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.

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.

scholarly journals LISMA_HDS language for modeling heterogeneous dynamic systems

2021 ◽  
pp. 103-122
Author(s):  
Evgeny Popov ◽  
◽  
Yury Shornikov ◽  
Keyword(s):  
Dynamic Systems ◽  
Initial Value Problems ◽  
Method Of Lines ◽  
System Of Equations ◽  
Modeling Languages ◽  
Cauchy Problems ◽  
Systems Of Equations ◽  
Initial Value ◽  
Algebraic Systems ◽  
Different Types

Heterogeneous dynamic systems (HDS) simultaneously describe processes of different physical nature. Systems of this kind are typical for numerous applications. HDSs are characterized by the following features. They are often multimode or hybrid systems. In general, their modes are defined as initial value problems (Cauchy problems) for implicit differential-algebraic systems of equations. Due to the presence of heterogeneous dynamic components or processes evolving in both time and space, the dimension of the complete system of equations may be pretty high. In some cases, the system of equations has an internal structure, for instance, the differential-algebraic system of equations approximating a partial differential equation by the method of lines. An original huge system of equations can then be algorithmically rewritten in a compact form. Moreover, heterogeneous hybrid dynamical systems can generate events of qualitatively different types. Therefore one has to use different numerical event detection algorithms. Nowadays, HDSs are modeled and simulated in computer environments. The modeling languages widely used by engineers do not allow them to fully specify all the properties of the systems of this class. For instance, they do not include event typing constructs. That is why a declarative general-purpose modeling language named LISMA_HDS has been developed for the computer-aided modeling and ISMA simulation environment. The language takes into account all of the characteristic features of HDSs. It includes constructs for plain or algorithmic declaration of model constants, initial value problems for explicit differential-algebraic systems of equations, and initial guesses for variables. It also allows researchers to define explicit time events, modes and transitions between them upon the occurrence of events of different types, to use macros and implement event control. LISMA_HDS is defined by a generative grammar in an extended Backus-Naur form and semantic constraints. It is proved that the grammar belongs to the LL(2) subclass of context-free grammars.

scholarly journals Exploring the Time Domain with Synoptic Sky Surveys

2011 ◽  
Vol 7 (S285) ◽  
pp. 141-146 ◽  
Author(s):  
S. G. Djorgovski ◽  
A. A. Mahabal ◽  
A. J. Drake ◽  
M. J. Graham ◽  
C. Donalek ◽  
...  
Keyword(s):  
Time Domain ◽  
Lessons Learned ◽  
Sky Surveys ◽  
The Past ◽  
Systematic Exploration ◽  
The Time Domain ◽  
New Research

AbstractSynoptic sky surveys are becoming the largest data generators in astronomy, and they are opening a new research frontier that touches practically every field of astronomy. Opening the time domain to a systematic exploration will strengthen our understanding of a number of interesting known phenomena, and may lead to the discoveries of as yet unknown ones. We describe some lessons learned over the past decade, and offer some ideas that may guide strategic considerations in the planning and execution of future synoptic sky surveys.

Stability Evaluations of Semi-Submersible Heavy Transport Vessels by a Progressive Flooding Simulation Tool

2012 ◽  
Author(s):  
Hendrik Dankowski ◽  
Hannes Hatecke
Keyword(s):  
Time Domain ◽  
Simulation Method ◽  
Intermediate Step ◽  
Viscous Effects ◽  
The Past ◽  
Discharge Coefficients ◽  
Damage Stability ◽  
Offshore Industry ◽  
The Stability ◽  
The Time Domain

Rising needs for heavy transport operations are intensified by the expanding offshore industry worldwide. Whenever very large and heavy objects have to be transported, only semi-submersible heavy transport vessels are capable of carrying this special cargo. Accidents in the past during operations of these vessels highlight the requirement of analyzing the operation procedures in more detail. Especially the submerging process of the main working deck is very critical regarding the hydrostatic stability. A new numerical progressive flooding simulation method will be presented for applications like accident investigations or damage stability assessments. This method is modified to fit the special requirements of simulating the operational behavior of semi-submersible vessels in the time-domain. A direct approach is chosen, which computes the flux between the compartments based on the Bernoulli equation and the current pressure heads at each intermediate step. Losses due to viscous effects are taken into account by empirical discharge coefficients. This method will be used to simulate the submerging operation in the time-domain to point out critical situations regarding the stability of the vessels and the cargo. This will be compared to accidents which occurred in the past. Furthermore, recommendations for operational procedures are proposed.

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.

STUDY ON A SORT OF CONTROLLABLE NONLINEAR LEFT-HANDED MATERIALS

2009 ◽  
Vol 18 (03) ◽  
pp. 441-456 ◽  
Author(s):  
HONG XIN ZHANG ◽  
LAN ZHAO ◽  
YING HUA LU
Keyword(s):  
Resonance Frequency ◽  
Time Domain ◽  
Material Properties ◽  
Finite Difference Time Domain ◽  
Transmission Properties ◽  
The Past ◽  
Left Handed ◽  
High Harmonics ◽  
Fdtd Simulations ◽  
Difference Time

In this paper, three kinds of controllable nonlinear left-handed materials (DNLHMs) are proposed and analyzed, which are designed by introducing inductors and capacitors into the traditional nonlinear left-handed materials (NLHMs) as inhomogeneous doped elements. Due to such changes, several new transmission properties have been presented through finite-difference time-domain (FDTD) simulations. These have brought new features to our DNLHMs. On one hand, the original passband in the traditional nonlinear left-handed material is narrowed after introducing inductors. In addition, a new passband, which does not exist in doped linear LHMs, is generated. On the other hand, through introducing capacitors, the original passband of the nonlinear left-handed material can be shifted, resonance frequency can be changed, and a new passband can be generated. When capacitors and inductors are introduced simultaneously, the material properties, such as the number of passbands, the characteristic resonance frequency, and the bandwidth, can also be changed. Noting these characteristics, the values of the introduced inductors and capacitors are varied to investigate the spectrum changes of DNLHMs. Then, a series of controllable properties of the DNLHMs can be retrieved. And more importantly, the designed DNLHMs give the adjustability of suppressing high harmonics, which is not possible in the past materials.

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