针对弱扰动下Bonhoeffer-Van Der Pol振子表现出复杂类型的振荡,采用Poincare mapping和回归映射等非线性动力学的分析方法对其进行了研究,考察了弱扰动周期与强度对混合模式振荡类型的影响.结果表明:虽然研究的动力系统是简单的,但是...针对弱扰动下Bonhoeffer-Van Der Pol振子表现出复杂类型的振荡,采用Poincare mapping和回归映射等非线性动力学的分析方法对其进行了研究,考察了弱扰动周期与强度对混合模式振荡类型的影响.结果表明:虽然研究的动力系统是简单的,但是表现出的动力学行为是比较复杂的;所观察到的现象与相似的模型有着相关性.展开更多
针对扩展bonhoeffer-van der pol(BVP)振子易受不确定因素影响的问题,提出了将非线性动力学分析与数值模拟相结合的方法,并考察了弱扰动对混合模式振荡类型和同步行为的影响.根据模拟结果得知,多种类型的混合模式振荡受弱扰动的影响出...针对扩展bonhoeffer-van der pol(BVP)振子易受不确定因素影响的问题,提出了将非线性动力学分析与数值模拟相结合的方法,并考察了弱扰动对混合模式振荡类型和同步行为的影响.根据模拟结果得知,多种类型的混合模式振荡受弱扰动的影响出现了坍塌现象,且从理论上证明了两个耦合bonhoeffer-van der pol振子的膜电压比慢变量到达完全同步时所需的耦合强度要大,在二维参数平面上,膜电压到达同步时所取参数范围应小些.结果表明,与膜电压相比,慢变量更容易达到同步,且变量之间呈现一种线性关系.展开更多
In the process of deep projects excavation,deep rock often experiences a full stress process from high stress to unloading and then to impact disturbance failure.To study the dynamic characteristics of three-dimension...In the process of deep projects excavation,deep rock often experiences a full stress process from high stress to unloading and then to impact disturbance failure.To study the dynamic characteristics of three-dimensional high stressed red sandstone subjected to unloading and impact loads,impact compression tests were conducted on red sandstone under confining pressure unloading conditions using a modified split Hopkinson pressure bar.Impact disturbance tests of uniaxial pre-stressed rock were also conducted(without considering confining pressure unloading effect).The results demonstrate that the impact compression strength of red sandstone shows an obvious strain rate effect.With an approximately equal strain rate,the dynamic strength of red sandstone under confining unloading conditions is less than that in the uniaxial pre-stressed impact compression test.Confining pressure unloading produces a strength-weakening effect,and the dynamic strength weakening factor(DSWF)is also defined.The results also indicate that the strain rate of the rock and the incident energy change in a logarithmic relation.With similar incident energies,unloading results in a higher strain rate in pre-stressed rock.According to the experimental analysis,unloading does not affect the failure mode,but reduces the dynamic strength of pre-stressed rock.The influence of confining pressure unloading on the shear strength parameters(cohesion and friction angle)is discussed.Under the same external energy impact compression,prestressed rock subjected to unloading is more likely to be destroyed.Thus,the effect of unloading on the rock mechanical characteristics should be considered in deep rock project excavation design.展开更多
Tensile failure(spalling or slabbing)often occurs on the sidewall of deep tunnel,which is closely related to the coupled stress state of deep rock mass under high pre-static load and dynamic disturbance.To reveal the ...Tensile failure(spalling or slabbing)often occurs on the sidewall of deep tunnel,which is closely related to the coupled stress state of deep rock mass under high pre-static load and dynamic disturbance.To reveal the mechanism of rock tensile failure caused by this coupled stress mode,the Brazilian disc tests were carried on red sandstone under high pre-static load induced by dynamic disturbance.Based on the pure static tensile fracture load of red sandstone specimen,two static load levels(80%and 90%of the pure static tensile fracture load)were selected as the initial high pre-static loading state,and then the dynamic disturbance load was applied until the rock specimen was destroyed.The dynamic disturbance loading mode adopted a sinusoidal wave(sine-wave)load,and the loading wave amplitude was 20%and 10%of the pure static tensile fracture load,respectively.The dynamic disturbance frequencies were set to 1,10,20,30,40,and 50 Hz.The results show that the tensile failure strength and peak displacement of red sandstone specimens under coupled load actions are lower than those under pure static tensile load,and both parameters decrease significantly with the increase of dynamic disturbance frequency.With the increase of dynamic disturbance frequency,the decrease range of tensile strength of red sandstone increased from 3.3%to 9.4%when the pre-static load level is 80%.While when the pre-static load level is 90%,the decrease range will increase from 7.4%to 11.6%.This weakening effect of tensile strength shows that the deep surrounding rock is more likely to fail under the coupled load actions of pre-static load and dynamic disturbance.In this tensile failure mechanism of the deep surrounding rock,the stress environment of deep sidewall rock determines that the failure mode of rock is a tensile failure,the pre-static load level dominates the tensile failure strength of surrounding rock,and dynamic disturbance promotes the strength-weakening effect and affects the weakening range.展开更多
文摘针对弱扰动下Bonhoeffer-Van Der Pol振子表现出复杂类型的振荡,采用Poincare mapping和回归映射等非线性动力学的分析方法对其进行了研究,考察了弱扰动周期与强度对混合模式振荡类型的影响.结果表明:虽然研究的动力系统是简单的,但是表现出的动力学行为是比较复杂的;所观察到的现象与相似的模型有着相关性.
文摘针对扩展bonhoeffer-van der pol(BVP)振子易受不确定因素影响的问题,提出了将非线性动力学分析与数值模拟相结合的方法,并考察了弱扰动对混合模式振荡类型和同步行为的影响.根据模拟结果得知,多种类型的混合模式振荡受弱扰动的影响出现了坍塌现象,且从理论上证明了两个耦合bonhoeffer-van der pol振子的膜电压比慢变量到达完全同步时所需的耦合强度要大,在二维参数平面上,膜电压到达同步时所取参数范围应小些.结果表明,与膜电压相比,慢变量更容易达到同步,且变量之间呈现一种线性关系.
基金Projects(42077244,41877272)supported by the National Natural Science Foundation of ChinaProject(2020-05)supported by the Open Research Fund of Guangdong Provincial Key Laboratory of Deep Earth Sciences and Geothermal Energy Exploitation and Utilization,China。
文摘In the process of deep projects excavation,deep rock often experiences a full stress process from high stress to unloading and then to impact disturbance failure.To study the dynamic characteristics of three-dimensional high stressed red sandstone subjected to unloading and impact loads,impact compression tests were conducted on red sandstone under confining pressure unloading conditions using a modified split Hopkinson pressure bar.Impact disturbance tests of uniaxial pre-stressed rock were also conducted(without considering confining pressure unloading effect).The results demonstrate that the impact compression strength of red sandstone shows an obvious strain rate effect.With an approximately equal strain rate,the dynamic strength of red sandstone under confining unloading conditions is less than that in the uniaxial pre-stressed impact compression test.Confining pressure unloading produces a strength-weakening effect,and the dynamic strength weakening factor(DSWF)is also defined.The results also indicate that the strain rate of the rock and the incident energy change in a logarithmic relation.With similar incident energies,unloading results in a higher strain rate in pre-stressed rock.According to the experimental analysis,unloading does not affect the failure mode,but reduces the dynamic strength of pre-stressed rock.The influence of confining pressure unloading on the shear strength parameters(cohesion and friction angle)is discussed.Under the same external energy impact compression,prestressed rock subjected to unloading is more likely to be destroyed.Thus,the effect of unloading on the rock mechanical characteristics should be considered in deep rock project excavation design.
基金Projects(42077244,41877272,41472269)supported by the National Natural Science Foundation of ChinaProject(2242020R10023)supported by the Fundamental Research Funds for the Central Universities of Southeast University,China。
文摘Tensile failure(spalling or slabbing)often occurs on the sidewall of deep tunnel,which is closely related to the coupled stress state of deep rock mass under high pre-static load and dynamic disturbance.To reveal the mechanism of rock tensile failure caused by this coupled stress mode,the Brazilian disc tests were carried on red sandstone under high pre-static load induced by dynamic disturbance.Based on the pure static tensile fracture load of red sandstone specimen,two static load levels(80%and 90%of the pure static tensile fracture load)were selected as the initial high pre-static loading state,and then the dynamic disturbance load was applied until the rock specimen was destroyed.The dynamic disturbance loading mode adopted a sinusoidal wave(sine-wave)load,and the loading wave amplitude was 20%and 10%of the pure static tensile fracture load,respectively.The dynamic disturbance frequencies were set to 1,10,20,30,40,and 50 Hz.The results show that the tensile failure strength and peak displacement of red sandstone specimens under coupled load actions are lower than those under pure static tensile load,and both parameters decrease significantly with the increase of dynamic disturbance frequency.With the increase of dynamic disturbance frequency,the decrease range of tensile strength of red sandstone increased from 3.3%to 9.4%when the pre-static load level is 80%.While when the pre-static load level is 90%,the decrease range will increase from 7.4%to 11.6%.This weakening effect of tensile strength shows that the deep surrounding rock is more likely to fail under the coupled load actions of pre-static load and dynamic disturbance.In this tensile failure mechanism of the deep surrounding rock,the stress environment of deep sidewall rock determines that the failure mode of rock is a tensile failure,the pre-static load level dominates the tensile failure strength of surrounding rock,and dynamic disturbance promotes the strength-weakening effect and affects the weakening range.
