The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The ...The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is for- mulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton＇s principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables.展开更多
Physico-mechanical properties are critically important parameters for rocks. This study aims to examine some of the rock properties of quartz-mica schist（QMS） rocks in a cost-effective manner by establishing correla...Physico-mechanical properties are critically important parameters for rocks. This study aims to examine some of the rock properties of quartz-mica schist（QMS） rocks in a cost-effective manner by establishing correlations between non-destructive and destructive tests. Using simple regression analysis, good correlations were obtained between the pulse wave velocities and the properties of QMS rocks. The results were further improved by using multiple regression analysis as compared to those obtained by the simple linear regression analysis. The results were also compared to the ones obtained by other empirical equations available. The general equations encompassing all types of rocks did not give reliable results of rock properties and showed large relative errors, ranging from 23% to 1146%. It is suggested that empirical correlations must be investigated separately for different types of rocks. The general empirical equations should not be used for the design and planning purposes before they are verified at least on one rock sample from the project site, as they may contain large unacceptable errors.展开更多
Despite growing interest in nano-sized fillers,micro-sized fillers with desired compatibility are still used for reinforcing rubbers,owing to their lower production cost and easier processing relative to nano-sized fi...Despite growing interest in nano-sized fillers,micro-sized fillers with desired compatibility are still used for reinforcing rubbers,owing to their lower production cost and easier processing relative to nano-sized fillers.Especially,the abundant and eco-friendly clay minerals are recognized as the materials of the twenty-first century.Herein,illite,a naturally occurring clay having dimension in micrometric scale,has been selected as filler to reinforce the SBR.To improve the compatibility of illite with SBR,the illite was modified by either bis[3-(triethoxysilyl)propyl]tetrasulfide(Si69-illite)or 3-mercaptopropyltriethoxysilane(KH580-illite).The interfacial interactions of SBR composites filled with pristine illite(illite/SBR)and Si69-illite(Si69-illite/SBR),or KH580-illite(KH580-illite/SBR)were characterized by bound rubber content and Payne effect measurements,while dynamic hysteresis losses of these uncured and cured composites were also analyzed under various strain amplitudes.It was found that the filler-rubber interactions were greatly improved for Si69-illite/SBR and KH580-illite/SBR systems compared to the illite/SBR composite.This leads to an increment of modulus at 300%strain of the composites from 3.46 MPa for illite/SBR to 7.70 MPa for Si69-illite/SBR and12.96 MPa for KH580-illite/SBR.Moreover,lower rolling resistance and better wear resistance without compromising wet traction of Si69-illite/SBR and KH580-illite/SBR have been achieved.This demonstrates the high possibility of Si69 and KH580 modified illites as promising alternative fillers for reinforcing rubbers.展开更多
The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical propertie...The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical properties of CWR on the bridge are analyzed to reveal the sensitive areas of the track,and the design method of CWR and track structures on the beam ends are proposed.The results show that the unidirectional Rail Expansion Joints(REJ)need to be installed on the beam end of the kilometer-span bridge to reduce rail longitudinal force.Due to the bridge characteristics,there is no CWR fixed area on the kilometer-span bridge,and rail longitudinal force on the main span caused by bending loads needs to be concerned.The deformation of track on the beam end is complex,which is the weak area on the kilometer bridge,the large relative displacement between the stock rail of REJ and the main beam can cause poor stability of ballast bed on beam end,small resistance fasteners need to be laid on the sides of stock rail on the main beam to increase the stability of ballast and fasteners on the beam end.To improve the driving safety and comfort of beam end,the Sleeper-Supporting Apparatus(SSA)should be specially designed to ensure the uniform transition of track on beam ends.Temperature and wind loads have a significant impact on track regularity on the kilometer span bridge,the dynamic response of trains and bridges under those loads needs to be attended to.展开更多
基金Project supported by the Ministry of Science and Higher Education of Poland(Nos.04/43/DSPB/0085and 02/21/DSPB/3464)
文摘The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is for- mulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton＇s principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables.
文摘Physico-mechanical properties are critically important parameters for rocks. This study aims to examine some of the rock properties of quartz-mica schist（QMS） rocks in a cost-effective manner by establishing correlations between non-destructive and destructive tests. Using simple regression analysis, good correlations were obtained between the pulse wave velocities and the properties of QMS rocks. The results were further improved by using multiple regression analysis as compared to those obtained by the simple linear regression analysis. The results were also compared to the ones obtained by other empirical equations available. The general equations encompassing all types of rocks did not give reliable results of rock properties and showed large relative errors, ranging from 23% to 1146%. It is suggested that empirical correlations must be investigated separately for different types of rocks. The general empirical equations should not be used for the design and planning purposes before they are verified at least on one rock sample from the project site, as they may contain large unacceptable errors.
文摘Despite growing interest in nano-sized fillers,micro-sized fillers with desired compatibility are still used for reinforcing rubbers,owing to their lower production cost and easier processing relative to nano-sized fillers.Especially,the abundant and eco-friendly clay minerals are recognized as the materials of the twenty-first century.Herein,illite,a naturally occurring clay having dimension in micrometric scale,has been selected as filler to reinforce the SBR.To improve the compatibility of illite with SBR,the illite was modified by either bis[3-(triethoxysilyl)propyl]tetrasulfide(Si69-illite)or 3-mercaptopropyltriethoxysilane(KH580-illite).The interfacial interactions of SBR composites filled with pristine illite(illite/SBR)and Si69-illite(Si69-illite/SBR),or KH580-illite(KH580-illite/SBR)were characterized by bound rubber content and Payne effect measurements,while dynamic hysteresis losses of these uncured and cured composites were also analyzed under various strain amplitudes.It was found that the filler-rubber interactions were greatly improved for Si69-illite/SBR and KH580-illite/SBR systems compared to the illite/SBR composite.This leads to an increment of modulus at 300%strain of the composites from 3.46 MPa for illite/SBR to 7.70 MPa for Si69-illite/SBR and12.96 MPa for KH580-illite/SBR.Moreover,lower rolling resistance and better wear resistance without compromising wet traction of Si69-illite/SBR and KH580-illite/SBR have been achieved.This demonstrates the high possibility of Si69 and KH580 modified illites as promising alternative fillers for reinforcing rubbers.
基金supported by the National Key R&D Program of China(2022YFB2602901)the National Natural Science Foundation of China(No.52178405).
文摘The complex bridge-track interaction between kilometer-span bridges and continuous Welded Rail(CWR)brings great challenges to CWR designing.Taking a suspension bridge with laying CWR as a case,the mechanical properties of CWR on the bridge are analyzed to reveal the sensitive areas of the track,and the design method of CWR and track structures on the beam ends are proposed.The results show that the unidirectional Rail Expansion Joints(REJ)need to be installed on the beam end of the kilometer-span bridge to reduce rail longitudinal force.Due to the bridge characteristics,there is no CWR fixed area on the kilometer-span bridge,and rail longitudinal force on the main span caused by bending loads needs to be concerned.The deformation of track on the beam end is complex,which is the weak area on the kilometer bridge,the large relative displacement between the stock rail of REJ and the main beam can cause poor stability of ballast bed on beam end,small resistance fasteners need to be laid on the sides of stock rail on the main beam to increase the stability of ballast and fasteners on the beam end.To improve the driving safety and comfort of beam end,the Sleeper-Supporting Apparatus(SSA)should be specially designed to ensure the uniform transition of track on beam ends.Temperature and wind loads have a significant impact on track regularity on the kilometer span bridge,the dynamic response of trains and bridges under those loads needs to be attended to.
