The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation metho...The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.展开更多
An solution to tooth deformation of parabola tooth belt has been obtainedby complex function method of plane elastic theory,with the tooth deformation specifiedand the middle line between neighboring teeth displaced.T...An solution to tooth deformation of parabola tooth belt has been obtainedby complex function method of plane elastic theory,with the tooth deformation specifiedand the middle line between neighboring teeth displaced.The law governing the toothdeformation under load and the effect of deformation on distribution of load are analysed aswell.Computer software has been compiled on the basis of this way of solution and anaccurate way of calculation is provided for study on tooth deformation and loaddistribution.展开更多
By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric...By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.展开更多
The limitations of several existing classical rock damage models were critically appraised. Thereafter, a description of a new model to estimate the response of rock was provided. The results of an investigation lead ...The limitations of several existing classical rock damage models were critically appraised. Thereafter, a description of a new model to estimate the response of rock was provided. The results of an investigation lead to the development and confirmation of a new index parabola damage model. The new model is divided into two parts, fictitious damage and real damage and bordered by the critical damage point. In fictitious damage, the damage variable follows the index distribution, while in the real damage a parabolic distribution is used. Thus, the so called index parabola damage model is derived. The proposed damage model is applied to simulate the damage procedure of marble under uni axial loading. The results of the tests show that the proposed model is in excellent agreement with experimental data, in particular the nonlinear characteristic of rock deformation is adequately represented. [展开更多
为快速拟定地锚式独塔悬索桥非对称主缆的合理设计参数,并估算主缆、锚碇、桥塔等工程量,提出非对称主缆合理设计参数计算方法。该方法基于传统抛物线理论,推导主缆的线形以及拉力近似解,通过比选得到满足工程实际控制因素的设计参数合...为快速拟定地锚式独塔悬索桥非对称主缆的合理设计参数,并估算主缆、锚碇、桥塔等工程量,提出非对称主缆合理设计参数计算方法。该方法基于传统抛物线理论,推导主缆的线形以及拉力近似解,通过比选得到满足工程实际控制因素的设计参数合理取值区间,确定主缆垂跨比与高跨比,估算主缆设计截面面积。以济新高速黄河三峡大桥--单跨510 m地锚式独塔回转缆钢桁梁悬索桥为背景,采用该方法计算主缆的合理设计参数,最终选择垂跨比为0.0675,高跨比为0.20,主缆截面面积为339024.2 mm 2,与节线法、分段悬链线法进行对比验证,结果表明:该计算方法路径明确,效率高,精度满足拟定方案与初步估算需要,可用于同类型桥梁的设计。展开更多
A diffraction-limited storage ring with a multi-bend achromat lattice suffers from a small dynamic aperture for conventional off-axis injection.Thus,a longitudinal on-axis injection scheme based on a new type of crab ...A diffraction-limited storage ring with a multi-bend achromat lattice suffers from a small dynamic aperture for conventional off-axis injection.Thus,a longitudinal on-axis injection scheme based on a new type of crab cavity is proposed in this paper.Particle tracking simulations were performed to study the disturbance of the stored beam and the motion of the injected beam during the injection process.The possibility of multi-bunch injections was discussed.In addition,the effect of the long-range wake field induced by the stored beam was analyzed.A C-band standing-wave crab cavity was designed and produced as requested,and its field distribution was measured.The corresponding results are consistent with the simulation results.展开更多
文摘The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.
文摘An solution to tooth deformation of parabola tooth belt has been obtainedby complex function method of plane elastic theory,with the tooth deformation specifiedand the middle line between neighboring teeth displaced.The law governing the toothdeformation under load and the effect of deformation on distribution of load are analysed aswell.Computer software has been compiled on the basis of this way of solution and anaccurate way of calculation is provided for study on tooth deformation and loaddistribution.
基金Project supported by the National Natural Science Foundation of China(No.10671179)the Natural Science Foundation of Yunnan Province of China(No.2003A0018M)
文摘By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.
文摘The limitations of several existing classical rock damage models were critically appraised. Thereafter, a description of a new model to estimate the response of rock was provided. The results of an investigation lead to the development and confirmation of a new index parabola damage model. The new model is divided into two parts, fictitious damage and real damage and bordered by the critical damage point. In fictitious damage, the damage variable follows the index distribution, while in the real damage a parabolic distribution is used. Thus, the so called index parabola damage model is derived. The proposed damage model is applied to simulate the damage procedure of marble under uni axial loading. The results of the tests show that the proposed model is in excellent agreement with experimental data, in particular the nonlinear characteristic of rock deformation is adequately represented. [
文摘为快速拟定地锚式独塔悬索桥非对称主缆的合理设计参数,并估算主缆、锚碇、桥塔等工程量,提出非对称主缆合理设计参数计算方法。该方法基于传统抛物线理论,推导主缆的线形以及拉力近似解,通过比选得到满足工程实际控制因素的设计参数合理取值区间,确定主缆垂跨比与高跨比,估算主缆设计截面面积。以济新高速黄河三峡大桥--单跨510 m地锚式独塔回转缆钢桁梁悬索桥为背景,采用该方法计算主缆的合理设计参数,最终选择垂跨比为0.0675,高跨比为0.20,主缆截面面积为339024.2 mm 2,与节线法、分段悬链线法进行对比验证,结果表明:该计算方法路径明确,效率高,精度满足拟定方案与初步估算需要,可用于同类型桥梁的设计。
基金the National Natural Science Foundation of China(Nos.11975298 and 12175292).
文摘A diffraction-limited storage ring with a multi-bend achromat lattice suffers from a small dynamic aperture for conventional off-axis injection.Thus,a longitudinal on-axis injection scheme based on a new type of crab cavity is proposed in this paper.Particle tracking simulations were performed to study the disturbance of the stored beam and the motion of the injected beam during the injection process.The possibility of multi-bunch injections was discussed.In addition,the effect of the long-range wake field induced by the stored beam was analyzed.A C-band standing-wave crab cavity was designed and produced as requested,and its field distribution was measured.The corresponding results are consistent with the simulation results.
