Crashworthiness analysis of aircraft fuselage with sine-wave beam structure

An integrated design concept for crashworthy fuselage using sine-wave beam and strut is proposed and investigated. The finite element model of aircraft fuselage is built first. The structures above cabin floor, occupant and seat are simplified as two rigid blocks. The fuselage frame is rede- signed, and the sine-wave beam is arranged under the frame. The impact dynamic performance of the aircraft with bottom sine-wave beam structure is studied and compared with that of conven- tional type. To obtain better crashworthiness performance, different rigidity of strut is combined with the sine-wave beam bottom structure. Numerical simulation result shows that the proposed sine-wave beam bottom structure could not only dissipate more proportion of impact kinetic energy but also reduce the initial peak acceleration. The structure and rigidity of strut have great influence on the crashworthiness performance. To give a better fuselage structure, both of the strut and bottom structure should be properly integrated and designed.

Resonant response of a strong electromagnetic wave beam to a gravitational wave in a static magnetic field

Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l and ωPg respectively. In the case of ωe?ωg, the PEMFs are manifested as the EM wave beams with frequency ωe and a standing EM wave with ωg. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ωg?ωe, all PEMFs are expressed as the standing EM waves with frequency ωg. The resonant response occurs in two cases of ωe = 1/2 ωg andωe, = ωg only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced. This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes of displaying perturbed effects induced by the standing GW withh = 10-33 - 10-35 and λg = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed.

Linear theory of beam–wave interaction in double-slot coupled cavity travelling wave tube

A three-dimensional model of the double-slot coupled cavity slow-wave structure （CCSWS） with a solid round elec- tron beam for the beam-wave interaction is presented. Based on the ＂cold＂ dispersion, the ＂hot＂ dispersion equation is derived with the Maxwell equations by using the variable separation method and the field-matching method. Through numerical calculations, the effects of the electron beam parameters and the staggered angle between adjacent walls on the linear gain are analyzed.

Theoretical and numerical investigation of HF elastic wave propagation in two-dimensional periodic beam lattices

The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane （with respect to the lattice plane） and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave prop- agation are highlighted in high frequency domains. One im- portant result presented herein is the comparison between the first Bloch wave modes to the membrane and bend- ing/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homog- enized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retro- propagating Bloch wave modes with a negative group veloc- ity, and of the corresponding ＂retro-propagating＂ frequency bands.

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.

A Novel Beam Design Method for mm Wave Multi-Antenna Arrays with Mutual Coupling Reduction

To overcome the mutual coupling (MC) of multiple antennas in millimeter wave (mmWave) communication systems, a novel beam design method with low complexity is proposed in this paper. Firstly, an equivalent channel model incorporating the effect of MC is analyzed and established, and then an optimal precoding / combiner vector for beamforming is derived. On this basis, by using greedy geometric (GG) algorithm, a novel hybrid beam design method is proposed. Finally, the performance of proposed method is analyzed and compared with other traditional ones. The simulation results show that the proposed method has better suppression of the MC effect as well as lower complexity.

NONLINEAR FLEXURAL WAVES IN LARGE-DEFLECTION BEAMS

The equation of motion for a large-deflection beam in the Lagrangian description are derived using the coupling of flexural deformation and midplane stretching as a key source of nonlinearity and taking into account the transverse, axial and rotary inertia effects. Assuming a traveling wave solution, the nonlinear partial differential equations are then transformed into ordinary differential equations. Qualitative analysis indicates that the system can have either a homoclinic orbit or a heteroclinic orbit, depending on whether the rotary inertia effect is taken into account. Furthermore, exact periodic solutions of the nonlinear wave equations are obtained by means of the Jacobi elliptic function expansion. When the modulus of the Jacobi elliptic function m→1 in the degenerate case, either a solitary wave solution or a shock wave solution can be obtained.

Gaussian beamed millimetre wave propagation characteristics due to reflecting behaviour in circle tunnel

Propagation characterization is one of the main building blocks for millimetre wave （MMW） communication. The Gaussian beam has attractive features to become a prospective wave form for millimetre radio communication, especially for the utility inside tunnels. A ray tracing method embedded with spectral features of Gaussian beam is employed to analyze mil- limetre wave propagation in a circle tunnel in this paper. In consideration of geometrical figure of the tunnel, the superposition behaviour of direct and reflective beams is analyzed via simplified approximation of Gaussian beam spectral feature. Then the propagation models are established to derive amplitude, phase, and delay spread of received wave. A typical straight tunnel model is used to simulate the propagation behaviour, where strong multi-path effect with deeply fading of signal intensity and dramatically enhancing of delay spread emerges. For investigation of the spectral feature of the multi-path effect, a reflection loss of 14 dB is taken into consideration at a designated point. To analyze the influences of frequency and transmission distance, the propagation characteristics at three different frequencies of 45 GHz, 65 GHz and 85 GHz are compared with the beam travelling down the tunnel. In addition, three different reflection losses of 14 dB, 20 dB, and 26 dB at the frequency of 65 GHz are also investigated to research the influence of the reflecting coefficient.

Research on Vibration Suppression of the Finite Plate with Square Steel Beams Using Traveling Wave Method

The vibration suppression of the finite plate with square steel beams is studied using traveling wave method. The finite plate with square beams is modeled as the coupling systems between the plate flexural motion and the flexural and torsional motions for the square beams. The vibration response at any position of the coupling structure can be obtained by wave method. Numerical results show that comparing to finite element method (FEM), not only the low frequency but also the medium-high frequency vibration response of the finite plate with square beam can be effectively calculated by wave method. The suppression effect can be increased as the square beam is located at one-third of the length of plate or increasing the height of the beam. The study provides reference for arranged square beams applying to vibration suppression of ship and train structures.

Analysis of wave propagation in micro/nanobeam-like structures: A size-dependent model

By incorporating the strain gradient elasticity into the classical Bernoulli-Euler beam and Timoshenko beam models, the size-dependent characteristics of wave propaga- tion in micro/nanobeams is studied. The formulations of dis- persion relation are explicitly derived for both strain gradi- ent beam models, and presented for different material length scale parameters （MLSPs）. For both phenomenological size- dependent beam models, the angular frequency, phase veloc- ity and group velocity increase with increasing wave num- ber. However, the velocity ratios approach different values for different beam models, indicating an interesting behavior of the asymptotic velocity ratio. The present theory is also compared with the nonlocal continuum beam models.

Effect of cyclotron resonance on ‘hot’ dispersion in a staggered double metallic grating sheet beam travelling wave tube

Based on the beam wave synchronous interaction in transverse and longitudinal directions at the same time and starting from Maxwell’s equation and linear Vlasov equation, the beam–wave interaction ‘hot’ dispersion equation considering both cyclotron resonance and Cherenkov resonance in a staggered double metallic grating traveling wave tube is deduced.Through the reasonable selection for geometric and electrical parameters, the numerical calculation and analysis of the ‘hot’ dispersion equation shows that the beam–wave interaction gain and frequency band with the cyclotron resonance enhancement effect are higher than those with only Cherenkov resonance radiation.

Complex modes and traveling waves in axially moving Timoshenko beams

Complex modes and traveling waves in axially moving Timoshenko beams are studied. Due to the axially moving velocity, complex modes emerge instead of real value modes. Correspondingly, traveling waves are present for the axially moving material while standing waves dominate in the traditional static structures. The analytical results obtained in this study are verified with a numerical differential quadrature method.

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

In this research, vibration and wave propagation analysis of a twisted micro- beam on Pasternak foundation is investigated. The strain-displacement relations （kine-matic equations） are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory （SGT） is used to implement the size dependent effect at micro-scale. Finally, using an energy method and Hamilton＇s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave prop- agation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is in- versely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.

Phased Array Beam Fields of Nonlinear Rayleigh Surface Waves

This study concerns calculation of phased array beam fields of the nonlinear Rayleigh surface waves based on the integral solutions for a nonparaxial wave equation. Since the parabolic approximation model for describing the nonlinear Rayleigh waves has certain limitations in modeling the sound beam fields of phased arrays, a more general model equation and integral forms of quasilinear solutions are introduced. Some features of steered and focused beam fields radiated from a linear phased array of the second harmonic Rayleigh wave are presented.

Forming of Space Charge Wave with Broad Frequency Spectrum in Helical Relativistic Two-Stream Electron Beams

We elaborate a quadratic nonlinear theory of plural interactions of growing space charge wave （SCW） harmonics during the development of the two-stream instability in helical relativistic electron beams. It is found that in helical two-stream electron beams the growth rate of the two-stream instability increases with the beam entrance angle. An SCW with the broad frequency spectrum, in which higher harmonics have higher amplitudes, forms when the frequency of the first SCW harmonic is much less than the critical frequency of the two-stream instability. For helical electron beams the spectrum expands with the increase of the beam entrance angle. Moreover, we obtain that utilizing helical electron beams in multiharmonic two-stream superheterodyne free-electron lasers leads to the improvement of their amplification characteristics, the frequency spectrum broadening in multiharmonic signal generation mode, and the reduction of the overall system dimensions.

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

We developed a cubic non-linear theory describing the dynamics of the multiharmonic spacecharge wave（SCW）, with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam（REB） parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.

Bessel-Beam Photoacoustic Microscopical Simulation Platform Based on k-Wave

We developed a Bessel-beam photoacoustic microscopical simulation platform by using the k-Wave: MATLAB toolbox. The simulation platform uses the ring slit method to generate Bessel beam. By controlling the inner and outer radius of the ring slit, the depth-of-field (DoF) of Bessel beam can be controlled. And the large volumetric image is obtained by point scanning. The simulation experiments on blood vessels were carried out to demonstrate the feasibility of the simulation platform. This simulation work can be used as an auxiliary tool for the research of Bessel-beam photoacoustic microscopy.

Ultrasonic beam focusing characteristics of shear-vertical waves for contact-type linear phased array in solid

We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.

Electromagnetic Resonance of Astigmatic Gaussian Beam to the High Frequency Gravitational Waves

The high frequency gravitational waves （around lOS-lO12 Hz） could interact with a specially designed electro- magnetic resonance system. It is found that the power of transverse perturbative photon flux （PPF） of an electromagnetic resonance system can be improved significantly by virtue of an astigmatic Caussian beam. Cor- respondingly the signal-to-noise ratio （SNR） would also be improved. When the eccentric ratio of waist satisfying w0x ： w0y 〉 1, the peak value of signal photon flux could be raised by 2-4 times with typical systematic parameters, while the background photon flux would be depressed. Therefore, the ratio of transverse PPF to background photon flux （i.e., SNR） can be further improved 3-8 times with dimensionless amplitude of relic gravitational wave ht = 10-36.

DESIGN OF BEAM-WAVE INTERACTION BASED ON HIGH EFFICIENCY OF A HIGH-POWER BROADBAND KLYSTRON

The paper mainly presents the design of beam-wave interaction of a C-band high-peakpower high-efficiency broadband klystron.The beam-wave interaction section is designed based on considerations of efficiency and bandwidth synthetically.As a part of beam-wave interaction section,buncher section is simulated by Particle-In-Cell(PIC) code to observe the bunching process of electron beam to achieve high conversion efficiency of electron beam and RF field.When it comes to the other part,output circuit is designed as a three-section filter by an output cavity loaded with Chebyshev filter,and the cold test results are given.The beam-wave interaction is simulated by EGUN code and Arsenal-MSU code respectively.The simulated results indicated that,the existence of power dips in the operating bandwidth is verified by Arsenal-MSU code,comparing proper results by EGUN code.Then,the method that design parameters are not adjusted except parameters of buncher cavities to remove potential power dips is described.What is more,the simulated results of electron optics system are given by EGUN code and Arsenal-MSU code respectively.The further hot test results of klystron prove that the whole design of beam-wave interaction is effective.