Traveling Wave Approach Research Articles

An alternative to the traveling-wave approach for use in two-port descriptions of acoustic bores.

For more than a decade, the digital waveguide model for musical instruments has been improved through the simulation of cylindrical and conical bores. But several difficulties remain, such as instabilities due to growing exponentials which appear when two conical bores are connected with decreasing taper. In this paper, an alternative overcoming these difficulties is proposed and can be extended to shapes other than cylinders, cones, and hyperbolic horns. A two-port model with more general state variables than usual traveling waves works efficiently for any shape without discontinuities in cross section. The equations for connecting separate elements at discontinuities make this two-port model appropriate for use in time domain simulation of the physical behavior of the wind instrument and its interactions with the player. The potential of this new approach is illustrated by several detailed examples.

Active Vibration Control of a Multi-Story Structure by Impedance Matching.

This study considers active vibration control of a multi-story structure which consists of bar-connected masses repeated in the vertical direction with active mass drivers installed on the top. As an alternative to the vibration mode approach, the traveling wave approach is applied. To implement the impedance matching controller which is proposed for a damped mass-spring system, the loop shaping design procedure is used to consider the dynamics of the actuator and the sensor noise. The designed controller has similar properties of the impedance matching controller, that is, it is efficient for the disturbance at any position and the towers with any stories. Experimental results are shown to evaluate efficiency.

Radiation characteristics of thin-wire V-antennas excited by arbitrary time-dependent currents

This paper studies, from the point of view of the traveling-wave approach, the transient radiation by V-antennas including the dependence of the maximum directivity on the interior angle, on the length of the arms and on the characteristics of the exciting pulse. As particular examples, the cases when the antenna is excited by a harmonic signal and a Gaussian pulse are analyzed and the results obtained using the traveling-wave approach are compared with the ones obtained using numerical methods.

A WAVE-BASED CONTROLLER DESIGN FOR GENERAL FLEXIBLE STRUCTURES

This paper treats a travelling-wave approach to suppressing vibration of general flexible structures. This approach aims to minimize all of the reflective waves at actuator positions located at the structural boundaries. A variation of the transfer matrix method shows the property that the elastic motion is obtained by superposing the waves travelling in a flexible structure; this transfer matrix method is based on the finite element method for structural analysis. Moreover, the method gives the propagation and scattering relations of the waves in the structure. Since these relations are described by a complex-valued function with respect to Laplace variable, they are transformed into a real-valued form to design a controller by a lot of state–space methods. This transformation is given by diagonalizing the unity transfer matrix into a real-Jordan form. The problem is then formulated as an Hxoptimization problem to find a compensator minimizing the reflective waves at the actuators. The designed compensator is based only on the scattering relations at the controller positions and on the sensor-input/controller-output relations. A multispan flexible beam is used to verify the validity of the present approach. It is numerically shown that the approach is able to achieve good damping improvement in the closed-loop system.

波動吸収制御による構造物振動と姿勢角変更の同時制御

Slew maneuver of a flexible space structure is studied in this paper to control both orientation and flextural vibration with using one control input only. The control method uses the concept of wave-absorbing control which is to absorb traveling waves in flexible structure at actuator positions. The wave-absorbing control is applied to suppress the excited vibration of flexible structure during slew maneuver and some significant requirements and limitations for the controller design are presented through analysis of the system using the traveling wave approach. Numerical simulation is used to analyze the performance in the frequency and time domains and satisfactory vibration suppression is shown in the low frequency band. Hardware experiment is also conducted to verify the validity of the numerical simulation and good agreement is shown in its performance of the present control algorithm.

AN OVERVIEW OF THE DIGITAL FAULT LOCATION ALGORITHMS FOR THE POWER TRANSMISSION LINE PROTECTION BASED ON THE STEADY-STATE PHASOR APPROACHES

ABSTRACT The fault location algorithm is a key element in the digital relay for power transmission line protection. The core of the algorithm is the relaying function which relates the fault distance to the sampled waveforms. Various relaying functions are used, so fax, based mainly on the steady-state phasor approach, the differential equation approach and the traveling-wave approach, respectively. In this paper, the steady-state phasor approaches are reviewed. The effect of various algorithms on relay speed and accuracy is examined regarding the selection of the system model, the relaying function and the filtering technique.

Topological Spin Polarization and a VB Picture of Infinite Model Systems for Organic Polymer Magnets in Terms of Electronic Band Calculations

Abstract This paper deals with a polymer version of the topological π-spin polarization interrelated to the topological superdegeneracy of crystal orbitals of infinite or extended polymeric spin systems and also with a VB picture of their spin structure in terms of simple electronic band calculations. We stress that the theoretical models (traveling wave approach) introduced predict essential features of magnetic properties of polymeric systems which yield crucial aspects for their materials design. The model calculation has also been made for various types of inter-polymer interactions in order to understand the topological spin polarization of higher-dimensional infinite or extended polymeric spin systems and the topological nature of inter-polymer contacts (inter-polymer connectedness). The results have shown that the connectedness gives rise to the prominent modulation of band structures and π spin polarizations which is highly dependent on the topology of the contacts. Thus, the results serve for mol...

Numerical computation of wave localization in large disordered beam-like lattice trusses

Wave localization in randomly disordered multiwave structures is investigated. The smallest localization factor is of particular interest and is related to the smallest positive Lyapunov exponent. The numerical algorithm by Wolf et al. is modified to determine all of the Lyapunov exponents. The wave localization in a large beamlike lattice truss modeled as an equivalent continuous Timoshenko beam is studied. ANY engineering structures are designed to be composed of identically constructed elements assembled end to end to form a spatially periodic structure, such as long space antennae or large beamlike lattice trusses used in space solar power stations. Periodic structures behave like bandpass filters when propagating stress waves. If damping is neglected, waves are classified as traveling waves that propagate without attenuation and nontraveling or attenuating waves whose amplitudes attenuate as the waves propagate. For single-wave periodic structures, the frequency axis is divided into alternating passbands and stopbands. In the frequency passbands, the wave is a traveling wave, whereas in the frequency stopbands, the wave is an attenuating wave. For multiwave structures, in a given frequency band, some of the waves may be traveling waves and the others nontraveling waves. However, due to defects in manufacture and assembly, no structure designed as a periodic structure can be perfectly periodic. Disorder can occur in the geometry of configuration s and material properties of the structure. In a disordered periodic structure, wave amplitudes of all waves will be attenuated, even those that are traveling waves in the perfectly periodic counterpart. This means that the vibrational energy imparted to the structure by an external source cannot propagate to arbitrarily long distances but is instead substantially confined to a region close to the source. This phenomenon is known as wave localization. In disordered periodic structures, it is therefore of great practical importance to study the localization behavior and evaluate the so-called localization factors, namely, the exponential rates at which the amplitudes of the waves propagating in the structures decay. The reciprocal of the localization factor gives the localization length, which characterizes the distance that the propagating wave extends in the structure. As an application, the range of damage that is spread in a structure due to impact at some location can be estimated. There are d waves in a d-wave disordered periodic structure; each wave attenuates at a certain exponential rate or corresponds to a certain localization factor, which implies that each wave will extend to a certain localization length. The smallest localization factor or the largest localization length is of particular interest for multiwave structures, since it corresponds to the wave that has potentially the least amount of decay or that carries energy along the multiwave structure farther than any other waves. The study of the localization phenomenon has been and remains an active research area in solid state physics after the celebrated work of Anderson. 1 Hodges2 was the first to recognize the relevance of localization theory to dynamical behavior of periodic engineering structures. Since then, there have been several studies on the localization of vibration of structures. In a series of publications, Pierre and Dowell,3 Pierre,4 and Cha and Pierre5 studied the localization phenomenon for monocoupled disordered structural systems. Cai and Lin6 developed a perturbation scheme to calculate the localization factor based on a generic periodic structure. Kissel7 and Ariaratnam and Xie8'9 used a traveling wave approach to investigate the localization effects in one-dimension al periodic engineering structures. A transfer matrix formulation, including wave transfer matrices, was used to model disordered periodic structures. Furstenberg's theorem10 for products of random matrices was applied to calculate the localization effect as a function of frequency. The localization factor was related to the largest Lyapunov exponent. In these publications, only one-dimensional or monocoupled periodic structures were considered, in which the transfer matrices are of dimension 2. Few studies have been done on the localization behavior of multiwave periodic structures. Kissel11 derived the localization factor as a function of the transmission matrix for multiwave disordered systems using the multiplicative ergodic theorem of Oseledec. 12 The difficulty in the study of multiwave periodic structures is that the localization factor is related to the smallest positive Lyapunov exponent and not the largest Lyapunov exponent as in the singlewave case. The numerical algorithms used previously for evaluating the largest Lyapunov exponent for single-wave periodic structures cannot be employed for multiwave structures. In this paper, a modification of an algorithm due to Wolf et al.13 is used to determine all of the Lyapunov exponents for randomly disordered multiwave periodic structures. The localization factor of a large beamlike lattice truss, modeled as an equivalent continuous Timoshenko beam, is evaluated.

Statistical energy analysis: a critical overview

For the benefit of the ‘enquirer within’, who may not be familiar with the background and concepts of SEA, this overview opens with a discussion of the rationale for the use of probabilistic energetic models for high-frequency vibration prediction, and introduces the postulate upon which conventional SEA is based. It compares and relates the modal and travelling wave approaches, discusses the strengths and weaknesses of SEA as currently practised and points out needs and directions for future research. Critical discussions of individual contributions to the development of the subject are presented only in as much as they treat specific matters of concept, principle or reliability. The roles of SEA in providing a framework for experimental investigations of the high-frequency dynamic behaviour of systems and in interpreting observations on operating systems, although equally important, are not substantially addressed. Nor are specific experimental techniques which involve considerations of transducers, spatial sampling, signal processing, error analysis and data interpretation, which require a critical review in their own right.

An overview of digital fault location algorithms for power transmission lines using transient waveforms

A digital fault location algorithm for calculating the fault distance on a power transmission line can be designed using any of three approaches: the steady-state phasor approach, the differential equation approach and the travelling-wave approach. In this paper, the algorithms utilizing the differential equation and the travelling-wave approach are reviewed. The effect of various algorithms on the relay speed and accuracy is examined. The associated filtering techniques are discussed.

H(infinity) optimized wave-absorbing control - Analytical and experimental results

The wave-absorbing control is a control concept to absorb waves traveling in a flexible structure at actuator positions. This paper presents an approach to design a broadband compensator by applying the //«, control theory to the wave-absorbing control method. This approach aims to minimize effects of the incoming waves on the outgoing waves at the actuator positions in the sense that the //«, norm of the closed-loop scattering matrix is minimum. Vibration suppression control for a flexible beam is studied analytically and demonstrated experimentally to exemplify the controller design approach. Compensators are designed for a collocated torque actuator and angle sensor and also for a noncollocated torque actuator and bending moment sensor. Performance of the compensators is analyzed in the frequency domain, and measured open- and closed-loop transfer functions are obtained from random excitation tests. The designed compensators are shown to attain good broadband damping, and results of the experiments are shown to agree well for the range of frequency below 50 Hz with those of the numerical simulations. I. Introduction A CTIVE control of vibrations in large flexible structures has received considerable attention in recent years. The modal model is a powerful technique both for the dynamic analysis and for the control design. However, limitations on the applicability of the structural modal analysis exist1 when the requirements for vibration suppression and pointing accuracy for flexible structures become stringent. The flexible mode frequencies and shapes are extremely sensitive to inevitable modeling errors, and modal analysis cannot provide a sufficiently accurate design model over a modally rich frequency range. One alternative is the traveling wave approach. This approach is based on the property that the response of a flexible structure to a typical locally applied force can be viewed in terms of traveling elastic disturbances. Mathematically, traveling waves belong to homogeneous solutions of partial differential equations describing the vibration of continua. At controller positions, relations between incoming and outgoing wave vectors and control inputs are derived in a matrix form by representing boundary conditions in terms of the traveling wave vectors. Outgoing waves are produced by the reflection of the incoming waves and are generated by control inputs. Transfer functions from the incoming wave and control input vectors to the outgoing wave vector are called scattering and generating matrices, respectively. Control inputs are set to be in the output-feedback form. This leads to the closed-loop relations between outgoing and incoming waves. Compensators are selected so that the effects of the incoming waves on the outgoing waves are reduced in some sense by adequately selecting elements of the closed-loop scattering matrix. Characteristic elements of the wave-propagation model, such as a scattering matrix, are smooth functions with respect to frequency and are more insensitive to model uncertainties than mode frequencies and shapes. The approach can provide a sufficiently accurate model for a controller design over a modally dense frequency region, and considerable research has been done on the wave control methods.18 However these methods also have drawbacks, such as 1) the designed compensator is not guaranteed to be a causal and real function with

Traveling-wave parametric generation of widely tunable, highly coherent femtosecond light pulses

We report on the generation of ultrashort tunable pulses with a cavityless traveling-wave scheme consisting of a parametric superfluorescence seed source and a parametric amplifier. We show that the traveling-wave approach, with its advantages of simplicity and direct generation of tunable energetic single pulses, can be used in the femtosecond regime, and to this end we discuss the performances that were obtained with pump pulses of ≈1-ps and 200-fs duration at wavelengths of 0.53 and 0.6 μm, respectively. Of particular interest is the β-barium borate-based traveling-wave parametric generator (type-II phase matching), since it offers the possibility of generating nearly transform-limited pulses that are continuously tunable within a wide spectral range to as high as 3 μm in the IR. With a diffraction-limited pump at 0.53 μm. we obtained tunable pulses in a 1.2× diffraction-limited beam, which could be focused, with an f/20 optics lens, to an intensity of 1013 GW/cm2. A temperature-tuned lithium triborate-based femtosecond parametric generator, with its smaller group-velocity dispersion and absence of walk-off, can operate at a pump energy of as low as 30 μJ in a 200-fs pulse.

High-power high-frequency picosecond pulse generation by passively Q-switched 1.55 mu m diode lasers

A theoretical study of high-power, high-frequency, picosecond pulse generation by passively-Q-switched multiple-contact 1.55- mu m Fabry-Perot diode lasers is presented. The numerical model is based on a travelling-wave approach which takes into account gain/loss saturation in each section of the laser and calculates the spatial distribution of gain, absorption, and recombination time along the length of the laser cavity. The generation of pulses as short as 3-10 ps with 1-5-W peak power at 1-10-GHz repetition rate by a triple-contact 1.55- mu m laser is predicted. The model is used to show the dependence of optical pulse parameters on laser structure and drive condition. >

Experiment of a noncollocated controller for wave cancellation

Wave-absorbing control for vibration suppression of flexible space structures is demonstrated experimentally. The experimental model is a hung flexible beam with a sensor and a noncollocated torque actuator. The wave-absorbing control employs partial differential equations as the mathematical model of structural dynamics, and the controller can be designed without any use of the modal expansion. Thus, the control is free from the crucial truncation effect. The structural vibration is expressed in terms of propagating disturbances in the frequency domain. The control forces are applied to eliminate outgoing waves at the boundaries of the structure. The controller is implemented in the form of a nonrecursive digital filter. Details of the controller implementation are discussed, including the digital filter as a compensator, filter truncation, and the hardware. Experimental results show satisfactory performance of the controller and good agreement with the performance predicted analytically. ARGE space structures (LSS) will be inevitably flexible in their structure, and their structural vibration will be easily excited. Therefore, control techniques of structural vibration are necessary to satisfy performance of LSS. Most of the studies on the control problem of LSS employ the dynamic model with a discretized description for flexible structures that are inherently distributed parameter systems. The discretization is usually employed to adopt the conventional state-space method. Methods free from the discretization are natural and suitable to the control of such distributed parameter systems as the LSS. This paper treats through the experiment the wave-absorbing control for vibration suppression of flexible structures. The wave-absorbing control employs partial differential equations as the mathematical model of structural dynamics to design the controller, and the discretization method is not employed in the analyses. The controller obtained is thus free from the crucial truncation effect. The equations are Laplace transformed with respect to time to describe the structural responses in terms of propagating disturbances in the frequency domain. Boundary conditions of the system are expressed as relations between incoming waves, outgoing waves, and external control forces at the boundaries. External control forces are applied to eliminate outgoing waves at the boundaries. Resulting closed-loop behavior of the system shows drastic improvement for disturbance attenuation in comparison with open-loop behavior. The concept of the traveling wave approach is applied to the control problem of LSS by von Flotow.13 He introduces the viewpoint that the elastic response of LSS may be aptly viewed in terms of the disturbance propagation characteristics of the structure. Active vibration isolation by cancelling traveling waves based on the same concept is studied in Refs. 4-8. The technique aims to isolate one part of a structure from disturbances excited elsewhere in the structure. Actuators are located at midpoints of structural members and cancel passing disturbances so that the disturbances do not disturb downstream portions. A generic description of the traveling wave control for structural networks is given in Ref. 9. Miller et al.

Experimental results using active control of traveling wave power flow

Active structural control experiments conducted on a 24-ft pinned-free beam derived feedback compensators on the basis of a traveling-wave approach. A compensator is thus obtained which eliminates resonant behavior by absorbing all impinging power. A causal solution is derived for this noncausal compensator which mimics its behavior in a given frequency range, using the Wiener-Hopf. This optimal Wiener-Hopf compensator's structure-damping performance is found to exceed any obtainable by means of rate feedback. Performance limitations encompassed the discovery of frequencies above which the sensor and actuator were no longer dual and an inadvertent coupling of the control hardware to unmodeled structure torsion modes.

A traveling wave approach to plasma pumping for X-ray sources

Progress in high-brightness excimer lasers and in optical angular multiplexing of excimer lasers presents an opportunity to provide very intense pumping of X-ray sources, both in favorable geometry and in traveling waves, all at low cost. The traveling-wave strategy can be tailored to the parameters of the system to be pumped. This design option can be of great importance for systems lasing at wavelengths in the kilovolt regime where upper level lifetimes are short, and where mirror technology is presently tenuous. Features of several design strategies are explored.

A travelling wave approach to power flow in structural networks

A structural network is an assemblage of slender one-dimensional members. Each member is demarcated, by definition, by two junctions. A junction may involve only one member (a termination) or may be an interconnection of many members. In this paper, computationally and theoretically, the dynamics of such networks are investigated. The focus of the analysis is on elastic disturbance propagation and power flow in the networks. Spatially local models are assembled into a global, frequency domain description. This global description of the response is then investigated for local and global power flow. The procedures serves to identify disturbance transmission paths and to choose and evaluate control procedures, both active and passive. The techniques are demonstrated by application to several examples.

Unifying concepts in non-linear unsteady processes part II: Multicomponent waves, competition and diffusion

The travelling wave approach to some unsteady transfer processes, developed for ‘one-component’ systems in Part I ( Chem. Eng. Process., 21 (1987) 167–178), is generalized to multicomponent systems, with particular concern for adsorption, electrophoresis, and diffusion. For systems in which a given order of ‘mobility’ or ‘competitiveness’ of the components exists, the multicomponent waves obey a set of relatively simple and general qualitative rules of behaviour. These rules govern, in particular, the number of distinct waves generated by a step perturbation, the concentration changes of the components relative to one another in each wave, and the spreading or sharpening tendency of these waves. This ‘competitive’ behaviour is shown to be related to the structure of the matrix coupling the conservation equations of the components, and especially to the orientation of its eigenvectors in the space of concentrations. On the basis of this analysis, a profound mathematical and also physical analogy is shown between fixed-bed Langmuir adsorption, electrophoresis with constant relative mobility, and Stefan-Maxwell diffusion. It is conjectured that, beyond the special form of the equilibrium or transfer laws considered above, the same qualitative trends should hold for all systems where several species compete for a limited resource or space, according to a definite hierarchy, a given order of competitiveness.

Ultra High Speed Relay for EHV/UHV Transmission Lines -- Development, Design and Application

A new protective relay that solves many of the problems associated with the protection of EHV and future UHV systems is described. Based on a traveling wave approach the relay system operates at ultra high speed and can detect and determine the direction to a fault in a few milliseconds. The relay operating principle, design and application are presented as well as results from computer simulation studies and laboratory tests. The first relay system was installed in the USA in Bonneville Power Administration's 500 kV system and represents a substantial contribution to present efforts to shorten fault clearing times as a method to improve system stability and power transfer capability.

Ultra High Speed Relay for EHV/UHV Transmission Lines -- Installation-Staged Fault Tests and Operational Experience

A new protective relay that solves many of the problems associated with the protection of EHV systems has been developed by ASEA, Sweden. Based on a traveling wave approach the relay system operates at ultra-high speed and can detect and determine the direction to a fault within a few milliseconds. The first relay system was installed in Wonneville Power Administration's (BPA) 500 kV system in April 1976. It represents a substantial contribution to BPA's present effort to shorten fault clearance times. The relay's setting procedure is described. The outcome of staged fault tests and one year's operational experience is presented and has confirmed the validity of the relay concept showing an ultra-high speed performance consistent with earlier laboratory results, with operating times of two to six milliseconds.