Vol 199-200 ◽  
pp. 999-1004
Author(s):  
Zhi Gang Hu ◽  
Yong Lin Zhang ◽  
Jian Ping Ye ◽  
Shao Yun Song ◽  
Li Ping Chen
Keyword(s):  
Time Domain ◽  
Road Surface ◽  
Domain Model ◽  
Surface Model ◽  
One Dimensional ◽  
Power Spectral ◽  
Sample Data ◽  
Road Excitation ◽  
The One ◽  
The Time Domain

Based on the power spectral density (PSD) function of stochastic irregularities of the standard grade road and by means of inverse fast Fouerier transform (IFFT) based on discretized PSD sampling, an equivalent sample of stochastic road surface model in time domain was built. A one-dimensional model of stochastic road was developed into a 2D model of stochastic road surface. Through computer simulation practice based on the MATlab, a 2D sample of stochastic road surface in time domain was regenerated. Furthermore, given the sample data, the PSD was estimated and then compared with the theoretical 2D PSD Equation deduced from the one-dimensional PSD expreesion so as to prove the effectiveness and accuracy of the time-domain model regeneration of 2D stochastic road surface by means of IFFT method. The 2D stochastic road surface model directly provided basic road excitation input data for virtual prototyping (VP) and virtual proving ground (VPG) technology.

scholarly journals The Method of Lines in the time domain

2013 ◽  
Vol 11 ◽  
pp. 15-21
Author(s):  
S. F. Helfert
Keyword(s):  
Time Domain ◽  
Initial Value Problems ◽  
Method Of Lines ◽  
Initial Value ◽  
One Dimensional ◽  
The Past ◽  
Left Handed ◽  
The Method Of Lines ◽  
Homogeneous Structures ◽  
The Time Domain

Abstract. The Method of Lines (MoL) is a semi-analytical numerical algorithm that has been used in the past to solve Maxwell's equations for waveguide problems. It is mainly used in the frequency domain. In this paper it is shown how the MoL can be used to solve initial value problems in the time domain. The required expressions are derived for one-dimensional structures, where the materials may be dispersive. The algorithm is verified with numerical results for homogeneous structures, and for the concatenation of standard dielectric and left handed materials.

A wave propagation model of blood flow in large vessels using an approximate velocity profile function

2007 ◽  
Vol 580 ◽  
pp. 145-168 ◽  
Author(s):  
DAVID BESSEMS ◽  
MARCEL RUTTEN ◽  
FRANS VAN DE VOSSE
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Three Dimensional ◽  
Local Pressure ◽  
Profile Function ◽  
Propagation Models ◽  
One Dimensional ◽  
Friction Term ◽  
The Time Domain ◽  
Dimensional Wave

Lumped-parameter models (zero-dimensional) and wave-propagation models (one-dimensional) for pressure and flow in large vessels, as well as fully three-dimensional fluid–structure interaction models for pressure and velocity, can contribute valuably to answering physiological and patho-physiological questions that arise in the diagnostics and treatment of cardiovascular diseases. Lumped-parameter models are of importance mainly for the modelling of the complete cardiovascular system but provide little detail on local pressure and flow wave phenomena. Fully three-dimensional fluid–structure interaction models consume a large amount of computer time and must be provided with suitable boundary conditions that are often not known. One-dimensional wave-propagation models in the frequency and time domain are well suited to obtaining clinically relevant information on local pressure and flow waves travelling through the arterial system. They can also be used to provide boundary conditions for fully three-dimensional models, provided that they are defined in, or transferred to, the time domain.Most of the one-dimensional wave propagation models in the time domain described in the literature assume velocity profiles and therefore frictional forces to be in phase with the flow, whereas from exact solutions in the frequency domain a phase difference between the flow and the wall shear stress is known to exist. In this study an approximate velocity profile function more suitable for one-dimensional wave propagation is introduced and evaluated. It will be shown that this profile function provides first-order approximations for the wall shear stress and the nonlinear term in the momentum equation, as a function of local flow and pressure gradient in the time domain. The convective term as well as the approximate friction term are compared to their counterparts obtained from Womersley profiles and show good agreement in the complete range of the Womersley parameter α. In the limiting cases, for Womersley parameters α → 0 and α → ∞, they completely coincide. It is shown that in one-dimensional wave propagation, the friction term based on the newly introduced approximate profile function is important when considering pressure and flow wave propagation in intermediate-sized vessels.

Comments on the electromagnetic “smoke ring” concept

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 1908-1913 ◽  
Author(s):  
James E. Reid ◽  
James C. Macnae
Keyword(s):  
Electric Field ◽  
Half Space ◽  
Time Domain ◽  
Current System ◽  
One Dimensional ◽  
Homogeneous Half Space ◽  
Conductivity Structure ◽  
The Time Domain ◽  
Smoke Ring ◽  
Number Of Authors

The electromagnetic (EM) fields in a one‐dimensional (1-D) earth due to a dipole or loop transmitter have been studied by a number of authors, including Lewis and Lee (1978), Pridmore (1978), Nabighian (1979), and Hoversten and Morrison (1982). Nabighian (1979) aptly described the time‐domain‐induced current system in a homogeneous half‐space as resembling a “smoke ring” blown by the transmitter, which moves outwards and downwards and diminishes in amplitude with increasing time after the transmitter is turned off. In a homogeneous half‐space, the physical electric field maximum moves outward from the transmitter loop edge at an angle of approximately 30° with the surface. Hoversten and Morrison (1982) show how the direction of propagation of the time‐domain electric field maximum is affected by conductivity structure. In the case of a highly conductive overburden over a resistive basement, the electric field maximum travels essentially horizontally away from the transmitter, and is effectively trapped in the upper layer.

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