This paper studies the coupling mechanism between the nonlinear stiffness and damping coefficients of Active Elastic Support/Dry Friction Damper(AESDFD)and rotor system.First,parameters for evaluating the vibration re...This paper studies the coupling mechanism between the nonlinear stiffness and damping coefficients of Active Elastic Support/Dry Friction Damper(AESDFD)and rotor system.First,parameters for evaluating the vibration reduction characteristics are proposed to facilitate the design of the AESDFD.To achieve this,the nonlinear friction force is initially represented as equivalent stiffness and damping coefficients,based on the ball-plate friction model.Second,three evaluation parameters—optimal slipping displacement,loss factor,and controllability—are proposed to reveal the vibration reduction characteristics of the AESDFD,alongside determining the optimal normal force.Subsequently,the finite element method,in conjunction with the ball-plate friction model,is introduced to formulate the governing equation of a low-pressure rotor system equipped with AESDFDs.The steady-state responses of the AESDFDs-rotor system are solved using the harmonic balance method combined with an efficient iteration method.Finally,the solutions are validated on the AESDFDs-rotor system both numerically and experimentally.The results indicate that controllability effectively assesses the vibration reduction performance of the AESDFD and is relatively insensitive to variations in low normal force.Away from the critical speed,the AESDFD suppresses vibration by altering the resonance position of the rotor system through its stiffness coefficient.Near the critical speed,vibration reduction is achieved primarily through energy dissipation by the damping coefficient.If the loss factor is less than one,the stiffness coefficient can diminish the vibration reduction effect of the damping coefficient.Notably,the optimal normal force of the AESDFD achieves optimal vibration reduction effect.This study reveals that changes in rotor system unbalance do not affect the vibration reduction characteristics of the AESDFD,with the same upper limit to the vibration reduction effect of the AESDFD.展开更多
This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We c...This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We consider both focusing and defocusing nonlinearities,with exponents of the nonlinearityσ∈[0,2)andσ∈[0,∞),and prove the polynomial mixing which implies the uniqueness of the invariant measure by using a coupling method.In the focusing case,our result generalizes the earlier results in[12],whereσ=1.展开更多
In recent years,with the increasing attention to issues related to carbon emissions,such as carbon tariffs and government netzero carbon emission policies,carbon emissions have become an important indicator that is be...In recent years,with the increasing attention to issues related to carbon emissions,such as carbon tariffs and government netzero carbon emission policies,carbon emissions have become an important indicator that is being prioritized by governments worldwide.The Google Environmental Insights Explorer(EIE)tool has been developed to facilitate the collection and integration of data in this context.This study focuses on Tainan City and utilizes EIE to analyze greenhouse gas emissions from transportation.By using EIE,the study obtains data on greenhouse gas emissions from transportation activities in Tainan City.EIE utilizes data collected by Google and simulation functions to estimate data based on actual measurements of transportation activities.This tool saves time and resources by eliminating the need for on-site investigations while providing data that closely represent the real emissions from transportation activities in urban areas.Transportation vehicles contribute to greenhouse gas emissions in two ways:through direct combustion of fossil fuels and through the consumption of electricity in electric vehicles(EVs).The level of greenhouse gas emissions in a city’s transportation industry depends on factors such as transportation modes,fuel types,fleet age and energy efficiency,total distance traveled,and annual mileage.EIE estimates the greenhouse gas emissions from Tainan City’s transportation industry in 2022 to be 3,320,000 metric tons,including emissions from buses,motorcycles,cars,walking,railways,bicycles,and other modes of transportation.展开更多
We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argum...We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.展开更多
基金supported by the National Science and Technology Major Project,China,the China Scholarship Council(No.202306290109)National Natural Science Foundation of China(Nos.52472456 and 52361165620)。
文摘This paper studies the coupling mechanism between the nonlinear stiffness and damping coefficients of Active Elastic Support/Dry Friction Damper(AESDFD)and rotor system.First,parameters for evaluating the vibration reduction characteristics are proposed to facilitate the design of the AESDFD.To achieve this,the nonlinear friction force is initially represented as equivalent stiffness and damping coefficients,based on the ball-plate friction model.Second,three evaluation parameters—optimal slipping displacement,loss factor,and controllability—are proposed to reveal the vibration reduction characteristics of the AESDFD,alongside determining the optimal normal force.Subsequently,the finite element method,in conjunction with the ball-plate friction model,is introduced to formulate the governing equation of a low-pressure rotor system equipped with AESDFDs.The steady-state responses of the AESDFDs-rotor system are solved using the harmonic balance method combined with an efficient iteration method.Finally,the solutions are validated on the AESDFDs-rotor system both numerically and experimentally.The results indicate that controllability effectively assesses the vibration reduction performance of the AESDFD and is relatively insensitive to variations in low normal force.Away from the critical speed,the AESDFD suppresses vibration by altering the resonance position of the rotor system through its stiffness coefficient.Near the critical speed,vibration reduction is achieved primarily through energy dissipation by the damping coefficient.If the loss factor is less than one,the stiffness coefficient can diminish the vibration reduction effect of the damping coefficient.Notably,the optimal normal force of the AESDFD achieves optimal vibration reduction effect.This study reveals that changes in rotor system unbalance do not affect the vibration reduction characteristics of the AESDFD,with the same upper limit to the vibration reduction effect of the AESDFD.
基金supported by the National Key R&D Program of China(2023YFA1009200)the NSFC(11925102)the Liaoning Revitalization Talents Program(XLYC2202042)。
文摘This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We consider both focusing and defocusing nonlinearities,with exponents of the nonlinearityσ∈[0,2)andσ∈[0,∞),and prove the polynomial mixing which implies the uniqueness of the invariant measure by using a coupling method.In the focusing case,our result generalizes the earlier results in[12],whereσ=1.
文摘In recent years,with the increasing attention to issues related to carbon emissions,such as carbon tariffs and government netzero carbon emission policies,carbon emissions have become an important indicator that is being prioritized by governments worldwide.The Google Environmental Insights Explorer(EIE)tool has been developed to facilitate the collection and integration of data in this context.This study focuses on Tainan City and utilizes EIE to analyze greenhouse gas emissions from transportation.By using EIE,the study obtains data on greenhouse gas emissions from transportation activities in Tainan City.EIE utilizes data collected by Google and simulation functions to estimate data based on actual measurements of transportation activities.This tool saves time and resources by eliminating the need for on-site investigations while providing data that closely represent the real emissions from transportation activities in urban areas.Transportation vehicles contribute to greenhouse gas emissions in two ways:through direct combustion of fossil fuels and through the consumption of electricity in electric vehicles(EVs).The level of greenhouse gas emissions in a city’s transportation industry depends on factors such as transportation modes,fuel types,fleet age and energy efficiency,total distance traveled,and annual mileage.EIE estimates the greenhouse gas emissions from Tainan City’s transportation industry in 2022 to be 3,320,000 metric tons,including emissions from buses,motorcycles,cars,walking,railways,bicycles,and other modes of transportation.
基金Supported by National Natural Science Foundation of China(Grant No.62363005).
文摘We investigate the blow-up effect of solutions for a non-homogeneous wave equation u_(tt)−∆u−∆u_(t)=I_(0+)^(α)(|u|^(p))+ω(x),where p>1,0≤α<1 andω(x)with∫_(R)^(N)ω(x)dx>0.By a way of combining the argument by contradiction with the test function techniques,we prove that not only any non-trivial solution blows up in finite time under 0<α<1,N≥1 and p>1,but also any non-trivial solution blows up in finite time underα=0,2≤N≤4 and p being the Strauss exponent.
