Structures Of Finite Length Research Articles

Investigation of sound transmission through a finite length cylindrical shell in the presence of an exterior turbulent boundary layer

This paper studies sound transmission through a thin cylindrical shell of finite length. The structure is subjected to an exterior turbulent boundary layer (TBL) excitation and the boundary conditions of its two ends are considered as simply-supported. The classical shell theory (CST) is employed to derive wave propagation in the cylindrical shell, and the Corcos model is applied to describe pressure fluctuation due to TBL. According to the existence of two axial and radial modes, a complete convergence study is presented. To examine sound transmission through the structure, a comprehensive parameters study is provided on the resulting power spectral density (PSD) of the kinetic energy. To validate the results of the present method, the statistical energy analysis (SEA) method is used. For this purpose, modeling is performed by SEA in VA One software, which shows the high accuracy of the results of the present method. The analytical predictions suggest that the sound insulation performance of such a finite length structure is enhanced considerably by increasing the thickness of the shell in a broad-band frequency range. Similar effects on sound transmission are observed for Young’s modulus and density of the shell particularly in the low and high-frequency ranges, respectively. Whereas, enhancing the turbulent pressure and freestream velocity adversely affects sound radiation into the structure.

Transverse vibrations of underground pipeline with pinched ends

The study of transverse oscillations of extended underground structures from the action of constant harmonic forces is of practical interest. Transverse vibrations of an underground cylindrical structure of finite length under the action of a system of concentrated forces that change according to a harmonic law are considered. The environment surrounding the structure is assumed to be elastic, while the interaction of the “environment-structure” system is studied. When considering the problem, the Fourier method and the results of solving the problem of vibrations of an unbounded cylindrical structure in an elastic medium from the action of concentrated harmonic forces were used. The problem of transverse vibrations of a cylindrical rod of finite length interacting with an elastic homogeneous medium is solved by the method of compensating loads. In this case, the structure is considered a source of waves radiated into space and satisfying the conditions of radiation to infinity. The resulting solution is approximate and reliable within the length of the rod. The analysis of the influence of soil conditions and geometric dimensions on the amplitude of oscillations of an underground structure was carried out according to the graphs of the amplitude-frequency characteristic of the object.

Triple Ladder Lumped Circuit With Sixth Order Modal Exceptional Degeneracy

We introduce a circuit topology based on a simple triple-ladder circuit realized with lumped reactive components that provides a sixth order degenerate band-edge (6DBE). The 6DBE is a special kind of sixth-order exceptional point of degeneracy in a lossless and gainless periodic ladder. This degeneracy provides a very flat band edge in the phase-frequency dispersion diagram. The proposed topology exhibits unique structured resonance features associated with a high loaded Q-factor. We investigate the Floquet-Bloch modes in an infinite-length periodic triple-ladder and their dispersion relation using the S parameter formalism. We also provide the approximate analytic expressions of the eigenmodes and dispersion relation around the degenerate point based on the Puiseux series expansion. We investigate the filtering characteristics of a finite-length structure terminated with loads to highlight the special properties of the 6DBE compared to ladders with regular band edge (RBE) and fourth order degenerate band edge (DBE). The circuit framework introduced here with a 6DBE can be exploited in designing novel high Q-factor oscillators, filters, sensors, and pulse shaping networks.

Optimization of the Radiating Features of 1-D Unidirectional Leaky-Wave Antennas

The optimization of antenna parameters such as gain is an important aspect of all antenna design. In the context of leaky-wave antennas (LWAs), it is important to have accurate design rules for optimizing the gain of the antenna for practical finite-length structures. In this work, taking advantage of the recent formulas derived for the accurate evaluation of the beamwidth in finite-size 1-D unidirectional LWAs, we obtain optimum conditions for this general class of antennas. In particular, design rules for minimizing the beamwidth or maximizing the gain are obtained. The latter is evaluated with a fully analytical procedure through the definition of a correction function that improves the accuracy of the common gain–beamwidth relation. The effects of material losses are also discussed to show how they can affect the optimization procedure. These results apply to any 1-D unidirectional LWA, because no assumptions are made on the wavenumber dispersion, which is instead structure-specific. However, the optimization of two practical examples, namely a holey and a slitted LWA, is discussed to show practical application of the proposed design rules.

Förster resonance energy transfer in finite length systems and porous media

Förster Resonance Energy Transfer (FRET) is a mechanism widely used to describe the luminescent behavior of a great variety of systems. However, there is a strong need for a complete model of Förster theory to understand donor-acceptor interactions in different confinement geometries and their effects on the luminescent dynamics. Here, a methodology based on Förster theory that allows finding the probability distribution of donors and acceptors in systems of any geometry is presented. We have considered the particular cases of lines with finite length, finite cylinders, and bi-dimensional arrangements of lines and cylinders. Furthermore, using our results, we calculate the quantum yield as a function of the geometric parameters of the structures. Our numerical results show that this methodology is useful to calculate and predict the donor luminescent dynamics in structures of finite length. We find that our model explains the decrease of the transferred energy from donors to acceptors with the separation between lines or cylinders, this behavior is physically consistent. The model presented here extends the use of FRET to the study of structures with bi-dimensional arrays of lines or cylinders (as could be the case of porous media), and finite cylinder structures (as could be the case of nanotubes). In our knowledge, this work is the first theoretical approach to describe the donor-acceptor luminescent dynamics in this kind of systems.

Time response analysis of periodic structures via wave-based absorbing boundary conditions

A finite element procedure is proposed to compute the dynamic response of infinite periodic structures subject to localized time-dependent excitations. Straight periodic structures which are made up of cells/substructures of arbitrary shapes (e.g., 2D substructures) are analyzed. The proposed approach involves considering a periodic structure of finite length with excitation sources and absorbing boundary conditions which are expressed in the time domain. The absorbing boundary conditions are first described in the frequency domain by means of impedance matrices using a wave approach. Afterwards, they are switched to the time domain by decomposing the impedance matrices via rational functions, and expressing these rational functions in terms of polynomials of the frequency iω up to order 2. The related matrix system involves the usual vectors of displacements, velocities and accelerations, as well as vectors of supplementary variables. As such, it can be simply and quickly convert to the time domain yielding a classical second-order time differential equation which can be integrated with the Newmark algorithm. Numerical experiments are proposed which highlight the relevance of the approach.

Theoretical prediction of morphological selection in amphiphilic systems.

Biological and synthetic amphiphilic systems exhibit a wide range of morphologies. A density functional model for amphiphilic polymer phase mixtures is utilized to quantify localized equilibria and their stability, and ultimately predict and explain morphological preference. This is done by utilizing matched asymptotic expansions, which produces explicit connections between model parameters and macroscopic properties of equilibrium structures. Bilayers, cylindrical, and spherical micelle and vesicle configurations are found, and formulas which connect their geometry to ambient chemical potential are derived. Dynamics are studied in the context of a free boundary problem which describes the evolution of the hydrophobic-solvent domain interface. Linearization of this problem is used to explicitly determine growth rates and parameter regions of stability. All equilibria are found to have two branches of solutions terminating at a fold in the bifurcation diagram which signals the crossover from competitive stability to instability leading to ripening behavior. Ideally flat bilayers are determined to always possess a long wavelength buckling instability, suggesting that curved structures should be generically preferred. Spherical micelles exhibit morphological instabilities which are suppressed by large enough surface tension. Cylindrical micelles may have short-wavelength pearling and long-wavelength Rayleigh-Plateau-type instabilities. In addition, ideally infinite cylinders have an undulatory instability, suggesting that only finite length structures should be observed. A morphological phase diagram can be assembled which takes into account both existence and stability of different geometries. Consistent with experimental evidence, a bifurcation sequence from spheres to cylinders to vesicles is found as either surface tension or polymer composition increases. Coexistence of different stable morphologies is also observed.

On wave propagation in repetitive structures: Two forms of transfer matrix

Two forms of dynamic transfer matrix are derived for a one-dimensional (beam-like) repetitive pin-jointed structure with point masses located at nodal cross-sections, the displacement-force transfer matrix G, and the displacement-displacement transfer matrix, H. Similarity matrices are introduced to relate G and H, together with their respective metrics. Symplectic orthogonality relationships for the eigenvectors of both G and H are derived, together with relationships between their respective sets of eigenvectors. New expressions for the group velocity are derived. For repetitive structures of finite length, natural frequency equations are derived employing both G and H, including phase-closure and the direct application of boundary (end) conditions. Besides an exposition of the theory, some familiar but much new, the focus of the present paper is on the relationships between the two forms of transfer matrix, including their respective (dis)advantages. Numerical results, together with further theory necessary for interpretation, are presented in companion papers.

Experimental Demonstration of Degenerate Band Edge in Metallic Periodically Loaded Circular Waveguide

We experimentally demonstrate for the first time the degenerate band edge (DBE) condition, namely the degeneracy of four Bloch modes, in loaded circular metallic waveguides. The four modes forming the DBE represent a degeneracy of fourth order occurring in a periodic structure where four Bloch modes, two propagating and two evanescent, coalesce. It leads to a very flat wavenumber-frequency dispersion relation, and the finite length structure's quality factor scales as $N^5$ where $N$ is the number of unit cells. The proposed waveguide in which DBE is observed here is designed by periodically loading a circular waveguide with misaligned elliptical metallic rings, supported by a low-index dielectric. We validate the existence of the DBE in such structure using measurements and we report good agreement between full-wave simulation and the measured response of the waveguide near the DBE frequency; taking into account metallic losses. We correlate our finding to theoretical and simulation results utilizing various techniques including dispersion synthesis, as well as observing how quality factor and group delay scale as the structure length increases. Moreover, the reported geometry is only an example of metallic waveguide with DBE: DBE and its characteristics can also be designed in many other kinds of waveguides and various applications can be contemplated as high microwave generation in amplifiers and oscillators based on an electron beam interaction or solid state devices, pulse compressors and microwave sensors.

Radiation loss of planar surface plasmon polaritons transmission lines at microwave frequencies

Radiation loss of a typical spoof surface plasmon polaritons (SSPPs) transmission line (TL) is investigated in this paper. A 325 mm-long SSPPs TL is designed and fabricated. Simulated results show that radiation loss contributes more to transmission loss than dielectric loss and conductor loss from 2 GHz to 10 GHz. Radiation loss of the SSPPs TL could be divided into two parts, one is caused by the input mode converter, and the other is caused by the corrugated metallic strip. This paper explains mechanisms of radiation loss from different parts, designs a loaded SSPPs TL with a series of resistors to absorb electromagnetic energy on corrugated metallic strip, and then discriminates radiation loss from the input mode converter, proposes the concept of average radiation length (ARL) to evaluate radiation loss from SSPPs of finite length, and concludes that radiation loss is mainly caused by corrugated structure of finite length at low frequency band and by the input mode converter at high frequency band. To suppress radiation loss, a mixed slow wave TL based on the combination of coplanar waveguides (CPWs) and SSPPs is presented. The designed structure, sample fabrication and experimental verification are discussed.

Modulation of TE propagation modes in rectangular metal waveguide with integrated graphene structure in the sub-terahertz frequency range

The propagation of TE modes in a rectangular metal waveguide with an integrated structure of finite length containing a graphene monolayer was studied by a modal decomposition method. The modal decomposition method generates a number of linear algebraic equations related to waveguide modes taken into account. The system of linear algebraic equations for the amplitudes of all modes was derived taking into account the propagation as well as a number of local evanescent modes. Truncation errors in the function of the number of modes taken were quantified by using the discontinuities of the boundary conditions for the transverse electric and magnetic field components at the interface of the discontinuities of the structure. The transmitted and reflected TE01 mode amplitudes were calculated versus the graphene layer length, its position inside the waveguide cavity and the graphene electrons chemical potential. It was shown that the symmetrical positioning of the graphene layer inside the waveguide cavity is the most suitable to achieve the largest amplitude modulation, whereas an asymmetrical positioning is suitable to achieve a large phase modulation of the transmitted mode. It was shown that the phase modulation increases with a transmission coefficient modulation increase and decreases with a transmission coefficient increase. It was found that the phase modulation firstly increases almost proportionally with the graphene layer length for relatively short structures; however, after passing through a maximum, the phase modulation becomes almost constant and hence only weakly dependent on the graphene layer length. Typical phase modulation values turn out to be about 15–20 degrees for minimal transmission coefficients of about 0.6–0.4; however, the phase modulation reaches a value of about 45 degrees if the transmission coefficient modulation equals 50%.

Transition from two-dimensional photonic crystals to dielectric metasurfaces in the optical diffraction with a fine structure.

We study experimentally a fine structure of the optical Laue diffraction from two-dimensional periodic photonic lattices. The periodic photonic lattices with the C4v square symmetry, orthogonal C2v symmetry, and hexagonal C6v symmetry are composed of submicron dielectric elements fabricated by the direct laser writing technique. We observe surprisingly strong optical diffraction from a finite number of elements that provides an excellent tool to determine not only the symmetry but also exact number of particles in the finite-length structure and the sample shape. Using different samples with orthogonal C2v symmetry and varying the lattice spacing, we observe experimentally a transition between the regime of multi-order diffraction, being typical for photonic crystals to the regime where only the zero-order diffraction can be observed, being is a clear fingerprint of dielectric metasurfaces characterized by effective parameters.

Supratransmission in a disordered nonlinear periodic structure

We study the interaction among dispersion, nonlinearity, and disorder effects in the context of wave transmission through a discrete periodic structure, subjected to continuous harmonic excitation in its stop band. We consider a damped nonlinear periodic structure of finite length with disorder. Disorder is introduced throughout the structure by small changes in the stiffness parameters drawn from a uniform statistical distribution. Dispersion effects forbid wave transmission within the stop band of the linear periodic structure. However, nonlinearity leads to supratransmission phenomenon, by which enhanced wave transmission occurs within the stop band of the periodic structure when forced at an amplitude exceeding a certain threshold. The frequency components of the transmitted waves lie within the pass band of the linear structure, where disorder is known to cause Anderson localization. There is therefore a competition between dispersion, nonlinearity, and disorder in the context of supratransmission. We show that supratransmission persists in the presence of disorder. The influence of disorder decreases in general as the forcing frequency moves away from the pass band edge, reminiscent of dispersion effects subsuming disorder effects in linear periodic structures. We compute the dependence of the supratransmission force threshold on nonlinearity and strength of coupling between units. We observe that nonlinear forces are confined to the driven unit for weakly coupled systems. This observation, together with the truncation of higher-order nonlinear terms, permits us to develop closed-form expressions for the supratransmission force threshold. In sum, in the frequency range studied here, disorder does not influence the supratransmission force threshold in the ensemble-average sense, but it does reduce the average transmitted wave energy.

Analysis on the Radiation Property of the Bounded Modes of Periodic Leaky-Wave Structure with Finite-Length Using a Hybrid Method.

In this paper the radiation property of the one-dimensional periodic leaky-wave structure is analysed using a new hybrid method, which involves the mode expansion method for expanding the periodic aperture field in terms of spatial harmonics and the method of effective radiation sections for transforming the expanded fields into far fields. Using this method, the radiation of each spatial harmonic can be achieved, and the contributions of the harmonics (especially the bounded modes) to the total radiation of the periodic leaky-wave structure can be calculated. The main findings in this paper demonstrate that the bounded modes in a finite length structure have obvious contribution to the far-field radiation, which was considered to be non-radiative and always ignored in the conventional researches.

유한 길이 구조물과 무한 길이 도파관 구조물의 임피던스 연성을 이용한 진동 해석

유한 길이 구조물과 무한 길이 도파관 구조물의 임피던스 연성을 이용한 진동 해석

Correlated disorder: a novel approach to filter design

Successful application of positional correlated disorder to filter design could lead to the major breakthrough in development and simulation of novel optical devices. The goal of this manuscript is to investigate the feasibility of this approach by modeling light propagation through the periodic-on-average dielectric structures consisting from two alternating layers, when the thickness of one of the layers is affected by the disorder. Based on the principles of Anderson localization we impose correlated disorder into our model through the long-range correlator with the step-wise power spectrum. In our numerical experiments, we study transmitting and reflective properties of spatially disordered periodic-on-average structures of finite length to emulate industrially applicable filters. Special attention is dedicated to the effect of stochastic resonances on the performance of reflection and transmission filters. We show that the concept of positional correlated disorder can be successfully applied to the design of narrow band reflection filters despite the presence of stochastic resonances. On the other hand, its application to narrow band transmission filters is quite limited, and we discuss a possible approach to reduce the effect of stochastic resonances on transmission filters performance.

Acoustic wave guides as infinite-dimensional dynamical systems

We prove the unique solvability, passivity/conservativity and some regularity results of two mathematical models for acoustic wave propagation in curved, variable diameter tubular structures of finite length. The first of the models is the generalised Webster’s model that includes dissipation and curvature of the 1D waveguide. The second model is the scattering passive, boundary controlled wave equation on 3D waveguides. The two models are treated in an unified fashion so that the results on the wave equation reduce to the corresponding results of approximating Webster’s model at the limit of vanishing waveguide intersection.

Impedance studies of 2D azimuthally symmetric devices of finite length

In particle accelerators, the beam quality can be strongly affected by the interaction with self-induced electromagnetic fields excited by the beam in the passage through the elements of the accelerator. The beam coupling impedance quantifies this interaction and allows predicting the stability of the dynamics of high intensity, high brilliance beams. The coupling impedance can be evaluated with finite element methods or using analytical approaches, such as field matching or mode matching. In this paper we present an application of the mode matching technique for an azimuthally uniform structure of finite length: a cylindrical cavity loaded with a toroidal slab of lossy dielectric, connected with cylindrical beam pipes. In order to take into account the finite length of the structure, with respect to the infinite length approximation, we decompose the fields in the cavity into a set of orthonormal modes. We obtain a complete set of equations using the magnetic field matching and the nonuniform convergence of the electric field on the cavity boundaries. We present benchmarks done with CST Particle Studio simulations and existing analytical formulas and codes, pointing out the effect of different material conductivities, finite length, and nonultrarelativistic particle beam velocity.

Sound radiation by parallel coated plates separated by a fluid layer: Now and Then

In 1987, I had the opportunity to work with Miguel Junger on a paper entitled “Sound Radiation by parallel coated plates separated by a fluid layer.” A critical piece of the analysis involved analytically inverting a 5x5 matrix, which resulted in an extremely complex algebraic expression for the far-field of a point-excited 5-layer configuration. In order to understand the physical mechanisms, and validate the results, Dr. Junger developed asymptotic forms of the solution for familiar configurations and made use of spring-mass models to understand resonance enhancement effects. This talk introduces our current semi-analytical waveguide analysis of sound radiation by parallel, multi-layer plates. An advantage of the waveguide approach is that finite-length structures can be modeled, and axial discontinuities, including ribs and wavebearing bulkheads, can also be included very efficiently. Physical mechanisms are interpreted in terms of the propagating and evanescent waves of the structures. A focus of this talk is the extension of the perfectly matched layer (PML) model of the exterior fluid to waveguide models.

The finite element method applied to the study of two-dimensional photonic crystals and resonant cavities

A critical assessment of the finite element (FE) method for studying two-dimensional dielectric photonic crystals is made. Photonic band structures, transmission coefficients, and quality factors of various two-dimensional, periodic and aperiodic, dielectric photonic crystals are calculated by using the FE (real-space) method and the plane wave expansion or the finite difference time domain (FDTD) methods and a comparison is established between those results. It is found that, contrarily to popular belief, the FE method (FEM) not only reproduces extremely well the results obtained with the standard plane wave method with regards to the eigenvalue analysis (photonic band structure and density of states calculations) but it also allows to study very easily the time-harmonic propagation of electromagnetic fields in finite clusters of arbitrary complexity and, thus, to calculate their transmission coefficients in a simple way. Moreover, the advantages of using this real space method in the context of point defect cluster quality factor calculations are also stressed by comparing the results obtained with this method with those obtained with the FDTD one. As a result of this study, FEM comes out as an stable, robust, rigorous, and reliable tool to study light propagation and confinement in both periodic and aperiodic dielectric photonic crystals and clusters.