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, occupa...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.展开更多
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 p...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.展开更多
Active control of bending waves in a periodic beam by the Timoshenko beam theory is concerned. A discussion about the possible wave solutions for periodic beams and their control by forces is presented. Wave propagati...Active control of bending waves in a periodic beam by the Timoshenko beam theory is concerned. A discussion about the possible wave solutions for periodic beams and their control by forces is presented. Wave propagation in a periodic beam is studied. The transfer matrix between two consecutive unit cells is obtained based on the continuity conditions. Wave amplitudes are derived by employing the Bloch-Floquet theorem and the transfer matrix. The influences of the propagating constant on the wave amplitudes are considered. It is shown that vibrations are still needed to be suppressed in the pass-band regions. Wave-suppression strategy described in this paper is employed to eliminate the propagating disturbance of an infinite periodic beam. A minimum wave-suppression strategy is compared with the classical wave-suppression strategy.展开更多
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＂ di...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.展开更多
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 ...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.展开更多
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 deri...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.展开更多
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 mod...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.展开更多
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 t...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.展开更多
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...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.展开更多
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 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.展开更多
This paper is concerned with the wave propagation behavior of rotating functionally graded（FG）temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform...This paper is concerned with the wave propagation behavior of rotating functionally graded（FG）temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform,linear and nonlinear temperature distributions across the thickness are investigated.Thermo-elastic properties of FG beam change gradually according to the Mori–Tanaka distribution model in the spatial coordinate.The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function.The governing equations are derived by Hamilton’s principle as a function of axial force due to centrifugal stiffening and displacement.The solution of these equations is provided employing a Galerkin-based approach which has the potential to capture various boundary conditions.By applying an analytical solution and solving an eigenvalue problem,the dispersion relations of rotating FG nanobeam are obtained.Numerical results illustrate that various parameters including temperature change,angular velocity,nonlocality parameter,wave number and gradient index have significant effects on the wave dispersion characteristics of the nanobeam under study.The outcome of this study can provide beneficial information for the next-generation research and the exact design of nano-machines including nanoscale molecular bearings,nanogears,etc.展开更多
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 formulati...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.展开更多
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...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.展开更多
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 ...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.展开更多
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...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.展开更多
On studying traveling waves on a nonlinearly suspended bridge,the following partial differential equation has been considered:\$\$u\-\{tt\}+u\-\{xxxx\}+f(u)=0,\$\$where f(u)=u\++-1 .Here the bridge is seen as a vib...On studying traveling waves on a nonlinearly suspended bridge,the following partial differential equation has been considered:\$\$u\-\{tt\}+u\-\{xxxx\}+f(u)=0,\$\$where f(u)=u\++-1 .Here the bridge is seen as a vibrating beam supported by cables,which are treated as a spring with a one\|sided restoring force.The existence of a traveling wave solution to the above piece\|wise linear equation has been proved by solving the equation explicitly (McKenna & Walter in 1990).Recently the result has been extended to a group of equations with more general nonlinearities such as f(u)=u\++-1+g(u) (Chen & McKenna,1997).However,the restrictions on g(u) do not allow the resulting restoring force function to increase faster than the linear function u-1 for u >1.Since an interesting “multiton” behavior,that is ,two traveling waves appear to emerge intact after interacting nonlinearly with each other,has been observed in numerical experiments for a fast\|increasing nonlinearity f(u)=e u-1 -1 ,it hints that the conclusion of the existence of a traveling wave solution with fast\|increasing nonlinearities shall be valid as well.\;In this paper,the restoring force function of the form f(u)=u·h(u)-1 is considered.It is shown that a traveling wave solution exists when h(u)≥1 for u≥1 (with other assumptions which will be detailed in the paper),and hence allows f to grow faster than u-1 .It is shown that a solution can be obtained as a saddle point in a variational formulation.It is also easy to construct such fast\|increasing f(u) 's for more numerical tests.展开更多
In this paper, the disturbance propagation and active vibration control of a finite L-shaped beam axe studied. The dynamic response of the structure is obtained by the travelling wave approach. The active vibration su...In this paper, the disturbance propagation and active vibration control of a finite L-shaped beam axe studied. The dynamic response of the structure is obtained by the travelling wave approach. The active vibration suppression of the finite L-shaped beam is performed based on the structural vibration power flow. In the numerical calculation, the influences of the near field effect of the error sensor and the small error of the control forces on the control results are all considered. The simulation results indicate that the structural vibration response in the medium and high frequency regions can be effectively computed by the travelling wave method. The effect of the active control by controlling the power flow is much better than that by controlling the acceleration in some cases. And the control results by the power flow method are slightly affected by the locations of the error sensor and the small error of the control forces.展开更多
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 describi...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.展开更多
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 ...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.展开更多
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 relati...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.展开更多
基金co-supported by the National Natural Science Foundation of China(No.11402011)the Fundamental Research Funds for the Central Universities
文摘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.
基金We thank Profs. V. N. Rudenko and M. V. Sazhin for their helpful discussions and suggestions, colleagues of Sternberg Astronomical Institute of Moscow University for their hospitality, and Prof. Luo Jun of Huazhong University of Science and Technology fo
文摘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.
基金Project supported by the National Natural Science Foundation of China (No. 11102047)Special Funds of Central Basic Scientific Research Operating Expensesthe Fundamental Research Foundation of Harbin Engineering University(No. 002110260746)
文摘Active control of bending waves in a periodic beam by the Timoshenko beam theory is concerned. A discussion about the possible wave solutions for periodic beams and their control by forces is presented. Wave propagation in a periodic beam is studied. The transfer matrix between two consecutive unit cells is obtained based on the continuity conditions. Wave amplitudes are derived by employing the Bloch-Floquet theorem and the transfer matrix. The influences of the propagating constant on the wave amplitudes are considered. It is shown that vibrations are still needed to be suppressed in the pass-band regions. Wave-suppression strategy described in this paper is employed to eliminate the propagating disturbance of an infinite periodic beam. A minimum wave-suppression strategy is compared with the classical wave-suppression strategy.
基金Project supported by the National Natural Science Foundation of China(Grant No.11205162)
文摘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.
文摘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.
文摘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.
基金supported by Aeronautical Science Foundation of China (2017ZC52021)the Major Program of National Natural Science Foundation of China (61827801)
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.10772129 and 10702047).
文摘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.
基金supported by the Shanghai Leading Academic Discipline Project (Grant No.S30108)the Science and Technology Commission of Shanghai Municipality (Grant No.08DZ2231100)
文摘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.
基金National Natural Science Foundation of China ( No. 10972065) Natural Science Foundation of Heilongjiang Province of China( No. ZD200905)
文摘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.
文摘This paper is concerned with the wave propagation behavior of rotating functionally graded（FG）temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform,linear and nonlinear temperature distributions across the thickness are investigated.Thermo-elastic properties of FG beam change gradually according to the Mori–Tanaka distribution model in the spatial coordinate.The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function.The governing equations are derived by Hamilton’s principle as a function of axial force due to centrifugal stiffening and displacement.The solution of these equations is provided employing a Galerkin-based approach which has the potential to capture various boundary conditions.By applying an analytical solution and solving an eigenvalue problem,the dispersion relations of rotating FG nanobeam are obtained.Numerical results illustrate that various parameters including temperature change,angular velocity,nonlocality parameter,wave number and gradient index have significant effects on the wave dispersion characteristics of the nanobeam under study.The outcome of this study can provide beneficial information for the next-generation research and the exact design of nano-machines including nanoscale molecular bearings,nanogears,etc.
基金supported by the National Natural Science Foundation of China(11202117,11272186,11172231 and 50928601)the Postdoctoral Science Foundation of China(2012M521326)+3 种基金the Natural Science Fund of Shandong Province(ZR2012AM014 and BS2012ZZ006)Independent Innovation Fund of Shandong University(2011GN055)National Science Foundation(CMMI-0643726),DARPA(W91CRB-11-C-0112)Changjiang Scholar Program from Ministry of Education of China
文摘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.
基金supported by National Natural Science Foundation of China(No.61671431)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Nos.11672007 and11672186)the Training Scheme for the Youth Teachers of Higher Education of Shanghai(No.ZZyyy12035)the "Chen Guang" Project(No.14CG57)
文摘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.
基金Project supported by the Iranian Nanotechnology Development Committee and the University of Kashan(No.463855/11)
文摘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.
基金Project supported by National Natural Science Foundation of China! (19701029) by Outstanding Young Teacher Foundation of Chi
文摘On studying traveling waves on a nonlinearly suspended bridge,the following partial differential equation has been considered:\$\$u\-\{tt\}+u\-\{xxxx\}+f(u)=0,\$\$where f(u)=u\++-1 .Here the bridge is seen as a vibrating beam supported by cables,which are treated as a spring with a one\|sided restoring force.The existence of a traveling wave solution to the above piece\|wise linear equation has been proved by solving the equation explicitly (McKenna & Walter in 1990).Recently the result has been extended to a group of equations with more general nonlinearities such as f(u)=u\++-1+g(u) (Chen & McKenna,1997).However,the restrictions on g(u) do not allow the resulting restoring force function to increase faster than the linear function u-1 for u >1.Since an interesting “multiton” behavior,that is ,two traveling waves appear to emerge intact after interacting nonlinearly with each other,has been observed in numerical experiments for a fast\|increasing nonlinearity f(u)=e u-1 -1 ,it hints that the conclusion of the existence of a traveling wave solution with fast\|increasing nonlinearities shall be valid as well.\;In this paper,the restoring force function of the form f(u)=u·h(u)-1 is considered.It is shown that a traveling wave solution exists when h(u)≥1 for u≥1 (with other assumptions which will be detailed in the paper),and hence allows f to grow faster than u-1 .It is shown that a solution can be obtained as a saddle point in a variational formulation.It is also easy to construct such fast\|increasing f(u) 's for more numerical tests.
基金Project supported by the National Natural Science Foundation of China (Nos. 10672017 and 10632020)
文摘In this paper, the disturbance propagation and active vibration control of a finite L-shaped beam axe studied. The dynamic response of the structure is obtained by the travelling wave approach. The active vibration suppression of the finite L-shaped beam is performed based on the structural vibration power flow. In the numerical calculation, the influences of the near field effect of the error sensor and the small error of the control forces on the control results are all considered. The simulation results indicate that the structural vibration response in the medium and high frequency regions can be effectively computed by the travelling wave method. The effect of the active control by controlling the power flow is much better than that by controlling the acceleration in some cases. And the control results by the power flow method are slightly affected by the locations of the error sensor and the small error of the control forces.
基金Supported by the National Natural Science Foundation of China under Grant Nos 61271356 and 51575541the National Research Foundation of Korea under Grant Nos 2013-M2A2A9043241 and 2013-R1A2A2A01016042the Hunan Provincial Innovation Foundation For Postgraduate under Grant No CX2016B046
文摘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.
基金Supported by the Ministry of Education and Science of Ukraine under Grant No 0117U002253
文摘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.
基金supported by the Ministry of Education and Science of Ukraine under Grant No.0117U002253
文摘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.
