Harmonic Transmission Research Articles

High-order harmonic suppression by a glass capillary array

A glass capillary array with a rectangular cross-section of each individual capillary has been tested as a high-harmonic suppressor for synchrotron radiation beamlines. Using double reflection in the capillary, the high harmonics of a double-crystal Si (1 1 1) monochromator were reduced by a factor of 10 −4–10 −5 from their initial value. The beam spread due to glass surface roughness was measured to be ∼30 arcsec. A first harmonic transmission efficiency of 35% was measured at 7500 eV.

CALCULATION OF VIBRATORY POWER TRANSMISSION FOR USE IN ACTIVE VIBRATION CONTROL

Typical active vibration isolation experiments use point measurements of acceleration or force at the junction between the vibratory source and the receiving structure. This does not necessarily lead to the minimization of the transmitted vibrational energy. A simple method is described to generate a signal which is proportional to the harmonic vibratory power transmission at the driving frequency, which is suitable for use as an error signal with an existing filtered- x feedforward active vibration controller.

Active control of harmonic sound transmission into an acoustic enclosure using both structural and acoustic actuators

This paper describes an analytical and experimental investigation into the active control of harmonic sound transmission in a structural-acoustic coupled system. A rectangular enclosure is considered that has five acoustically rigid walls and a flexible plate on the remaining side through which a harmonic sound wave is transmitted into the enclosure. The control system is designed to globally reduce the sound field inside the enclosure, and the roles of structural and acoustic actuators are of particular interest. Three control configurations, classified by the type of actuators, are compared and discussed. They are: (i) use of a single point-force actuator, (ii) use of a single acoustic piston source, and (iii) simultaneous use of both a point-force actuator and an acoustic piston source. It is shown both analytically and experimentally that the point-force actuator is effective in controlling plate-dominated modes while the acoustic source is effective in controlling cavity-dominated modes. Since the transmitted sound field is governed by both plate- and cavity-dominated modes, the hybrid use of both types of actuators is shown to be a desirable configuration for the active control of sound transmission into a structural-acoustic coupled system.

A COMPARATIVE STUDY OF FEEDFORWARD CONTROL OF HARMONIC AND RANDOM SOUND TRANSMISSION INTO AN ACOUSTIC ENCLOSURE

This paper describes an analytical and experimental investigation which compares the feedforward control of harmonic and random sound transmission into an acoustic cavity. A rectangular enclosure is considered that has five acoustically rigid walls and a flexible plate on the remaining side through which a plane acoustic wave is transmitted into the enclosure. The control systems are designed to reduce the acoustic potential energy inside the enclosure when the incident sound is either harmonic or random. Three control configurations classified by the type of actuators are investigated both theoretically and experimentally. They are (i) use of a single point-force actuator, (ii) use of a single acoustic piston source and (iii) simultaneous use of both a point-force actuator and an acoustic piston source. It is shown that the configuration of both acoustic and structural actuators is desirable for the active control of both harmonic and random sound transmission into a coupled structural–acoustic system whose response is governed by plate and cavity-controlled modes.

Preferential and non-preferential transmission of formant information by an analogue cochlear implant using noise: the role of the nerve threshold

Previous experiments have shown that, in principle, the addition of noise to any vowel coded by an analogue multichannel cochlear implant can enhance the representation of formant information by the temporal pattern of evoked nerve discharges. The optimal addition of noise to some vowel stimuli caused a largely uniform transmission of all input harmonics, including those related to a formant. But for other vowel stimuli, the optimal addition of noise caused preferential transmission of the harmonic closest to a formant compared with other input harmonics. Such preferential transmission may be useful to a cochlear implantee for formant estimation, but the basis of this transmission is unknown. In the present study, the nature of this preferential transmission was investigated with a set of parallel discriminators (or level-crossing detectors) to determine whether the inherent threshold of a nerve fiber was the main cause of the effect. An explicit threshold was found to account for some but not all of the previously observed preferential transmission. Furthermore, many discriminators were required to obtain preferential transmission. Therefore, preferential transmission of a formant-related harmonic may be best achieved by pre-processing a stimulus and using methods associated with stochastic resonance.

Active control of harmonic and random sound transmission in a structural-acoustic system

The active control of sound transmission in structural-acoustic coupled systems has been of interest in recent years. Two particular problems that have received attention are the active control of harmonic sound transmission into aircraft, and control of random noise transmission into the payload bay of space rockets. This paper describes an analytical and experimental investigation to compare the feedforward control of harmonic and random sound transmission into an acoustic cavity. A rectangular enclosure is considered that has five acoustically rigid walls and a flexible plate on the remaining side through which a plane acoustic wave is transmitted into the enclosure. The control systems are designed to reduce the acoustic potential energy inside the enclosure when the incident sound is either harmonic or random. Three control configurations, classified by the type of actuators, are investigated both theoretically and experimentally. They are the use of a structural actuator, the use of an acoustic source, and the simultaneous use of both structural and acoustic actuators. It is shown that the use of both actuators is desirable for the active control of both harmonic and random sound transmission into a coupled structural-acoustic system whose response is governed by plate and cavity controlled modes.

Active control of sound transmission using structural error sensing

The active minimization of harmonic sound transmission into an arbitrarily shaped enclosure using error signals derived from structural vibration sensors is investigated numerically. It is shown that by considering the dynamics of the coupled system, it is possible to derive a set of “structural radiation” modes which are orthogonal with respect to the global potential energy of the coupled acoustic space and which can be sensed by structural vibration sensors. Minimization of the amplitudes of the “radiation modes” is thus guaranteed to minimize the interior acoustic potential energy. The coupled vibro-acoustic system under investigation is modelled using finite element analysis which allows systems with complex geometries to be investigated rather than limiting the analysis to simple analytically tractable systems. Issues regarding the practical implementation of sensing the orthonormal sets of structural radiation modes are discussed. Specific examples relating to the minimization of the total acoustic potential energy within a longitudinally stiffened cylinder are given, comparing the performance offered using error sensing of the radiation modes on the structure against the more traditional error criteria; namely, the discrete sensing of the structural kinetic energy on the boundary and the acoustic potential energy in the enclosed space.

Computation of the electromagnetic harmonics generation by stratified systems containing nonlinear layers

We propose a computational technique to evaluate the reflectivity and the transmission of the harmonics generated by a planar-stratified material containing nonlinear layers. Maxwell's equations are solved and the scattering boundary conditions are implemented using a transfer matrix technique. As our goal beyond this study is to model sum-frequency generation spectra, our approach is limited to second-order processes. The great advantage of this algorithm is that owing to a self-consistent procedure the nonlinear scattering problem is reduced to the repeated solving of linear equations. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 763–770, 1998

Harmonic and anharmonic rate constants and transmission coefficients obtained from ab initio data

Recent ab initio information of Kraka and Dunning on the reaction OH+H2→H2O+H is used to construct a potential energy surface in the vicinity of the reaction path. The resultant energy surface reproduces the ab initio reactant and product properties and provides a good fit to the ab initio data in the interaction region. Anharmonic vibrational energy levels involving the bound degrees of freedom orthogonal to the reaction coordinate are obtained using perturbation theory through second order for cubic terms and first order for quartic terms, with resonance effects removed. These energy levels are used in the calculation of transmission coefficients and thermal rate constants over the temperature range from 200 to 2400 K. The results are compared with those obtained from harmonic vibrational energy levels.

Plasma density determination by transmission of laser-generated surface harmonics

A diagnostic is proposed for determining the density of laser-generated plasmas. The scheme exploits surface harmonics generated by short, intense laser pulses reflected from an overdense plasma layer. At sufficiently high intensities (I${\ensuremath{\lambda}}^{2}$>${10}^{18}$ W ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$), the reflected spectrum contains harmonics well above the plasma frequency, corresponding to the maximum plasma density. The transmitted spectrum, on the other hand, exhibits a low-frequency cutoff for \ensuremath{\omega}${\mathrm{\ensuremath{\omega}}}_{\mathrm{p}}$, offering a simple means of deducing the plasma density.

ACTIVE CONTROL OF VIBRATION TRANSMISSION IN A CYLINDRICAL SHELL

The theoretical analysis of active control of harmonic power transmission in a semi-infinite cylinder using a circumferential array of control forces and a circumferential array of error sensors is considered, and the extent of control which is achievable for a realistic control force configuration is examined.The model considered is a semi-infinite cylinder, simply supported at one end, anechoically terminated at the other end and excited harmonically by an array of in-phase primary forces arranged in a line around its circumference. Control is achieved by an array of independent control forces applied downstream from the primary forces. For three or more control forces it is possible to achieve a power transmission reduction of 30 dB for both acceleration and power transmission cost functions, provided that the error sensors are in the far field of the primary and control forces.

Fluctuation subharmonic and multiharmonic phonon transmission and Kapitza conductance between solids with very different vibrational spectra

It is shown that nonlinear interaction of bulk acoustic phonons with fluctuation resonant vibrations of a two-dimensional transition layer at clean interface between two media (a rigid and a soft crystal) with very different elastic properties leads to the subharmonic transmission across the interface of acoustic phonons incident from a rigid crystal with frequencies above the highest frequency in a soft crystal, and to the second- (and multi) harmonic transmission of acoustic phonons incident from a soft crystal. These inelastic interface dynamical phenomena can substantially contribute to the Kapitza thermal boundary conductance between solids with very different vibrational spectra (such as diamond and soft crystal asPb orAu) and to the thermal conductance across a helium-solid interface also.

Active control of vibratory power transmission along a semi-infinite plate

The feedforward active control of harmonic vibratory power transmission along a semi-infinite plate of finite width has been investigated analytically. One end of the plate was terminated anechoically, the other end was free and the remaining two sides were simply supported. Primary and control source configurations consisted of single sources in various locations and multiple sources arranged in a line across the plate. The primary sources were always located close to the free end of the plate, while the secondary sources were located further along towards the anechoic end. These latter sources were driven in such a way as to minimize the power transmission from the primary sources to the anechoically terminated end of plate. Results show that with careful selection of the control actuator location, the power transmission from a simple harmonic primary excitation can be reduced by approximately 15 dB over a wide frequency range using only one control actuator. Using a number of independently controlled forces placed in a line across the plate produced significant power transmission reductions over a wide range of forcing frequencies with a theoretically achievable maximum of 120 dB for an ideal controller.

Fluctuation subharmonic and multiharmonic phonon transmission and Kapitza conductance between crystals with very different vibrational spectra.

The existence of low-frequency, almost dispersionless intrinsic resonant vibrational modes in a transition layer at clean interface between two media (a rigid and a soft crystal) with very different elastic properties is predicted. It is shown that nonlinear interaction of bulk acoustic phonons with fluctuation resonant vibrations of a two-dimensional transition layer leads to subharmonic transmission across the interface of acoustic phonons incident from a rigid crystal with frequencies above the highest frequency in a soft crystal, and to the second- (and multiple-) harmonic transmission of acoustic phonons incident from a soft crystal. It is shown that contrary to subharmonic and multiharmonic generation of coherent acoustic waves, the coefficients of fluctuation subharmonic and multiharmonic phonon transmission do not depend on the amplitude of incident acoustic wave and are determined by temperature-dependent mean-square amplitudes of relative interface fluctuation displacements. It is emphasized that fluctuation subharmonic phonon transmission is a nonthreshold dynamical phenomenon which is significant for its contribution to Kapitza thermal boundary conductance across the interface. In both cases of fluctuation subharmonic and multiharmonic phonon transmission, two-dimensional resonant interface transition layer leads to the considerable enhancement of the coupling between phonons in the media with very different elastic properties. It is shown that inelastic interface dynamical phenomena can substantially contribute at elevated temperatures to the Kapitza conductance between solids with very different vibrational spectra (such as diamond and soft crystal) and to the thermal conductance across a helium-solid interface also.

An analytical investigation of the active control of the transmission of sound through plates

An analytical model of a vibrating plate is used to explore the mechanisms of control involved in the reduction of harmonic sound transmission through the active control of plate vibration. A general model of the plate vibrations (previously used by Berry et al.) is presented, with the boundary conditions of the plate being modelled as variable rotational and translational elastic restraints at the edges of the plate. A variational formulation of the problem is presented and the equation of motion of the plate is derived by using a Rayleigh-Ritz method. Both an elastic plate with clamped edges and a rigid panel with free edges are considered. For the rigid panel it is found that large attenuations in transmitted sound can be obtained if either three control actuators are used (one for each rigid body mode) or the motion of the panel is restricted to piston type translation along an axis perpendicular to the panel. For the elastic plate two mechanisms of control are observed: “modal control” where the amplitudes of those modes which dominate sound radiation are reduced, and “modal rearrangement” where the relative amplitudes and phases of plate modes are adjusted to produce a vibration distribution of low radiation efficiency. The latter mechanism is shown to be both subtle (often involving little change in mode amplitudes and little change in the overall vibration amplitude of the plate) and very effective (accounting for a large proportion of the attenuations in radiated sound at most frequencies). For the frequency range of interest (0.92 less than kaless than 2.75) large attenuations in the transmitted sound could always be achieved if the number and positioning of the secondary forces is correctly chosen. The simulations also demonstrate the phenomenon of “spill-over”, where inefficiently radiating plate modes are strongly excited with the introduction of control often resulting in an overall increase in the plate vibration.

Software predicts harmonic problems and simulates alternative solutions

HI WAVE is a harmonic analysis program that predicts harmonic distortion levels through detailed power system simulation before they occur. In order to predict the harmonic distortion level in a power system, each system element must be modeled as a frequency dependent component. Recommendations for power system element modeling and network modeling are presented. These elements include harmonic sources, feeders and transmission lines, capacitors and filters, transformers, and system loads. By modeling each of these components, the basic tools of harmonic domain analysis can be implemented. These tools consist of harmonic load flow studies, voltage/current distortion studies, and harmonic frequency scans. >

The Effect of Error Sensor Location and Type on the Active Control of Beam Vibration

The effectiveness of using vibration amplitude as the cost function for an active control system designed to minimize harmonic flexural vibratory power transmission in a beam of infinite length is examined theoretically. Clearly, the best cost function to use is the vibratory power itself, but this is much more difficult to measure accurately, and indeed, it is shown here that it is often only necessary to measure vibration amplitude to achieve satisfactory control of vibratory power transmission. Vibratory power transmission from both primary and control sources under controlled conditions is also calculated, and the results are used to illustrate the physical mechanisms involved.

Quantum Kramers model: Solution of the turnover problem.

The quantum-mechanical version of the Kramers turnover problem is considered. The multidimensional character of the problem is taken into account via transformation to normal modes. This eliminates the coupling to the bath near the barrier top allowing the use of a simple harmonic transmission coefficient for the barrier dynamics. The well dynamics is described by a continuum form of a master equation for the energy in the unstable normal mode. Within first-order perturbation theory, the equations of motion for the stable normal modes have the form of a forced oscillator. The transition probability kernel is found using the known solution for the quantum forced oscillator problem. An expression for the quantum escape rate is derived. It encompasses all previously known limiting results in the thermally activated tunneling regime. The depopulation factor, which accounts for the nonequilibrium energy distribution is evaluated. The quantum transition probability kernel is broader than the classical and is skewed towards lower energies. Interplay between these two effects, together with a positive tunneling contribution, determines the relative magnitude of the quantum rate compared to the classical one. The theory is valid for arbitrary dissipation. Its use is illustrated for the case of a cubic potential with Ohmic (Markovian) dissipation.

Reciprocal relations for transmission coefficients: theory and application

The authors present a rigorous proof of certain intuitively plausible reciprocal relations for time harmonic plane-wave transmission and reflection at the interface between a fluid and an anisotropic elastic solid. Precise forms of the reciprocity relations for the transmission coefficients and for the transmitted energy fluxes are derived, based on the reciprocity theorem of elastodynamics. It is shown that the reciprocity relations can be used in conjunction with measured values of peak amplitudes for transmission through a slab of the solid (water-solid-water) to obtain the water-solid coefficients. Experiments were performed for a slab of a unidirectional fiber-reinforced composite. Good agreement of the experimentally measured transmission coefficients with theoretical values was obtained.

Soft X-ray grating efficiencies: Reciprocity theorem, blaze maximum and isoefficiency curves

In this article data are presented that show the validity of the reciprocity theorem for diffraction by a blazed grating in the soft X-ray region. With this theorem, a simple formula for the calculation of the diffraction efficiency in blaze maximum can intuitively be derived. Calculations with this formula will be compared to experimental data for first and second order diffraction. Isoefficiency curves for these orders can also be drawn from the experimental data. These will be used to discuss the working parameters of some monochromator designs. By combining the advantages of two well-known monochromator concepts, a new design will be proposed that will allow high resolution while it can be optimized for high transmission and good suppression of higher harmonics.