The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic material...The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic materials,the direct applications of the traditional single edge notched beam(SENB)method that ignores those typical structural characters may cause errors.To measure the surface fracture toughness more accurately,the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered.In this paper,a modified single edge V-notched beam(MSEVNB)method with typical structural characters is developed.According to the finite element analysis(FEA),the geometry factor of the multilayer structure is recalculated.Owing to the narrower V-notches,a more accurate critical fracture stress is obtained.Based on the Griffith energy balance,the reduction of the crack surface caused by micro-defects is corrected.The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.展开更多
Red-green-blue(RGB)beam combiners are widely used in scenarios such as augmented reality/virtual reality(AR/VR),laser projection,biochemical detection,and other fields.Optical waveguide combiners have attracted extens...Red-green-blue(RGB)beam combiners are widely used in scenarios such as augmented reality/virtual reality(AR/VR),laser projection,biochemical detection,and other fields.Optical waveguide combiners have attracted extensive attention due to their advantages of small size,high multiplexing efficiency,convenient mass production,and low cost.An RGB beam combiner based on directional couplers is designed,with a core-cladding relative refractive index difference of 0.75%.The RGB beam combiner is optimized from the perspective of parameter optimization.Using the beam propagation method(BPM),the relationship between the performance of the RGB beam combiner and individual parameters is studied,achieving preliminary optimization of the device’s performance.The key parameters of the RGB beam combiner are optimized using the entropy weight-technique for order preference by similarity to an ideal solution TOPSIS method,establishing the optimal parameter scheme and further improving the device’s performance indicators.The results show that after optimization,the multiplexing efficiencies for red,green,and blue lights,as well as the average multiplexing efficiency,reached 99.17%,99.76%,96.63%and 98.52%,respectively.The size of the RGB beam combiner is 4.768 mm×0.062 mm.展开更多
In this study,we design and numerically investigate a novel all optical D flip-flop(AODFF)based on linear photonic crystal(LPhC)structure that is composed of optical waveguides using the finite difference time domain(...In this study,we design and numerically investigate a novel all optical D flip-flop(AODFF)based on linear photonic crystal(LPhC)structure that is composed of optical waveguides using the finite difference time domain(FDTD)method.The proposed structure has the hexagonal close packed of 16×20 circular rods that are suspended in the air substrate with a lattice constant of 606 nm.The plane wave expansion(PWE)method is used to obtain the band diagram for AODFF at an operating wavelength of 1550 nm.The proposed optical flip-flop achieves a low delay time of 0.2 ps and a high contrast ratio(CR)of 10.33 dB.The main advantage of this design is that the input power as low as 1 mW/μm^(2) is sufficient for its operation,since no nonlinear rods are included.In addition,the footprint of the proposed AODFF is 100μm^(2),which is smaller compared to the structures reported in the literature,and it has a fast switching frequency of 5 Tbit/s.展开更多
As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gauss...As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.展开更多
A novel Eulerian Gaussian beam method was developed in[8]to compute the Schrödinger equation efficiently in the semiclassical regime.In this paper,we introduce an efficient semi-Eulerian implementation of this me...A novel Eulerian Gaussian beam method was developed in[8]to compute the Schrödinger equation efficiently in the semiclassical regime.In this paper,we introduce an efficient semi-Eulerian implementation of this method.The new algorithm inherits the essence of the Eulerian Gaussian beam method where the Hessian is computed through the derivatives of the complexified level set functions instead of solving the dynamic ray tracing equation.The difference lies in that,we solve the ray tracing equations to determine the centers of the beams and then compute quantities of interests only around these centers.This yields effectively a local level set implementation,and the beam summation can be carried out on the initial physical space instead of the phase plane.As a consequence,it reduces the computational cost and also avoids the delicate issue of beam summation around the caustics in the Eulerian Gaussian beam method.Moreover,the semi-Eulerian Gaussian beam method can be easily generalized to higher order Gaussian beam methods,which is the topic of the second part of this paper.Several numerical examples are provided to verify the accuracy and efficiency of both the first order and higher order semi-Eulerian methods.展开更多
A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first ...A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.展开更多
Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained result...Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.展开更多
The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, fl...The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.展开更多
With the third innovation in science and technology worldwide, China has also experienced thismarvelous progress. Concerning the longwall mining in China, the ＂masonry beam theory＂ （MBT） wasfirst proposed in the 1...With the third innovation in science and technology worldwide, China has also experienced thismarvelous progress. Concerning the longwall mining in China, the ＂masonry beam theory＂ （MBT） wasfirst proposed in the 1960s, illustrating that the transmission and equilibrium method of overburdenpressure using reserved coal pillar in mined-out areas can be realized. This forms the so-called ＂121mining method＂, which lays a solid foundation for development of mining science and technology inChina. The ＂transfer rock beam theory＂ （TRBT） proposed in the 1980s gives a further understanding forthe transmission path of stope overburden pressure and pressure distribution in high-stress areas. In thisregard, the advanced 121 mining method was proposed with smaller coal pillar for excavation design,making significant contributions to improvement of the coal recovery rate in that era. In the 21st century,the traditional mining technologies faced great challenges and, under the theoretical developmentspioneered by Profs. Minggao Qian and Zhenqi Song, the ＂cutting cantilever beam theory＂ （CCBT） wasproposed in 2008. After that the 110 mining method is formulated subsequently, namely one stope face,after the first mining cycle, needs one advanced gateway excavation, while the other one is automaticallyformed during the last mining cycle without coal pillars left in the mining area. This method can beimplemented using the CCBT by incorporating the key technologies, including the directional presplittingroof cutting, constant resistance and large deformation （CRLD） bolt/anchor supporting systemwith negative Poisson＇s ratio （NPR） effect material, and remote real-time monitoring technology. TheCCBT and 110 mining method will provide the theoretical and technical basis for the development ofmining industry in China.展开更多
Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the...Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.展开更多
Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for st...Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method（FEM） results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli（EB） beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.展开更多
In this paper, a new analytical method for vibration analysis of a cracked simply supported beam is investigated. By considering a nonlinear model for the fatigue crack, the governing equation of motion of the cracked...In this paper, a new analytical method for vibration analysis of a cracked simply supported beam is investigated. By considering a nonlinear model for the fatigue crack, the governing equation of motion of the cracked beam is solved using perturbation method. The solution of the governing equation reveals the superhaxmonics of the fundamental frequency due to the nonlinear effects in the dynamic response of the cracked beam. Furthermore, considering such a solution, an explicit expression is also derived for the system damping changes due to the changes in the crack parameters, geometric dimensions and mechanical properties of the cracked beam. The results show that an increase in the crack severity and approaching the crack location to the middle of the beam increase the system damping. In order to validate the results, changes in the fundamental frequency ratios against the fatigue crack severities are compared with those of experimental results available in the literature. Also, a comparison is made between the free response of the cracked beam with a given crack depth and location obtained by the proposed analytical solution and that of the numerical method. The results of the proposed method agree with the experimental and numerical results.展开更多
A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly wi...A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly without any increase of the computation time,whereas the error in the ordinary wide-angle beam propagation method is typically o (Δ x ) 2.With trivial programming changes,the accuracy is higher,especially in wide-angle propagation.展开更多
A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite...A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.展开更多
The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. T...The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional derivatives.展开更多
The bearing beams and the supporting beams under low velocity impact may be in four different strain stages of deformation depending on the impact intensity and beam structure strength.Based on the different judging c...The bearing beams and the supporting beams under low velocity impact may be in four different strain stages of deformation depending on the impact intensity and beam structure strength.Based on the different judging conditions of deformation stages,the corresponding calculation models are proposed,the calculation formulae for the determination of the impact force and the beam's lateral displacement are obtained.Calculation shows that the beam's total deflection is small when the flexibility of the supporting component is high and the effect of diminishing deflection disappears almost when the stiffness of the supporting component is high.展开更多
This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-...This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-mmthick titanium component was proposed,in which a column–cone combined heat source model was used to simulate the temperature field and a thermo-elastic–plastic model to analyze residual stress in a weld joint based on ABAQUS software.Considering the uncertainty of welding simulation,the computation was calibrated by experimental data of contour measurement method.Both test and simulated results show that residual stresses on the surface and inside the weld zone are significantly different and present a narrow and large gradient feature in the weld joint.The peak tensile stress exceeds the yield strength of base materials inside weld,which are distinctly different from residual stress of the thin Ti-6Al-4V alloy plates presented in references before.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
The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The r...The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the eff ects of the Winkler coeffi cient, Pasternak coeffi cient and damping coeffi cient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary diff erential equations with variable coeffi cients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verifi ed through two numerical examples. The infl uences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with diff erent taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.展开更多
The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a ...The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.12172048 and 12027901)the National Science and Technology Major Project of China(Nos.2019-Ⅶ-0007-0147 and 2017-Ⅵ-0020-0093)。
文摘The surface fracture toughness is an important mechanical parameter for studying the failure behavior of air plasma sprayed(APS)thermal barrier coatings(TBCs).As APS TBCs are typical multilayer porous ceramic materials,the direct applications of the traditional single edge notched beam(SENB)method that ignores those typical structural characters may cause errors.To measure the surface fracture toughness more accurately,the effects of multilayer and porous characters on the fracture toughness of APS TBCs should be considered.In this paper,a modified single edge V-notched beam(MSEVNB)method with typical structural characters is developed.According to the finite element analysis(FEA),the geometry factor of the multilayer structure is recalculated.Owing to the narrower V-notches,a more accurate critical fracture stress is obtained.Based on the Griffith energy balance,the reduction of the crack surface caused by micro-defects is corrected.The MSEVNB method can measure the surface fracture toughness more accurately than the SENB method.
基金Project(52175445)supported by the National Natural Science Foundation of ChinaProject(2022JJ30743)supported by the Natural Science Foundation of Hunan Province,China+1 种基金Project(2023GK2024)supported by the Key Research and Development Program of Hunan Province,ChinaProject(2023ZZTS0391)supported by the Fundamental Research Funds for the Central Universities of China。
文摘Red-green-blue(RGB)beam combiners are widely used in scenarios such as augmented reality/virtual reality(AR/VR),laser projection,biochemical detection,and other fields.Optical waveguide combiners have attracted extensive attention due to their advantages of small size,high multiplexing efficiency,convenient mass production,and low cost.An RGB beam combiner based on directional couplers is designed,with a core-cladding relative refractive index difference of 0.75%.The RGB beam combiner is optimized from the perspective of parameter optimization.Using the beam propagation method(BPM),the relationship between the performance of the RGB beam combiner and individual parameters is studied,achieving preliminary optimization of the device’s performance.The key parameters of the RGB beam combiner are optimized using the entropy weight-technique for order preference by similarity to an ideal solution TOPSIS method,establishing the optimal parameter scheme and further improving the device’s performance indicators.The results show that after optimization,the multiplexing efficiencies for red,green,and blue lights,as well as the average multiplexing efficiency,reached 99.17%,99.76%,96.63%and 98.52%,respectively.The size of the RGB beam combiner is 4.768 mm×0.062 mm.
文摘In this study,we design and numerically investigate a novel all optical D flip-flop(AODFF)based on linear photonic crystal(LPhC)structure that is composed of optical waveguides using the finite difference time domain(FDTD)method.The proposed structure has the hexagonal close packed of 16×20 circular rods that are suspended in the air substrate with a lattice constant of 606 nm.The plane wave expansion(PWE)method is used to obtain the band diagram for AODFF at an operating wavelength of 1550 nm.The proposed optical flip-flop achieves a low delay time of 0.2 ps and a high contrast ratio(CR)of 10.33 dB.The main advantage of this design is that the input power as low as 1 mW/μm^(2) is sufficient for its operation,since no nonlinear rods are included.In addition,the footprint of the proposed AODFF is 100μm^(2),which is smaller compared to the structures reported in the literature,and it has a fast switching frequency of 5 Tbit/s.
基金Research Program of China under the grant 2005CB321701supported by a Van Vleck Distinguished Research Prize from University of Wisconsin-Madison
文摘As an important model in quantum semiconductor devices, the SchrSdinger-Poisson equations have generated widespread interests in both analysis and numerical simulations in recent years. In this paper, we present Gaussian beam methods for the numerical simulation of the one-dimensional Schrodinger-Poisson equations. The Gaussian beam methods for high frequency waves outperform the geometrical optics method in that the former are accurate even around caustics. The purposes of the paper are first to develop the Gaussian beam methods, based on our previous methods for the linear SchrSdinger equation, for the Schrodinger-Poisson equations, and then check their validity for this weakly-nonlinear system.
基金This work was partially supported by NSF grant No.DMS-0608720,NSF FRG grant DMS-0757285,NSAF Projects 10676017,NSFC Projects 10971115the National Basic Research Program of China under the grant 2005CB321701.SJin was also supported by a Van Vleck Distinguished Research Prize from University of Wisconsin-Madison.
文摘A novel Eulerian Gaussian beam method was developed in[8]to compute the Schrödinger equation efficiently in the semiclassical regime.In this paper,we introduce an efficient semi-Eulerian implementation of this method.The new algorithm inherits the essence of the Eulerian Gaussian beam method where the Hessian is computed through the derivatives of the complexified level set functions instead of solving the dynamic ray tracing equation.The difference lies in that,we solve the ray tracing equations to determine the centers of the beams and then compute quantities of interests only around these centers.This yields effectively a local level set implementation,and the beam summation can be carried out on the initial physical space instead of the phase plane.As a consequence,it reduces the computational cost and also avoids the delicate issue of beam summation around the caustics in the Eulerian Gaussian beam method.Moreover,the semi-Eulerian Gaussian beam method can be easily generalized to higher order Gaussian beam methods,which is the topic of the second part of this paper.Several numerical examples are provided to verify the accuracy and efficiency of both the first order and higher order semi-Eulerian methods.
文摘A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.
文摘Chaotic vibrations of flexible non-linear Euler-Bernoulli beams subjected to harmonic load and with various boundary conditions（symmetric and non-symmetric）are studied in this work.Reliability of the obtained results is verified by the finite difference method（FDM）and the finite element method（FEM）with the Bubnov-Galerkin approximation for various boundary conditions and various dynamic regimes（regular and non-regular）.The influence of boundary conditions on the Euler-Bernoulli beams dynamics is studied mainly,dynamic behavior vs.control parameters { ωp,q0 } is reported,and scenarios of the system transition into chaos are illustrated.
基金Project supported by the National Natural Science Foundation of China(Nos.11672007,11402028,11322214,and 11290152)the Beijing Natural Science Foundation(No.3172003)the Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education,Northeastern University(No.VCAME201601)
文摘The mathematical modeling of a rotating tapered Timoshenko beam with preset and pre-twist angles is constructed. The partial differential equations governing the six degrees, i.e., three displacements in the axial, flapwise, and edgewise directions and three cross-sectional angles of torsion, flapwise bending, and edgewise bending, are obtained by the Euler angle descriptions. The power series method is then used to inves- tigate the natural frequencies and the corresponding complex mode functions. It is found that all the natural frequencies are increased by the centrifugal stiffening except the twist frequency, which is slightly decreased. The tapering ratio increases the first transverse, torsional, and axial frequencies, while decreases the second transverse frequency. Because of the pre-twist, all the directions are gyroscopically coupled with the phase differences among the six degrees.
基金supported by the National Natural Science Foundation of China (No. 51404278)the State Key Program of National Natural Science Foundation of China (No. 51134005)
文摘With the third innovation in science and technology worldwide, China has also experienced thismarvelous progress. Concerning the longwall mining in China, the ＂masonry beam theory＂ （MBT） wasfirst proposed in the 1960s, illustrating that the transmission and equilibrium method of overburdenpressure using reserved coal pillar in mined-out areas can be realized. This forms the so-called ＂121mining method＂, which lays a solid foundation for development of mining science and technology inChina. The ＂transfer rock beam theory＂ （TRBT） proposed in the 1980s gives a further understanding forthe transmission path of stope overburden pressure and pressure distribution in high-stress areas. In thisregard, the advanced 121 mining method was proposed with smaller coal pillar for excavation design,making significant contributions to improvement of the coal recovery rate in that era. In the 21st century,the traditional mining technologies faced great challenges and, under the theoretical developmentspioneered by Profs. Minggao Qian and Zhenqi Song, the ＂cutting cantilever beam theory＂ （CCBT） wasproposed in 2008. After that the 110 mining method is formulated subsequently, namely one stope face,after the first mining cycle, needs one advanced gateway excavation, while the other one is automaticallyformed during the last mining cycle without coal pillars left in the mining area. This method can beimplemented using the CCBT by incorporating the key technologies, including the directional presplittingroof cutting, constant resistance and large deformation （CRLD） bolt/anchor supporting systemwith negative Poisson＇s ratio （NPR） effect material, and remote real-time monitoring technology. TheCCBT and 110 mining method will provide the theoretical and technical basis for the development ofmining industry in China.
基金Project supported by the China Postdoctoral Science Foundation(No.2018M630167)
文摘Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.
基金Project supported by the Program for New Century Excellent Talents in Universities(NCET)by the Ministry of Education of China(No.NCET-04-0373)
文摘Based on the method of reverberation ray matrix（MRRM）, a reverberation matrix for planar framed structures composed of anisotropic Timoshenko（T） beam members containing completely hinged joints is developed for static analysis of such structures.In the MRRM for dynamic analysis, amplitudes of arriving and departing waves for joints are chosen as unknown quantities. However, for the present case of static analysis, displacements and rotational angles at the ends of each beam member are directly considered as unknown quantities. The expressions for stiffness matrices for anisotropic beam members are developed. A corresponding reverberation matrix is derived analytically for exact and unified determination on the displacements and internal forces at both ends of each member and arbitrary cross sectional locations in the structure. Numerical examples are given and compared with the finite element method（FEM） results to validate the present model. The characteristic parameter analysis is performed to demonstrate accuracy of the present model with the T beam theory in contrast with errors in the usual model based on the Euler-Bernoulli（EB） beam theory. The resulting reverberation matrix can be used for exact calculation of anisotropic framed structures as well as for parameter analysis of geometrical and material properties of the framed structures.
文摘In this paper, a new analytical method for vibration analysis of a cracked simply supported beam is investigated. By considering a nonlinear model for the fatigue crack, the governing equation of motion of the cracked beam is solved using perturbation method. The solution of the governing equation reveals the superhaxmonics of the fundamental frequency due to the nonlinear effects in the dynamic response of the cracked beam. Furthermore, considering such a solution, an explicit expression is also derived for the system damping changes due to the changes in the crack parameters, geometric dimensions and mechanical properties of the cracked beam. The results show that an increase in the crack severity and approaching the crack location to the middle of the beam increase the system damping. In order to validate the results, changes in the fundamental frequency ratios against the fatigue crack severities are compared with those of experimental results available in the literature. Also, a comparison is made between the free response of the cracked beam with a given crack depth and location obtained by the proposed analytical solution and that of the numerical method. The results of the proposed method agree with the experimental and numerical results.
文摘A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly without any increase of the computation time,whereas the error in the ordinary wide-angle beam propagation method is typically o (Δ x ) 2.With trivial programming changes,the accuracy is higher,especially in wide-angle propagation.
文摘A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.
基金Project supported by the National Natural Science Foundation of China(Nos.10547124 and 10475055)
文摘The analytical solution of a viscoelastic continuous beam whose damping characteristics are described in terms of a fractional derivative of arbitrary order was derived by means of the AdoInian decomposition method. The solution contains arbitrary initial conditions and zero input. For specific analysis, the initial conditions were assumed homogeneous, and the input force was treated as a special process with a particular beam. Two simple cases, step and impulse function responses, were considered respectively. Subsequently, some figures were plotted to show the displacement of the beam under different sets of parameters including different orders of the fractional derivatives.
基金the National Science Foundation of China(50578158)
文摘The bearing beams and the supporting beams under low velocity impact may be in four different strain stages of deformation depending on the impact intensity and beam structure strength.Based on the different judging conditions of deformation stages,the corresponding calculation models are proposed,the calculation formulae for the determination of the impact force and the beam's lateral displacement are obtained.Calculation shows that the beam's total deflection is small when the flexibility of the supporting component is high and the effect of diminishing deflection disappears almost when the stiffness of the supporting component is high.
基金supported by the National Natural Science Foundation of China (No.50935008)
文摘This work was to reveal the residual stress profile in electron beam welded Ti-6Al-4V alloy plates（50 mm thick） by using finite element and contour measurement methods.A three-dimensional finite element model of 50-mmthick titanium component was proposed,in which a column–cone combined heat source model was used to simulate the temperature field and a thermo-elastic–plastic model to analyze residual stress in a weld joint based on ABAQUS software.Considering the uncertainty of welding simulation,the computation was calibrated by experimental data of contour measurement method.Both test and simulated results show that residual stresses on the surface and inside the weld zone are significantly different and present a narrow and large gradient feature in the weld joint.The peak tensile stress exceeds the yield strength of base materials inside weld,which are distinctly different from residual stress of the thin Ti-6Al-4V alloy plates presented in references before.
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.
基金AHKJT of China under Grant Nos.1708085QE121 and 1808085ME147AHEDU of China under Grant No.TSKJ2017B13
文摘The characteristics of transverse free vibration of a tapered Timoshenko beam under an axially conservative compression resting on visco-Pasternak foundations are investigated by the interpolating matrix method. The research is executed in view of a three-parameter foundation which includes the eff ects of the Winkler coeffi cient, Pasternak coeffi cient and damping coeffi cient of the elastic medium. The governing equations of free vibration of a non-prismatic Timoshenko beam under an axially conservative force resting on visco-Pasternak foundations are transformed into ordinary diff erential equations with variable coeffi cients in light of the bending rotation angle and transverse displacement. All the natural frequencies orders together with the corresponding mode shapes of the beam are calculated at the same time, and a good convergence and accuracy of the proposed method is verifi ed through two numerical examples. The infl uences of foundation mechanical characteristics together with rotary inertia and shear deformation on natural frequencies of the beam with diff erent taper ratios are analyzed. A comprehensive parametric numerical study is carried out emphasizing the primary parameters that describe the dynamic property of the beam.
基金supported by the National Basic Research Program of China (Grant 2013CB733004)
文摘The dynamic characteristics of a beam-cable coupled system are investigated using an improved Chebyshev spectral element method in order to observe the effects of adding cables on the beam. The system is modeled as a double Timoshenko beam system interconnected by discrete springs. Utilizing Chebyshev series expansion and meshing the system according to the locations of its connections, numerical results of the natural frequencies and mode shapes are obtained using only a few elements, and the results are validated by comparing them with the results of a finite-element method. Then the effects of the cable parameters and layout of connections on the natural frequencies and mode shapes of a fixed-pinned beam are studied. The results show that the modes of a beam-cable coupled system can be classified into two types, beam mode and cable mode, according to the dominant deformation. To avoid undesirable vibrations of the cable, its parameters should be controlled in a reasonable range, or the layout of the connections should be optimized.
