In recent years,heavy ion accelerator technology has been rapidly developing worldwide and widely applied in the fields of space radiation simulation and particle therapy.Usually,a very high uniformity in the irradiat...In recent years,heavy ion accelerator technology has been rapidly developing worldwide and widely applied in the fields of space radiation simulation and particle therapy.Usually,a very high uniformity in the irradiation area is required for the extracted ion beams,which is crucial because it directly affects the experimental precision and therapeutic effect.Specifically,ultra-large-area and high-uniformity scanning are crucial requirements for spacecraft radiation effects assessment and serve as core specification for beamline terminal design.In the 300 MeV proton and heavy ion accelerator complex at the Space Environment Simulation and Research Infrastructure(SESRI),proton and heavy ion beams will be accelerated and ultimately delivered to three irradiation terminals.In order to achieve the required large irradiation area of 320 mm×320 mm,horizontal and vertical scanning magnets are used in the extraction beam line.However,considering the various requirements for beam species and energies,the tracking accuracy of power supplies(PSs),the eddy current effect of scanning magnets,and the fluctuation of ion bunch structure will reduce the irradiation uniformity.To mitigate these effects,a beam uniformity optimization method based on the measured beam distribution was proposed and applied in the accelerator complex at SESRI.In the experiment,the uniformity is successfully optimized from 75%to over 90%after five iterations of adjustment to the PS waveforms.In this paper,the method and experimental results were introduced.展开更多
The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients....The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.展开更多
In order to simulate the coupling vibration of a vehicle or train moves on a multi-span continuous bridge with non-uniform cross sections, a moving mass model is used according to the Finite Element Method, the effect...In order to simulate the coupling vibration of a vehicle or train moves on a multi-span continuous bridge with non-uniform cross sections, a moving mass model is used according to the Finite Element Method, the effect of the inertial force, Coriolis force and centrifugal force are considered by means of the additive matrices. For a non-uniform rectangular section beam with both linear and parabolic variable heights in a plane, the stiffness and mass matrices of the beam elements are presented. For a non-uniform box girder, Romberg numerical integral scheme is adopted, each coefficient of the stiffness matrix is obtained by means of a normal numerical computation. By applying these elements to calculate the non-uniform beam, the computational accuracy and efficiency are improved. The finite element method program is worked out and an entire dynamic response process of the beam with non-uniform cross sections subjected to a moving mass is simulated numerically, the results are compared to those previously published for some simple examples. For some complex multi-span bridges subjected to some moving vehicles with changeable velocity and friction, the computational results, which can be regarded as a reference for engineering design and scientific research, are also given simultaneously.展开更多
The paper investigates the response of non-initially stressed Euler-Bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and mo...The paper investigates the response of non-initially stressed Euler-Bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and moving mass problem in order to determine the behaviour of the system under consideration. The analytical method in terms of series solution and numerical method were used for the governing equation. The effect of various beam observed that the response amplitude due to the moving force is greater than that due to moving mass. It was also found that the response amplitude of the moving force problem with non-initial stress increase as mass of the mass of the load M increases.展开更多
Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent ...Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.展开更多
The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the no...The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.展开更多
This paper investigates the existence and uniform decay of global solutions to the initial and boundary value problem with clamped boundary conditions for a nonlinear beam equation with a strong damping.
In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force ...In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force function is an analytic function,then the deflection function can be derived and expressed in Maclaurin series.A recurrence relation for the coefficients of the Maclaurin series is derived.It is shown that the proposed solution method is accurate and efficient.The solution method can be successfully applied to the uniform cantilever beam and non-linear elastic rotational boundary problem.展开更多
Heavy-ion-driven fusion (HIF) is a scheme to achieve inertial confinement fusion (ICF). Investigation of the non-uniformity of heavy-ion beam (HIB) irradiation is one of the key issues for ICF driven by powerful...Heavy-ion-driven fusion (HIF) is a scheme to achieve inertial confinement fusion (ICF). Investigation of the non-uniformity of heavy-ion beam (HIB) irradiation is one of the key issues for ICF driven by powerful heavy-ion beams. Ions in HIB impinge on the pellet surface and deposit their energy in a relatively deep and wide area. Therefore, the non-uniformity of HIB irradiation should be evaluated in the volume of the deposition area in the absorber layer. By using the OK1 code with some corrections, the non-uniformity of heavy-ion beam irradiation for the different ion beams on two kinds of targets were evaluated in 12-beam, 20-beam, 60-beam and 120-beam irradiation schemes. The root-mean-square (RMS) non-uniformity value becomes aRMS = 8.39% in an aluminum mono-layer pellet structure and aRMS = 6.53% in a lead-aluminum layer target for the 12-uranium-beam system. The RMS non-uniformity for the lead-aluminum layer target was lower than that for the mono-layer target. The RMS and peak-to-valley (PTV) non-uniformities are reduced with the increase in beam number, and low at the Bragg peak layer.展开更多
Purpose: To quantitatively evaluate four different Proton SFUD PBS initial planning strategies for lung mobile tumor. Methods and Materials: A virtual lung patient’s four-dimensional computed tomography (4DCT) was ge...Purpose: To quantitatively evaluate four different Proton SFUD PBS initial planning strategies for lung mobile tumor. Methods and Materials: A virtual lung patient’s four-dimensional computed tomography (4DCT) was generated in this study. To avoid the uncertainties from target delineation and imaging artifacts, a sphere with diameter of 3 cm representing a rigid mobile target (GTV) was inserted into the right side of the lung. The target motion is set in superior-inferior (SI) direction from ?5 mm to 5 mm. Four SFUD planning strategies were used based on: 1) Maximum-In-tensity-Projection Image (MIP-CT);2) CT_average with ITV overridden to muscle density (CTavg_muscle);3) CT_average with ITV overridden to tumor density (CTavg_tumor);4) CT_average without any override density (CTavg_only). Dose distributions were recalculated on each individual phase and accumulated together to assess the “actual” treatment. To estimate the impact of proton range uncertainties, +/?3.5% CT calibration curve was applied to the 4DCT phase images. Results: Comparing initial plan to the dose accumulation: MIP-CT based GTV D98 degraded 2.42 Gy (60.10 Gy vs 57.68 Gy). Heart D1 increased 6.19 Gy (1.88 Gy vs 8.07 Gy);CTavg_tumor based GTV D98 degraded 0.34 Gy (60.07 Gy vs 59.73 Gy). Heart D1 increased 2.24 Gy (3.74 Gy vs 5.98 Gy);CTavg_muscle based initial GTV D98 degraded 0.31 Gy (60.4 Gy vs 60.19 Gy). Heart D1 increased 3.44 Gy (4.38 Gy vs 7.82 Gy);CTavg_only based Initial GTV D98 degraded 6.63 Gy (60.11 Gy vs 53.48 Gy). Heart D1 increased 0.30 Gy (2.69 Gy vs 2.96 Gy);in the presence of ±3.5% range uncertainties, CTavg_tumor based plan’s accumulated GTV D98 degraded to 57.99 Gy (+3.5%) 59.38 Gy (?3.5%), and CTavg_muscle based plan’s accumulated GTV D98 degraded to 59.37 Gy (+3.5%) 59.37 Gy (?3.5%). Conclusion: This study shows that CTavg_Tumor and CTavg_Muscle based planning strategies provide the most robust GTV coverage. However, clinicians need to be aware that the actual dose to OARs at distal end of target may increase. The study also indicates that the current SFUD PBS planning strategy might not be sufficient to compensate the CT calibration uncertainty.展开更多
基金Supported by National Key R&D Program of China(2019YFA0405400)。
文摘In recent years,heavy ion accelerator technology has been rapidly developing worldwide and widely applied in the fields of space radiation simulation and particle therapy.Usually,a very high uniformity in the irradiation area is required for the extracted ion beams,which is crucial because it directly affects the experimental precision and therapeutic effect.Specifically,ultra-large-area and high-uniformity scanning are crucial requirements for spacecraft radiation effects assessment and serve as core specification for beamline terminal design.In the 300 MeV proton and heavy ion accelerator complex at the Space Environment Simulation and Research Infrastructure(SESRI),proton and heavy ion beams will be accelerated and ultimately delivered to three irradiation terminals.In order to achieve the required large irradiation area of 320 mm×320 mm,horizontal and vertical scanning magnets are used in the extraction beam line.However,considering the various requirements for beam species and energies,the tracking accuracy of power supplies(PSs),the eddy current effect of scanning magnets,and the fluctuation of ion bunch structure will reduce the irradiation uniformity.To mitigate these effects,a beam uniformity optimization method based on the measured beam distribution was proposed and applied in the accelerator complex at SESRI.In the experiment,the uniformity is successfully optimized from 75%to over 90%after five iterations of adjustment to the PS waveforms.In this paper,the method and experimental results were introduced.
基金Project supported by the National Natural Science Foundation of China(No.11672008)
文摘The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.
文摘In order to simulate the coupling vibration of a vehicle or train moves on a multi-span continuous bridge with non-uniform cross sections, a moving mass model is used according to the Finite Element Method, the effect of the inertial force, Coriolis force and centrifugal force are considered by means of the additive matrices. For a non-uniform rectangular section beam with both linear and parabolic variable heights in a plane, the stiffness and mass matrices of the beam elements are presented. For a non-uniform box girder, Romberg numerical integral scheme is adopted, each coefficient of the stiffness matrix is obtained by means of a normal numerical computation. By applying these elements to calculate the non-uniform beam, the computational accuracy and efficiency are improved. The finite element method program is worked out and an entire dynamic response process of the beam with non-uniform cross sections subjected to a moving mass is simulated numerically, the results are compared to those previously published for some simple examples. For some complex multi-span bridges subjected to some moving vehicles with changeable velocity and friction, the computational results, which can be regarded as a reference for engineering design and scientific research, are also given simultaneously.
文摘The paper investigates the response of non-initially stressed Euler-Bernoulli beam to uniform partially distributed moving loads. The governing partial differential equations were analyzed for both moving force and moving mass problem in order to determine the behaviour of the system under consideration. The analytical method in terms of series solution and numerical method were used for the governing equation. The effect of various beam observed that the response amplitude due to the moving force is greater than that due to moving mass. It was also found that the response amplitude of the moving force problem with non-initial stress increase as mass of the mass of the load M increases.
基金Project supported by the National Natural Science Foundation of China(Nos.11072157,11272219,11227201,and 10932006)the National Basic Research Program of China(No.2012CB723301)the Training Program for Leading Talent in University Innovative Research Team in Hebei Province(No.LJRC006)
文摘Free and steady state forced transverse vibrations of non-uniform beams are investigated with a proposed method, leading to a series solution. The obtained series is verified to be convergent and linearly independent in a convergence test and by the non-zero value of the corresponding Wronski determinant, respectively. The obtained solution is rigorous, which can be reduced to a classical solution for uniform beams. The proposed method can deal with arbitrary non-uniform Euler-Bernoulli beams in principle, but the methods in terms of special functions or elementary functions can only work in some special cases.
文摘The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.
基金Supported by the NNSF of china(11271066,11326158)Supported by the grant of Shanghai Education Commission(13ZZ048)Supported by the Doctoral Innovational Fund of Donghua University(BC201138)
文摘This paper investigates the existence and uniform decay of global solutions to the initial and boundary value problem with clamped boundary conditions for a nonlinear beam equation with a strong damping.
文摘In the paper,the analytic static deflection solutions of uniform cantilever beams resting on nonlinear elastic rotational boundary are developed by the Modified Adomian Decomposition Method(MADM).If the applied force function is an analytic function,then the deflection function can be derived and expressed in Maclaurin series.A recurrence relation for the coefficients of the Maclaurin series is derived.It is shown that the proposed solution method is accurate and efficient.The solution method can be successfully applied to the uniform cantilever beam and non-linear elastic rotational boundary problem.
文摘Heavy-ion-driven fusion (HIF) is a scheme to achieve inertial confinement fusion (ICF). Investigation of the non-uniformity of heavy-ion beam (HIB) irradiation is one of the key issues for ICF driven by powerful heavy-ion beams. Ions in HIB impinge on the pellet surface and deposit their energy in a relatively deep and wide area. Therefore, the non-uniformity of HIB irradiation should be evaluated in the volume of the deposition area in the absorber layer. By using the OK1 code with some corrections, the non-uniformity of heavy-ion beam irradiation for the different ion beams on two kinds of targets were evaluated in 12-beam, 20-beam, 60-beam and 120-beam irradiation schemes. The root-mean-square (RMS) non-uniformity value becomes aRMS = 8.39% in an aluminum mono-layer pellet structure and aRMS = 6.53% in a lead-aluminum layer target for the 12-uranium-beam system. The RMS non-uniformity for the lead-aluminum layer target was lower than that for the mono-layer target. The RMS and peak-to-valley (PTV) non-uniformities are reduced with the increase in beam number, and low at the Bragg peak layer.
文摘Purpose: To quantitatively evaluate four different Proton SFUD PBS initial planning strategies for lung mobile tumor. Methods and Materials: A virtual lung patient’s four-dimensional computed tomography (4DCT) was generated in this study. To avoid the uncertainties from target delineation and imaging artifacts, a sphere with diameter of 3 cm representing a rigid mobile target (GTV) was inserted into the right side of the lung. The target motion is set in superior-inferior (SI) direction from ?5 mm to 5 mm. Four SFUD planning strategies were used based on: 1) Maximum-In-tensity-Projection Image (MIP-CT);2) CT_average with ITV overridden to muscle density (CTavg_muscle);3) CT_average with ITV overridden to tumor density (CTavg_tumor);4) CT_average without any override density (CTavg_only). Dose distributions were recalculated on each individual phase and accumulated together to assess the “actual” treatment. To estimate the impact of proton range uncertainties, +/?3.5% CT calibration curve was applied to the 4DCT phase images. Results: Comparing initial plan to the dose accumulation: MIP-CT based GTV D98 degraded 2.42 Gy (60.10 Gy vs 57.68 Gy). Heart D1 increased 6.19 Gy (1.88 Gy vs 8.07 Gy);CTavg_tumor based GTV D98 degraded 0.34 Gy (60.07 Gy vs 59.73 Gy). Heart D1 increased 2.24 Gy (3.74 Gy vs 5.98 Gy);CTavg_muscle based initial GTV D98 degraded 0.31 Gy (60.4 Gy vs 60.19 Gy). Heart D1 increased 3.44 Gy (4.38 Gy vs 7.82 Gy);CTavg_only based Initial GTV D98 degraded 6.63 Gy (60.11 Gy vs 53.48 Gy). Heart D1 increased 0.30 Gy (2.69 Gy vs 2.96 Gy);in the presence of ±3.5% range uncertainties, CTavg_tumor based plan’s accumulated GTV D98 degraded to 57.99 Gy (+3.5%) 59.38 Gy (?3.5%), and CTavg_muscle based plan’s accumulated GTV D98 degraded to 59.37 Gy (+3.5%) 59.37 Gy (?3.5%). Conclusion: This study shows that CTavg_Tumor and CTavg_Muscle based planning strategies provide the most robust GTV coverage. However, clinicians need to be aware that the actual dose to OARs at distal end of target may increase. The study also indicates that the current SFUD PBS planning strategy might not be sufficient to compensate the CT calibration uncertainty.