WAVE TRANSFORMATION AND BREAKING OVER A RECTANGULAR STEP

An idealized numerical wave flume has been established by finite element method on the bases of Navier Stokes equations through prescribing the appropriate boundary conditions for the open boundary,incident boundary,free surface and solid boundary in this paper.The characteristics of waves propagating over a step have been investigated by this numerical model.The breaker wave height is determined depending on the kinetic criterion.The numerical model is verified by laboratory experiments,and the empirical formula for the damping of wave height due to breaking is also given by experiments.

Study of a rectangular coupled cavity extended interaction oscillator in sub-terahertz waves

An extended interaction oscillator （EIO） generating 120 GHz wave in sub-terahertz waves is studied by using the three-dimensional electromagnetic simulation software CST and PIC codes. A rectangular reentrant coupled-cavity is proposed as the slow-wave structure of EIO. By CST, the circuit parameters including frequency-phase dispersion, interaction impedance and characteristic impedance are simulated and calculated. The operation mode of EIO is chosen very close to the point where βL = 2π with corresponding frequency 120 GHz, the beam voltage 12 kV and the dimensions of the cavity with the period 0.5mm, the height 3mm and the width 1.4mm. Simulation results of beam-wave interaction by PIC show that the exciting frequency is 120.85 GHz and output peak power 465 W with 12-period coupled-cavity with the perveance 0.17 μP. Simulation results indicate that the EIO has very wide range of the operation voltage.

EXACT ANALYSIS OF WAVE PROPAGATION IN AN INFINITE RECTANGULAR BEAM

The Fourier series method was extended for the exact analysis of wave propagation in an infinite rectangular beam.Initially,by solving the three-dimensional elastodynamic equations a general analytic solution was derived for wave motion within the beam.And then for the beam with stress-free boundaries,the propagation characteristics of elastic waves were presented.This accurate wave propagation model lays a solid foundation of simultaneous control of coupled waves in the beam.

Approximate Calculation of Oblique Wave Transmission from A Single-Row of Rectangular Piles

Transmissions of oblique incident wave from a row of rectangular piles are analyzed theoretically. The incident angle of plane wave is taken as g = 90° , there then is the transmission coefficient ｜T｜ = 1 （This is a paradox）. In this paper, by means of the approximate relation between the transmitted and incident wave angle found from the shape of a slit, the paradoxical phenomenon is removed. On the basis of the continuality of the pressure and flux and the analysis of flow resistance at the row of rectangular piles, formulas of reflection and transmission coefficients are obtained. The transmission and reflection coefficients predicted by the present model quite agree with those of laboratory experiments in previous references

THEORY AND EXPERIMENTAL INVESTIGAION OF FLEXURAL WAVE PROPAGATION IN THIN RECTANGULAR PLATE WITH PERIODIC STRUCTURE

With the idea of the phononic crystals, a thin rectangular plate with two-dimensional periodic structure is designed. Flexural wave band structures of such a plate with infinite structure are calculated with the plane-wave expansion （PWE） method, and directional band gaps are found in the ΓX direction. The acceleration frequency response in the ΓX direction of such a plate with finite structure is simulated with the finite element method and verified with a vibration experiment. The frequency ranges of sharp drops in the calculated and measured acceleration frequency response curves are in basic agreement with those in the band structures. Thin plate is a widely used component in the engineering structures. The existence of band gaps in such periodic structures gives a new idea in vibration control of thin plates.

Interaction of Oblique Waves and A Rectangular Structure with An Opening Near A Vertical Wall

With the method of separation of variables and the eigenfunction expansion employed, an analytical solution is presented for the radiation and diffraction of a rectangular structure with an opening near a vertical wall in oblique seas, in which the unknown coefficients are determined by the boundary conditions and matching requirement on the interface. The effects of the width of the opening and the angle of incidence on the hydrodynamic characteristics of a rectangular structure with an opening near a vertical wall are mainly studied. The comparisons of the calculation results with wall-present and with wall-absent are also made. The results indicate that the variation trends of the heave added mass and excitation force with wall-present are almost the same as those with wall-absent, and that the peak values in the former case are obviously larger than those in the latter due to the reflection of the vertical wall.

Stress Uniformity Process of Specimens in SHPB Test Under Different Loading Conditions of Rectangular and Half-Sine Input Waves

Based on the characteristics of 1D waves,the stress uniformity process in specimens under different loading conditions of rectangular and half-sine input waves was analyzed in split Hopkinson pressure bar (SHPB) test.The results show that the times of an elastic wave propa-gating from one end to the other in a specimen to attain stress equilibrium,is related to input wave-forms and relative mechanical impedance between the specimen and the input/output bars.Here-into,with the increae of the relative impedance,the times decreases under rectangular input waves loading,while it increases under half-sine input wave loading.The dimensionless stress value of specimen corresponding to the status of stress equilibrium increases with the increase of the rela-tive mechanical impedance.However,the dimensionless stress value under half-sine input wave loading is significantly lower than the value under rectangular input wave loading for specimen with low mechanical impedance,and the relative differentia of the dimensionless stress values under two loading conditions decreases with the increase of the relative mechanical impedance.In gen-eral,the forced state of specimen with relatively low mechanical impedance under half-sine input wave loading is evidently superior to the state under rectangular input wave loading in SHPB test,and the advantages of forced state under half-sine input wave loading turns weak with the increase of the relative mechanical impedance.

Small-signal analysis of a rectangular helix structure traveling-wave-tube

This paper investigates the properties of traveling wave-beam interaction in a rectangular helix traveling-wave-tube （TWT） for a solid sheet electron beam. The ＂hot＂ dispersion equation is obtained by means of the self-consistent field theory. The small signal analysis,which includes the effects of the beam parameters and slow-wave structure （SWS） parameters,is carried out by theoretical computation. The numerical results show that the bandwidth and the small-signal gain of the rectangular helix TWT increase as the beam current increases;and the beam voltage not obviously influences the small signal gain. Among different rectangular helix structures,the small-signal gain increases as the width of the rectangular helix SWS increases,however,the bandwidth decreases whether structure parameters a and L or ψ and L are fixed or not.In addition,a comparison of the small-signal gain of this structure with a conventional round helix is made.The presented analysis will be useful for the design of the TWT with a rectangular helix circuit.

An Open Rectangular Waveguide Grating for Millimeter-Wave Traveling-Wave Tubes

Millimeter-wave traveling-wave tube （TWT） prevails nowadays as the amplifier for radar, communication and electronic countermeasures. The rectangular waveguide grating is a promising all-metal interaction circuit for the millimeter-wave TWT with advantages of high power capacity, fine heat dissipation, scalability to smaller dimen- sions for shorter wavelengths, compact structure and robust performance. Compared with the traditional closed structure, the open rectangular waveguide grating （ORWG） has wider bandwidth, lower cut-off frequency, and higher machining precision for higher working frequencies due to the open transverse. It is a potential structure that can work in the millimeter wave and even Terahertz band. The rf characteristics including dispersion and interaction impedance are investigated by both theoretic calculation and software simulation. The influences of the structure parameters are also discussed and compared, and the theoretical results agree well with the simula- tion results. Based on the study, the ORWG will favor the design of a broadband and high-power millimeter-wave TWT.

Design of a Broadband E-Plane Power Combiner Based on Quarter-Arc Bent Rectangular Waveguides for Sub-THz and THz Wave

A method of designing an E-plane power combiner composed of two quarter-arc bent rectangular waveguides is proposed for sub-THz and THz waves. The quarter-arc bent-waveguide power combiner has a simple geometry which is easy to design and fabricate. By HFSS codes, the physical mechanism and performance of the power combiner are analyzed, and the relationship between the output characteristics and the structure/operating parameters is given. Simulation results show that our power combiner is suitable for the combining of two equalpower and reversed-phase signals, the bandwidth of the combiner is wide and can be adjusted by the radius of the quarter-arc, and the isolation performance of the combiner can be improved by adding thin film resistive septa at the junction of two quarter-arc bent waveguides. Meanwhile, an approximate method based on the analytic geometrical analysis is given to design this power combiner for different frequency bands.

STUDY ON RECTANGULAR WAVEGUIDE GRATING SLOW-WAVE STRUCTURE WITH COSINE-SHAPED GROOVES

This paper focuses on a new rectangular waveguide grating Slow-Wave Structure (SWS) with cosine-shaped grooves and studies the propagation characteristics of the wave in the SWS. By using the approximate field-matching conditions,the dispersion equation and the coupling impedance of this circuit are obtained. The dispersion curves and coupling impedances of the fundamental wave are calculated and the influences of the various geometrical dimensions are discussed. The results show that the bandwidth of the cosine-shaped groove SWS is much wider than that of rectangular-shaped groove one. And reducing the groove width can broaden the frequency-band and decrease the phase-velocity,while increment of the groove-depth can also decrease phase-velocity. For above cases,the coupling impedance is more than 16Ω. The present analysis will be helpful on further study and design of the RF systems used in millimeter wave Traveling Wave Tube (TWT).

基于ADMM算法优化的矩形网格隐式有限差分波动方程正演模拟

有限差分(FD)法广泛用于地震勘探领域的波动方程数值模拟.由于存在“饱和效应”,利用Taylor级数展开法(TE)计算高阶FD系数会在高频和粗网格条件下产生明显的数值频散.一般的常系数优化法能在较大波数区间取得更高的数值精度,但缺乏对中、低波数区间的误差约束;此外,它们大多沿单空间方向压制数值频散,因而无法缓解矩形网格模板的数值各向异性.本文基于隐式FD模板发展了一种多空间方向优化的波动方程正演模拟方法,以同时解决数值频散和数值各向异性问题.针对实用性更强的矩形网格单元,本文基于L_(1)范数建立目标函数并增加波传播角约束以减小数值各向异性,然后运用交替方向乘子法(ADMM)求解优化问题从而实现提高模拟精度的目的.理论误差曲线分析表明,相比传统TE方法和其他单向L_(1)范数、L_(2)范数、L_(∞)范数优化方法,本文基于L_(1)范数的多向优化方法在中、低波数区间具有最小的绝对误差,同时能更好的均衡各个方位角之间的误差分布.均匀介质、Marmousi-2地质模型的正演模拟算例均证明本文所提出的方法比其他三种优化方法在减小长时程测试下的误差积累方面更有优势.

一种新的X-wave仿真方法

目的 X-wave作为一种典型的非衍射波,具有很强的潜在价值,在使用有限孔径传感器的情况下,能够在较深的场域内保持不发散的优点,比传统的超声系统节省了动态聚焦的计算过程,能有效提高超声成像的速度。但X-wave的理论激励信号比较复杂,导致其在仿真经济成本和时间耗费过高。基于此,本文提出一种使用矩形波或三角波的简单波取代复杂的激励信号的方法。方法首先使用简单波(矩形波和三角波)取代原有的X-wave的激励信号,采用L2的优化算法选择哪一种简单波最接近原有的激励信号,再通过计算空间脉冲响应实现声场的仿真。结果声场仿真结果显示,该方法能最大限度减少激励信号的差异,减少X-wave仿真运算时间,并为降低X-wave的硬件成本提供空间。结论该方法可以在较高精度的前提下显著降低X-wave的仿真成本,为X-wave的应用提供一种新思路。

Suppression of Wave-Excited Vibration of Offshore Platform by Use of Tuned Liquid Dampers

This paper describes experimental and theoretical investigations of Tuned Liquid Damper (TLD) characteristics for suppressing the wave-excited structural vibration. The structural model for the experiments is scaled according to a full size offshore platform by matching their dynamic properties. Rectangular TLDs of different sizes with partially filled liquid are examined. By observing the performance and behavior of TLDs through laboratory experiments, the Study investigates the influence of a number of parameters, including container size, container shape, frequency ratio, and incident wave characteristics. In an analytical study, a mathematical model that describes the nonlinear behavior of liquid in TLD and the interaction of TLD and structure is prerequisite. The validity of the model is evaluated and simulating results can reasonably match the corresponding experimental results.

Performance Evaluation of Bottom-Standing Submerged Breakwaters in Regular Waves Using the Meshless Singular Boundary Method

In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. Both the single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. Only the impermeable breakwaters are considered in this study. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with the appropriate mixed-type boundary conditions, and it is solved numerically using the ISBM. The numerical results are presented in terms of the hydrodynamic quantities of reflection and transmission coefficients. The values are first validated against the data of previous studies, computed, and discussed for a variety of structural conditions, including the height, width, and spacing of breakwater submergence. An excellent agreement is observed between the ISBM results and those of other methods. The breakwater width is found to feature marginal effects compared with the height. The present method is shown to accurately predict the resonant conditions at which the maximum reflection and transmission occur. The trapezoidal breakwaters are found to generally present a wide spectrum of reflections, suggesting that they would function better than the rectangular breakwaters. The dual breakwater systems are confirmed to perform much better than single structures.

Effects of output waveforms on penetration for Nd :YAG laser welding

By using a Nd: YAG laser welding system devised for transmitting continuous, rectangular and pulsed waveforms, comprehensive and deep investigation is focused on the effects of several parameters of rectangular waveform and pulsed output wave superimposed on a rectangular waveform on the penetration depth of weld. Research results indicate that the average power, duty cycle, frequency and peak power of rectangular wave affect the weld penetration depth to different extent. Results of experiments and analysis also indicate that the pulse delay time, pulse width and the power ratio of pulse to rectangular waveform seriously influence the penetration when the pulsed wave is superimposed on a rectangular waveform.

Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic-electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch-Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the planewave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.

Submillimeter wave communication versus millimeter wave communication

This paper studies the performance of a submillimeter wave antenna operating between frequencies 0.1 THz and 10 THz with a 4-cyano-4-pentylbiphenyl[5CB]substrate.Since the size and shape of the antenna impact its gain/directivity,resonant frequency,bandwidth,and efficiency,the two antenna types considered in this paper are:(a)Rectangular Patch Antenna(RPA),and(b)Cylindrical Dielectric Resonator Antenna(CDRA).Here a submillimeter wave antenna is compared with a millimeter wave(a few GHz to 100 GHz)antenna.These popular mmwave antennas are chosen for the submillimeter wave antenna in order to understand changes in their performance as the result of changes in their geometrical shape.FEldberechnung bei Korpern mit beliebiger Oberflache(FEKO)software is used for the design and calculation of the Three-Dimensional(3D)ElectroMagnetic(EM)patterns.This paper also concentrates on the design and analysis of a massive submillimeter wave Multiple-Input Multiple-Output(MIMO)(8 by 8)RPA and CDRA.

Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.

Electronic Band Structure of Graphene Based on the Rectangular 4-Atom Unit Cell

The Wigner-Seitz unit cell (rhombus) for a honeycomb lattice fails to establish a k-vector in the 2D space, which is required for the Bloch electron dynamics. Phonon motion cannot be discussed in the triangular coordinates, either. In this paper, we propose a rectangular 4-atom unit cell model, which allows us to discuss the electron and phonon (wave packets) motion in the k-space. The present paper discusses the band structure of graphene based on the rectangular 4-atom unit cell model to establish an appropriate k-vector for the Bloch electron dynamics. To obtain the band energy of a Bloch electron in graphene, we extend the tight-binding calculations for the Wigner-Seitz (2-atom unit cell) model of Reich et al. (Physical Review B, 66, Article ID: 035412 (2002)) to the rectangular 4-atom unit cell model. It is shown that the graphene band structure based on the rectangular 4-atom unit cell model reveals the same band structure of the graphene based on the Wigner-Seitz 2-atom unit cell model;the π-band energy holds a linear dispersion (ε−k ) relations near the Fermi energy (crossing points of the valence and the conduction bands) in the first Brillouin zone of the rectangular reciprocal lattice. We then confirm the suitability of the proposed rectangular (orthogonal) unit cell model for graphene in order to establish a 2D k-vector responsible for the Bloch electron (wave packet) dynamics in graphene.