Design of shaped piezoelectric modal sensor for beam with arbitrary boundary conditions by using Adomian decomposition method

The theory for designing distributed piezoelectric modal sensors is well established for beam structures. However, the current modal sensor theory is limited in scope in that it can only be applied in the case of classical boundary conditions (i.e., either clamped, free, simply supported or sliding). In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a beam with arbitrary boundary conditions is proposed, using the Adomian decomposition method (ADM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a function of the second spatial derivative of the structural mode shape function. Based on the ADM and employing some simple mathematical operations, the closed-form series solution of the second spatial derivative of the mode shapes can be determined. Then the shapes of the designed modal sensors are obtained. Finally, some numerical examples are given to demonstrate the feasibility of the proposed modal sensors. It is shown that, for classical boundary conditions, the shapes of the modal sensors based on the ADM agree well with analytical and numerical results given in the literature. For general boundary conditions it is found that the shape of the modal sensors is influenced by the number of modes of interest because the second spatial derivatives of the mode shapes are not orthogonal to one another. The modal sensors for general boundary conditions can be considered as modal filters within a limited frequency band.     

Application of surface and normal ultrasonic waves for measuring the parameters of technical fluids: I. Shear viscosity measurements

The effect of the viscosity of a fluid on the propagation of the zero mode of a horizontally polarized normal wave in a thin (compared to the wavelength) waveguide immersed in the fluid is studied. It is shown that, to a first approximation in the ratio of the shear impedance of the fluid to the shear impedance of the waveguide, the wave amplitude decays exponentially as a function of the distance at a damping coefficient proportional to the square root of the shear viscosity of the fluid. The decrease in the wave amplitude induced by the shear viscosity of the fluid is numerically estimated, and the results obtained point to the possibility of developing a method for its measurement at a high accuracy. This method was developed and tested on a waveguide in the form of an aluminum ribbon 0.3 mm thick and 14 cm long at a frequency of 2 MHz. The decrease in the signal amplitude when the waveguide is immersed in distilled water (tabulated shear viscosity is 1.05 × 10^?3 Pa s) is found to be 0.42 dB as compared to the amplitude in the unloaded waveguide, which can be considered as the sensitivity of the experimental setup. A method for calibrating the sensor is described. The shear viscosities of solutions of saccharose in distilled water are measured, and the experimental results agree well with the theoretical estimates.     

A method of images for a penetrable acoustic waveguide

In this paper the complex-image approximation to the reflection coefficient for water over a seabed half-space is used to generate an image representation for a bounded acoustic waveguide with an underlying layered seabed. The images are true point sources; they have constant amplitudes which are raypath independent and, in the case of a Pekeris waveguide, frequency-independent. This image representation is ideal for constructing the Green's function kernel of the boundary integral equation method for target scattering in a waveguide. The singular behavior of the Green's function for an infinitesimal source/receiver separation, possibly with the target adjacent to one of the interfaces, is modeled correctly and the image expansion has a simple analytic form which can be analytically differentiated. The method is also accurate for significant source/receiver separations, which means that it can be used in the modeling of scattering from large-sized objects and can also be used as an efficient and accurate short-range propagation model for harmonic and broadband propagation in a penetrable waveguide.     

一种基于模态域波束形成的水平阵被动目标深度估计

水面水下目标分辨与识别一直是被动声呐探测领域的难题.利用一种水平阵模态域波束形成算法获得己知方位目标声源的各阶模态强度,将其与不同深度的各阶参考模态强度进行匹配,最终实现了对声源的深度估计.仿真结果表明,该算法可以在信噪比为-10 dB的情况下,用300Hz带宽的信号样本,实现对声源深度的有效估计.系统分析了不同参数和不同波导条件对该方法目标深度估计性能的影响.其中,阵元数越多,模态样本数越多,计算频段越宽,方位估计精度越高,有效阵长越长,深度估计的性能越好.阵元间距和波导深度的变化不会影响该方法的深度估计性能,并且该方法的深度估计性能在声速剖面、海底参数等波导条件存在扰动时具有鲁棒性.     

Design of shaped piezoelectric modal sensors for cantilever beams with intermediate support by using differential transformation method

In this paper a solution to the problem of finding the shape of piezoelectric modal sensors for a cantilever beam with intermediate support is proposed by using the differential transformation method (DTM). A general expression for designing the shape of a piezoelectric modal sensor is presented, in which the output signal of the designed sensor is proportional to the response of the target mode. Other modes are filtered out. The modal sensor shape is expressed as a linear function of the second spatial derivative of the structural mode shape function. By using boundary condition and continuity condition equations at intermediate support, the closed-form series solution of the second spatial derivative of the mode shapes can be determined based on DTM. Then the shapes of the designed modal sensors are obtained. Finally, numerical examples are given to demonstrate the feasibility of the proposed modal sensors for the cantilever beam with intermediate support.     

The design of a polarizing beam splitter made from a dielectric rectangular-groove grating

It has been reported that a polarizing beam splitter based on a rectangular-groove grating (a grating polarizing beam splitter) can be easily designed for specific applications using the modal method. In this paper, the eigenvalue equation of the modal method is transformed to a new form. Using this new form of the eigenvalue equation, it is shown that the design of a grating polarizing beam splitter can be independent of the incident wavelength. The period and the groove depth can be designed using values normalized to the incident wavelength, which apply to a range of wavelengths as long as the effects of dispersion can be neglected. Numerical simulations of fused silica gratings are presented and analyzed. It is concluded that the preferable choice for the grating period is 0.8–0.9 times the incident wavelength.     

Modal group time spreads in weakly range-dependent deep ocean environments

The temporal spread of modal group arrivals in weakly range-dependent deep ocean environments is considered. It is assumed that the range dependence is sufficiently weak that mode coupling is predominantly local in mode number. The phrase "modal group arrival" is taken here to mean the contribution to a transient wave field corresponding to a fixed mode number. There are three contributions to modal group time spreads which combine approximately in quadrature. These are the reciprocal bandwidth (the minimal pulse width), a deterministic dispersive contribution that is proportional to bandwidth and grows like range r, and a scattering-induced contribution that grows approximately like r(32). The latter two contributions are shown to be proportional to the waveguide invariant beta, a property of the background sound speed profile. The results presented, based mostly on asymptotic theory, are shown to agree well with full-wave numerical wave field simulations and available exact mode theoretical results. Simulations are shown that correspond approximately to conditions during the LOAPEX acoustic propagation experiment.     

Beam intensity striations and applications

The single-element spectrogram for a continuous broadband signal, plotted as a function of range, has been shown to exhibit striated bands of intensity maxima and minima. The slope of the striations is an invariant of the modal interference and is described by a waveguide invariant parameter "beta." The striation pattern is analyzed and modeled in this paper for the beam outputs of a horizontal line array obtained by conventional beamforming. Array beamforming makes it possible to measure the waveguide invariant parameter for weak signals due to the enhancement of signal levels by the array gain over that of a single element. It is shown that the signal beam spectrogram as a function of range exhibits the same striation pattern as that (predicted) for a single element. Specifically, for a broadside signal, the beam striation is identical to that of a single-element plus a constant signal gain. For a nonbroadside target, the signal beam intensity will be modified by a frequency-bearing dependent signal gain due to the signal spread over multiple beams, nevertheless the beam spectrogram retains the same striation pattern (slope) as for a single element. The sidelobe beams (outside the canonical cones containing the signal arrivals) exhibit an entirely different striation pattern as a function of frequency and range. For array processing, it is shown that a fast range-rate, close range target and a distant, slow range-rate interference source will have a different striation pattern (slope) in the corresponding beam spectrograms as a function of time, assuming no prior knowledge of the source ranges. The difference in the striations between the beam spectrograms can be used in array processing to suppress the interference contribution. A 5-7 dB interference suppression is demonstrated using simulated data.     

A uniform approximation for the eigenmodes of a planar dielectric waveguide

This paper derives a new approximation for the eigenmodes of a planar waveguide. The approximation is uniformly valid at both the high and low frequency regions of the dispersion relation. It is shown that a Pade approximation of the frequency equation leads to very accurate solutions. The new approximate solution is used to compute the frequency spectrum and the results compared with the exact analytical solution. The solutions presented here are ideal for analytically studying transient wave fields by means of modal summation.     

Anomalous modal structure in a waveguide with a photonic crystal core

We analyze a dielectric waveguide with a photonic crystal core. Using constant frequency contour analysis, we show that the modal behavior of this structure is drastically different from that of a conventional slab waveguide. In particular, at a given frequency the lowest-order guided mode can have an odd symmetry or can have more than one nodal plane in its field distribution. Also, there exist several single-mode regions with a different modal profile in each region. Finally, a single-mode waveguide for the fundamental mode with a large core and strong confinement can be realized. All these behaviors are confirmed by our three-dimensional finite-difference time-domain simulations.     

Modal depth function estimation using time-frequency analysis

Acoustic propagation in shallow water is characterized by a set of depth-dependent modes, the modal depth functions, which propagate in range according to their horizontal wavenumbers. For inversion purposes, modal depth function estimation in shallow water is an issue when the environment is not known. Classical methods that provide blind mode estimation rely on the singular value decomposition of the received field at different frequencies over a vertical array of transducers. These methods require that the vertical array spans the full water column. This is obviously a strong limitation for the application of such methods in an operational context. To overcome these shortcomings, this study proposes to replace the spatial diversity constraint by a frequency diversity condition, and thus considers the case of a field emanating from an impulsive source. Indeed, because of the discrete nature of the wavenumber spectrum and due to their dispersive behavior, the modes are separated in the time-frequency domain. This phenomenon enables the design of a modal filtering scheme for signals received on a single receiver. In the case of a vertical receiver array, the modal contributions can be isolated for each receiver even when using a partial water column spanning array. This method thus eliminates the receiving constraints of classical methods of modal depth function estimation, although it imposes the use of an impulsive source. The developed algorithm is benchmarked on numerical simulations and validated on laboratory experimental data recorded in an ultrasonic waveguide. Practical applications are also discussed.     

Study on RF Excited Waveguide CO_2 Laser with Two Different Channels

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Study on RF Excited Waveguide CO2 Laser with Two Different Channels

In this paper a waveguide CO2 laser with two unequal long channels excited by radio frequency (RF) is presented. The volume is 2.25×2.25×400 mm3 for the long channel and 2.25×2.25×200 mm3 for the short waveguide channel. Laser output power is about 8 W for the long channel and about 3.5 W for the short one.     

Existence of negative dispersion and band gap in a helically inner cladded annular circular waveguide

Helical waveguide, a different type of waveguide structure, has been considered for analysis of modal dispersion characteristics. This paper deals with the study of a new type of annular waveguide, in which the inner cladding is made by the helical windings i.e. sheath helix and the outer cladding is as usual simple step-index cladding. Using vector approach, the general characteristic equation for the proposed waveguide has been derived. The modal dispersion characteristics for the lowest order modes for different pitch angles and thickness are determined and analyzed. We have found that there is an existence of the negative dispersion curve in the helically inner cladded annular circular waveguide. It means that the inner cladding is responsible for the negative dispersion which is generally obtained in a photonic band gap.     

A New Distributional Approach to Signature Change

Colombeau's generalized functions are used to adapt the distributional approach to singular hypersurfaces in general relativity with signature change. Equations governing the dynamics of a singular hypersurface are derived and a specific non-vanishing form for the energy-momentum tensor of the singular hypersurface is obtained. It is shown that matching in the case of de Sitter space in the Lorentzian sector is possible along the boundary with minimum radius but leads to the vanishing of the energy-momentum tensor of the singular hypersurface.     

Experimental identification of pedestrian-induced lateral forces on footbridges

This paper presents a comprehensive experimental analysis of lateral forces generated by single pedestrians during continuous walking on a treadmill. Two different conditions are investigated; initially the treadmill is fixed and then it is laterally driven in a sinusoidal motion at varying combinations of frequencies (0.33-1.07 Hz) and amplitudes (4.5-48 mm). The experimental campaign involved 71 male and female human adults and covered approximately 55 km of walking distributed between 4954 individual tests. When walking on a laterally moving surface, motion-induced forces develop at the frequency of the movement and are herewith quantified through equivalent velocity and acceleration proportional coefficients. Their dependency on the vibration frequency and amplitude is presented, both in terms of mean values and probabilistically to illustrate the randomness associated with intra- and inter-subject variability. It is shown that the motion-induced portion of the pedestrian load (on average) inputs energy into the structure in the frequency range (normalised by the mean walking frequency) between approximately 0.6 and 1.2. Furthermore, it is shown that the load component in phase with the acceleration of the treadmill depends on the frequency of the movement, such that pedestrians (on average) subtract from the overall modal mass for low frequency motion and add to the overall modal mass at higher frequencies.     

Identification of a dynamical model for an acoustic enclosure using the wavelet transform

This paper presents results of research work in the identification of a dynamical model for an acoustic enclosure, a duct with rectangular cross-section, closed ends, and side-mounted speaker enclosures. An acoustic enclosure is excited randomly and random decrement functions are built to convert the random responses to free acoustic responses. It is shown that the estimation of resonance frequencies is possible using the wavelet transform of the system’s free response. Using a particular form of the son wavelet function, results are improved compared to those obtained with the traditionally Morlet wavelet function. An optimal value of a parameter of the son wavelet function is obtained by minimization of the wavelet entropy. The accuracy of this new technique is confirmed by applying it to a numerical example, and to an acoustic enclosure. The advantage of using the wavelet transform method over the Fourier-based modal analysis that would normally be used for the enclosure modes problem is established.     

Subwavelength diameter of light beams in active waveguides

It is shown that there is no frequency cutoff in a uniform cylindrical waveguide containing an amplifying medium. Waves of any frequency grow in the direction of propagation, and for small transverse sections the growth rate is inversely proportional to the waveguide diameter. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 12, 867–869 (25 June 1999)     

Effect of curvature of the boundary on the modal dispersion of a single-mode dielectric waveguide of core cross-section bounded by involuted spirals

In this paper, we are presenting an analytical study of the effect of curvature of the spiral shape on the modal dispersion characteristics of the waveguide whose core cross-section is bounded by two involuted spirals of the form 1/r=ξθ, where ξ is a constant and represents the curvature of the spiral taken to design the waveguide into consideration. This study has been done under the weak guidance approximation. Analyzing the dispersion curves for different curvature we found that this waveguide supports only the single mode, and their cutoff value decreases as the the curvature of the spiral increases.